Trans pixelate substitution scheme for denoising computed tomography images towards high diagnosis accuracy

Abstract

Medical images are obtained from different optical scanners and devices to provide in-body diagnosis and detection. Such scanned/acquired images are tampered with/ distorted by the unnecessary noise present in the pixel levels. A Trans-Pixelate Denoising Scheme (TPDS) is implemented to denoise these pictures to enhance the diagnosis’s precision. This scheme is specific for CT images with high noise between pixelated and non-pixelated boundaries. Therefore, the boundary detected from an input CT image is suggested for a trans-pixel substitution using a two-layer neural network. The first layer is responsible for verifying the substitution-based diagnosis accuracy, and the second is identifying trans-pixels that improve accuracy. The outcome of the neural network is used to train the noisy inputs under either of the conditions to improve the diagnosis accuracy. The Proposed TPDS improves diagnosis accuracy, precision, and pixel detection by 7.3%, 8.14%, and 13.05% under different trans-pixel rates/boundaries. Under the same variant, this scheme reduces error and detection time by 11.15% and 9.03%, respectively.

Introduction

Pixel-level noise must be addressed in medical imaging to improve CT scan diagnoses. Neural networks and other sophisticated denoising approaches reduce noise, notably at complex scan boundaries^1,2. The goal is to improve medical information clarity and diagnosis accuracy. Systematic refining improves precision and simplifies analysis for healthcare professionals^3,4. The breakthrough has transformed radiology, enabling confidence and precise medical diagnostic decisions⁵. Advanced CT image denoising methods will improve healthcare insights. These advances will improve patient care, confirming the relevance of sophisticated imaging technologies in medical diagnosis^6,7. Medical imaging uses pixel substitution to reduce CT picture pixel-level noise. These methods deliberately replace noisy pixels, especially in noisy regions, to improve picture quality and diagnostic accuracy^8,9. Pixel replacement approaches enhance images by replacing noisy pixels with more accurate information using complex algorithms¹⁰. This computationally sophisticated approach makes medical information more apparent. These computationally innovative methods reduce CT image noise, improving visual interpretation¹¹. Pixel replacement approaches might improve diagnostic accuracy and patient care in medical imaging¹².

Medical imaging CT scan quality is improved by sophisticated denoising learning¹³. Machine learning and deep learning algorithms help reduce CT medical imaging pixel-level noise. CNNs are trained on noisy and clean CT images to discover efficient denoising patterns^14,15. Transfer learning helps denoise tasks with limited data by adjusting pre-trained models¹⁶. Novel approaches include GANs and VAEs. VAEs simulate clean image probability distributions, unlike GANs, which produce denoised pictures using a generator-discriminator system. These learning algorithms can reduce CT medical picture noise to improve diagnostic accuracy^17,18.

Traditional filtering applies noise evenly over the picture, whereas TPDS smooths noise at pixel boundaries. When used to reduce salt-and-pepper noise, median filters often blur and lose minute structural features needed for CT interpretation. Gaussian filters can reduce contrast in diagnostic pictures by flattening crucial edges and noise despite their overall noise reduction effectiveness. Wavelet treatments may lose fine-scale textures and generate artifacts while reassembling the image. Wavelet treatments reduce noise selectively at many resolutions. Images are divided into several frequency bands. TPDS preserves edges and limits denoising to critical areas by carefully finding and replacing noisy pixels, making it better than these methods. This is feasible using trans-pixel substitution.

Using GANs to replace CT denoising improves boundary preservation and feature learning. GAN-based methods like Cycle GANs or conditional GANs may learn complicated noise patterns and rebuild smooth photos with little distortion. GANs provide adaptive denoising independent of noise, unlike TPDS, which employ fixed pixel replacement. GANs are taught to map clean and noisy pictures. GANs can use perceptual loss functions to maintain fine structural traits and minimize oversmoothing or edge loss. GANs may be too stochastic for medical applications that demand total reliability. GANs require large training datasets and may produce inconsistent results. TPDS’s targeted noise reduction and GANs’ adaptive learning can improve CT scan quality in hybrid systems.

Motivation

This study is driven by the desire to improve medical imaging, particularly Computed Tomography (CT) pictures, where pixel-level noise can wrongly diagnose patients. Current denoising technologies reduce noise. Unfortunately, they don’t always manage border noise between pixelated and non-pixelated sections, which is crucial for medical interpretation. More targeted denoising methods that remove noise while maintaining diagnostic information are needed to address this gap. The two-layer neural network-based Trans-Pixelate Denoising Scheme (TPDS) improves pixel border detection and replacement to help medical specialists read pictures. The project aims to fill this gap by developing advanced denoising methods to enhance diagnostic and patient outcomes.

Novelty

This paper presents a novel approach for reducing noise at the pixel level in CT scans, the Trans-Pixelate Denoising Scheme (TPDS). The goal is to improve the quality of medical images and the accuracy of medical diagnoses by eliminating border noise. Unlike conventional denoising methods, the TPDS utilizes targeted denoising at pixel boundaries to enhance diagnostic accuracy and picture clarity.

Defining the requirement of exact picture boundaries in medical CT scans and explaining how pixel-level noise impairs effective diagnosis might help to clarify the goal. Building a two-layer neural network capable of pixel categorization and replacement is the crux of the method. The first layer uses boundary detection to validate noisy pixels, while the second layer finds trans-pixels, which boosts diagnostic accuracy. Diagnostic accuracy is improved by identifying trans-pixels in the second layer after the first layer has validated noisy pixels using boundary detection. The main contributions of this study are:

• A Trans-Pixelate Denoising Scheme (TPDS) is implemented to denoise these pictures to enhance the diagnosis’s precision.

• The proposed TPDS uses targeted denoising at pixel boundaries to improve diagnostic accuracy and visual clarity.

• The specific design of a two-layer neural network to validate and identify noisy pixels through variations.

• The proposed scheme is validated via diagnosis accuracy, noisy pixel detection, error factor, detection time, diagnosis precision, structural similarity index, and RMSE.

Section “Related Works” follows the rest of the paper, discussing the latest literature on the proposed topic. Section “The Proposed Trans-Pixelate Denoising Scheme” describes the proposed Trans-Pixelate Denoising Scheme in detail. Section “Results and Discussion” enunciates the results and discussion, along with different metrics. The conclusion of the study is finally drawn in section“Conclusion”

Related works

Gu et al.¹⁹ projected a novel method for unsupervised low-dose CT denoising using AdaIN-based tunable CycleGAN.The model deviates from conventional two-generator approaches, opting for a simplified denoising process with a single generator. Training stability is a crucial feature of the proposed method, ensuring reliable performance even when faced with limited datasets. The method achieves superior results in low-dose CT denoising compared to existing approaches. A content-noise complementary learning (CNCL) approach to medical image denoising was presented by Geng et al.²⁰. This method uses the symbiotic link between material and noise to improve denoising performance. CNCL exhibits superior denoising results, as validated across diverse datasets, compared to existing algorithms. The method stands out for its exceptional performance and potential clinical impact in medicinal imaging denoising.

A method for low-dose CT image denoising was suggested by Yan et al.²¹ using a convolutional dictionary learning strategy and a neural network. The main goal of the technique is to improve denoising in LDCT (low-dose computed tomography) pictures. The model is fine-tuned for LDCT picture post-processing after being trained on a dataset of natural images using transfer learning. The method demonstrates a balanced noise reduction, preserving crucial details in LDCT images. A memory-efficient neural architecture search for low-dose CT noise reduction, M3NAS, was introduced by Lu et al.²². It operates on several scales and levels. By reducing background noise caused by reduced radiation levels, the technique aims to improve low-dose computed tomography (LDCT) images. To achieve better LDCT denoising, M3NAS employs a new method called Neural Architecture Search (NAS). The approach effectively reduces noise, which improves the overall quality of LDCT images.

Wu et al.²³developed a deep-learning approach for dynamic CT perfusion (CTP) picture denoising. The method aims to reduce radiation exposure in routine applications by addressing the challenges in CTP imaging. A self-supervised learning technique is proposed, eliminating the need for high-dose reference images during training. The method achieves improved image quality in CTP compared to traditional denoising methods. Zhao et al. suggested a deep-learning approach for reducing noise in integrated 3D low-dose PET/CT images²⁴. To collaboratively denoise low-dose PET and low-dose CT images, the MAC framework presents a self-supervised two-stage training method.MAC improves denoising by training networks with masked autoencoder (MAE) constraints applied at the pixel level. The proposed method achieves superior joint denoising performance for LDPET and LDCT images.

Zhang et al.²⁵ developed a denoising technique for low-dose CT (LDCT) images. Using a decoder’s dual-path transformer block (DPTB) to boost detail and restore structure increases the quality of LDCT images. A multi-feature spatial attention block (MSAB) is introduced to enhance the feature extraction process at shallow network levels by focusing on key regions. The approach effectively reduces noise in low-dose CT images, improving quality. Ma et al.²⁶ projected a method for denoising low-dose CT (LDCT) images using a residual dense network with self-calibrated convolutions (SCRDN). SCRDN employs jump connections, dense connections, and self-calibrated convolution to utilize original image features for better reconstruction. The approach enhances LDCT image quality by achieving a larger receptive field without adding extra parameters. The method contributes to improving diagnostic quality in LDCT images.

Chen et al.²⁷ presented a denoising technique for low-dose CT (LDCT) images using a Fractional-order Residual Convolutional Neural Network (FRCNN). FRCNN decreases radiation in LDCT while enhancing image details using Fractional-order Total Variation loss. The approach balances by dipping the dose and refining the images, making it easier for radiologists to understand. The method offers visually and numerically superior results that benefit radiologists in medical interpretation. Li et al.²⁸ created a method to improve low-dose CT (LDCT) images with an Adaptive Self-Guided Wavelet Convolutional Neural Network (ASWCNN). ASWCNN combines wavelet transform, sub-pixel convolution, and a self-guiding structure to enhance LDCT images. The goal is to produce high-quality images while minimizing radiation exposure during LDCT scans. The method effectively improves the overall quality of LDCT images.

An adversarial network for unsupervised low-dose CT (LDCT) denoising called a Dual-scale similarity-guided cycle (DSC-GAN) was suggested by Zhao et al.²⁹. This method offers a more realistic approach to denoising of unsupervised low-dose CT (LDCT). When training, DSC-GAN uses similarity-based pseudo-pairing to bridge the gap between supervised and unsupervised LDCT denoising. The method effectively reduces noise in LDCT scans without requiring paired samples for training. Thanh-Trung et al.³⁰ created a method using deep convolutional neural networks to denoise low-dose CT images. The approach integrates preprocessing and post-processing techniques within a dilated convolutional neural network for improved effectiveness. By extending receptive fields, the method allows distant pixels to enhance feature maps, enhancing denoising capabilities. The technique successfully reduces radiation dose in low-dose CT imaging.

An approach to denoising medical CT images was suggested by Zhang et al.³¹ using a moving decomposition approach. The approach utilizes Shearlet Transformation-based denoising for components with detailed information, enhancing the overall denoising process. BM3D filtering is applied to eradicate noise efficiently, achieving optimal denoising results in approximate components. The method effectively preserves local structure information in low-dose medical CT images. An automated technique for spinal segmentation was presented by Graf et al.³² using denoising diffusion-based MRI for CT image translation. The method primarily aimed to convert T1-weighted and T2-weighted MRI images into CT images using landmark-based registration. The DDIM picture mode produced the best results from all the tested approaches. The method improved spatial resolution when translating MRI to CT images.

Lei et al.³³ created SN2N, a self-supervised method for low-dose CT denoising in lung nodule categorization. The technique is designed to perform well without requiring paired normal-dose CT images during training.SN2N eliminates the need for paired normal-dose CT images by generating denoising supervision from noisy low-dose CT inputs. The approach demonstrates strong performance without needing paired normal-dose CT images. Denoising low-dose computed tomography (CT) images was suggested by Niknejad Mazandarani et al.³⁴ using a specialized neural network. A one-of-a-kind loss function is incorporated into the procedure to maintain crucial details and structural information. Utilizing this innovative denoising method enhances the standard of low-dose CT (LDCT) images. The approach effectively enhances LDCT image quality by addressing noise artefacts.

The diagnostic imaging technology low-dose computed tomography (LDCT) reduces patient radiation. However, reducing radiation exposure may lower CT image quality, affecting clinical diagnosis. Many innovative low-dose computed tomography (LDCT) methods have been developed by Liao et al.³⁵ to solve this problem. The algorithms are trained on LDCT-NDCT image pairings that match. Many existing denoising algorithms fail because they can’t distinguish visual information from non-uniformly distributed noise. The lack of well-connected healthcare datasets lowers their efficacy. This study used unpaired data to create a novel LDCT image-denoising framework. The multi-encoder deep feature transformation network (MDFTN) parallel processing architecture improves LDCT imaging with multisource data. This technique allows LDCT image processing from several sources in a single framework. The MDFTN should have a deep feature transformation module (DFTM) and several encoders and decoders. In forward propagation of network training, the DFTM compresses features taken in parallel by each encoder from their data sources into a common feature space. Multisource loss calculation continues with an inverse operation on each decoder. Yao et al.³⁶ proposed that MDFTN uses collaborative training to improve generalisability and flexibility by using distant data sources’ synergy. The suggested network design can manage multisource data in real-time while reducing noise and keeping fine-grained structures, according to comprehensive testing on three publicly available datasets, one privately held. Table 1 shows the comparative analysis of the survey.

Table 1.

Comparison table on literature survey.

Study	Method	Features	Advantages	Limitations
Gu et al.19	AdaIN-based tunable CycleGAN	Single generator for unsupervised low-dose CT denoising	Improved stability and denoising results	May struggle with very limited datasets
Geng et al.20	Content-noise complementary learning (CNCL)	A symbiotic relationship between noise and material for denoising	Superior performance on various datasets	High computational demand
Yan et al.21	Convolutional dictionary learning with neural network	Transfer learning on natural images for low-dose CT post-processing	Balanced noise reduction while preserving image details	Requires extensive fine-tuning
Lu et al22.	Memory-efficient Neural Architecture Search (M3NAS)	Multiscale and multi-level denoising for low-dose CT	Enhanced image quality and low-dose CT denoising	Limited applicability to large datasets
Wu et al.23	Self-supervised learning	Dynamic CT perfusion denoising	Reduced radiation exposure without high-dose reference images	It may not generalize well to all image types
Zhao et al.24	Masked Autoencoder Constraints (MAC)	Joint denoising of PET/CT using self-supervised learning	Enhanced joint denoising performance for PET/CT	Complex two-stage training
Zhang et al25.	Transformer-CNN hybrid	Multi-feature spatial attention block with dual-path transformer block	Improved low-dose CT image quality	High resource requirements
Ma et al.26	Residual Dense Network with Self-calibrated Convolutions (SCRDN)	Jump connections and dense connections for low-dose CT image denoising	Larger receptive field without additional parameters	High training time
Chen et al.27	Fractional-order Residual Convolutional Neural Network (FRCNN)	Reduces radiation dose with Fractional-order Total Variation loss	Superior results for radiologists	Limited clinical testing
Li et al.28	Adaptive Self-Guided Wavelet Convolutional Neural Network	Combines wavelet transform and sub-pixel convolution	High-quality, low-dose CT images with minimal radiation	Complexity in wavelet transformation
Zhao et al.29	Dual-scale Similarity-guided CycleGAN	Unsupervised low-dose CT denoising with similarity-based pairing	Reduces noise without paired samples for training	Performance dependent on similarity-based pairing effectiveness
Thanh-Trung et al.30	Dilated Convolutional Neural Networks	Extended receptive fields for low-dose CT denoising	Improved effectiveness of denoising	Struggles with preserving fine details

Mahmood et al.³⁷ discuss the newest deep learning-based medical image analysis applications for segmentation, acquisition, augmentation, registration, and classification. The essay discusses four cutting-edge deep learning models: CNN, DBN, SAE, and RNN. Searching benchmark academic databases, gathering relevant literature and indicators for analysis, prioritizing DL-based segmentation and classification methodologies, and analyzing performance metrics were used to choose studies. Clinicians and researchers struggle to build a highly accurate malignancy prediction framework using cutting-edge deep-learning algorithms. Also, future views are examined to overcome obstacles and develop medical image analysis.

Rehman et al.³⁸ suggest a novel prognosis-assisted kidney imaging and multilabel grading method. Swin-ViT and several modified deep learning-based pre-trained models underpin this technique. Transfer learning improves model performance and reduces data scale dependence in final layers. Transfer learning lowers training costs and improves model generalization and classification on smaller datasets. Performance can be increased via data augmentation and batch size reduction. The Swin-ViT model outperforms the competition in transfer learning multi-label classification of CKD pictures, and its attention mechanism helps identify lesions. The results indicate that Swin-ViT outperforms the competition. Generation of the attention mechanism GradCAM using the Swin-ViT model improves interpretability. Future studies on extracting complicated illnesses and high-level semantic data may aim to improve model performance.

Mahmood et al.³⁹ proposed strong deep-learning algorithms to improve breast lesion identification, localization, risk assessment, and classification. The algorithms were also designed to reduce human-caused false positives and delay convergence rates. The cLSFSO (Chaotic Leader Selective Filler Swarm Optimization) approach detected breast-dense lesions for the first time, a significant accomplishment. This method gathers statistics and text. Transfer learning improved deep learning models’ capacity to distinguish normal and worrisome mammography areas. These models used modified VGGNet and SE-ResNet152. This research presents CNN + LSTM and CNN + SVM hybrid deep neural network methods. These approaches employ pre-segmented ROIs to detect and grade malignant polyps. Grad-CAM increases analysis, which improves breast anomaly evaluations and diagnoses. We found that the algorithms improved mammography analysis on public and private datasets. Our algorithms had 0.99 sensitivity and 0.99 AUC.

Umirzakova et al.⁴⁰ introduces a novel method for distilling information that speeds the process, decreases the performance difference between instructor and student models, and eliminates the requirement for complicated knowledge representations. The proposed model performs better than traditional KD methods and state-of-the-art designs like ResNet and VGG networks in our comprehensive testing on the CIFAR-10 dataset. The proposed method maintains high levels of accuracy while significantly reducing training and validation losses. Based on the most relevant findings, the optimal values for the hyperparameters, which include temperature T = 15.0 and smoothing factor α = 0.7, lead to the highest validation accuracy and lower loss values. This research contributes to the current theoretical and practical understanding of knowledge distillation while laying the groundwork for optimization and compression of neural networks in future studies.

The article discusses previous medical picture denoising attempts, which led to the Trans-Pixelate Denoising Scheme (TPDS). Gu & Geng et al.'s research on low-dose CT denoising with generative models like CycleGAN and CNCL emphasises the need for efficient and robust techniques. Yan et al. and Wu et al. recommend neural networks and self-supervised learning, which indicate potential noise reduction but often need computational complexity and detail loss. The TPDS improves on CNN-FTV and SN2N’s general blurring by fine-tuning a two-layer neural network for boundary noise detection, diagnostic features, and structural integrity. Overall, the references emphasize the need for accurately reducing noise in CT scans. TPDS provides a more targeted and efficient strategy that enhances diagnostic precision and picture quality. Pixel substitution methods will likely reduce the noise in the medical image denoising process. The problem of pixel removal with high or low variance detected is crucial due to less training on specific features. Equally important, the peak-to-noise ratio affects the replacement procedure through similarity mismatches. Therefore, precision in diagnosis is formidable in reducing noise under dissimilar pixels. Unlike the methods discussed above, this article introduced the trans-pixelate denoising scheme using an exclusive two-layer neural network to minimize noise in medical images. The research study influenced the development of the Trans-Pixelate Denoising Scheme (TPDS) by drawing attention to the shortcomings of existing denoising methods for CT images, especially when it comes to reducing boundary noise. Insights from advanced networks such as GANs and VAEs influenced the design of TPDS’s two-layer neural network. This design improves diagnostic accuracy by implementing targeted trans-pixel substitution. To ensure TPDS fills in research gaps, the review directed the selection of evaluation measures and implementation tactics. In conclusion, TPDS is a novel method that enhances medical diagnosis’s accuracy and trustworthiness.

The study review suggests MDFTN, CNCL, CNN-FTV, and SN2N generative adversarial networks (GANs) for denoising. Since they focus on global noise reduction, these approaches fail to analyze minor structural details at pixel boundaries, which is crucial to CT image interpretation. CNN-FTV reduces radiation exposure with fractional total variation loss, however, border noise is a problem. With SN2N, paired training photographs are no longer needed, however, edge preservation is inaccurate. CNCL exploits noise-materials relationships but is computationally expensive. Multi-encoder deep feature transformation networks like MDFTN improve generalization but don’t address pixel border noise. TPDS employs trans-pixel substitution using a two-layer neural network to replace noisy pixels at boundaries instead of broad denoising.

The proposed trans-pixelate denoising scheme

This article uses a series of filters to remove noise in any medical images, like CT, MRI, X-ray, etc., through the Trans-Pixelate denoising Scheme. Trans-Pixel Substitution replaces noisy pixels with more accurate ones, focusing on pixels around pixelated and non-pixelated borders. A two-layer neural network finds noisy border pixels and finds replacement values to increase picture clarity. Trans-pixel replacement lowers noise and information loss by focusing on critical diagnostic regions, unlike uniform filtering-based denoising. The denoising process is one of the standard procedures in digital image processing. Removing the noise to preserve diagnostic information is a challenging problem in developing denoising algorithms. We can use filters to reduce vanished/distorted images. Many filters are available to perform noise reduction. The filter is ordered based on minimum, median, maximum filter, average filter, Gaussian filter, unsharp filter, log filter, etc., which are used for performing the denoising process in any medical image. We use a Median filter to achieve higher diagnosis accuracy than the standard linear filtering process. This filter is used to classify salt (pixelated) and pepper (non-pixelated) noises from the acquired medical images. The median filter is a non-linear filtering process that reduces either salt or pepper noise in medical images, but not both. Although it is known that indiscriminate median filtering can cause blurring, it is often employed to eliminate salt-and-pepper noise in digital images. When using the Trans-Pixelate Denoising Scheme, the median filter isn’t evenly applied to the whole picture; instead, it is targeted to the edges, where diagnostically significant features are typically concentrated, and noise is most damaging.

The TPDS’s two-layer neural network technique increases CT image noise categorization and removal, notably at pixel borders. The first network layer detects noisy pixels during boundary detection. We use spatial derivatives and intensity fluctuations to compare pixelated and non-pixelated regions. It determines noise-heavy pixels using SSI, MSE, and spatial frequency transformations. Because of its ECP recognition training, organ structures and tissue borders are retained, especially at high-contrast edges. ECP identification may be taught to the network. Here, we remove extraneous pixels and focus on the most critical ones for processing. Because of this, superfluous denoising won’t hide vital medical data. Trans-pixel removal or substitution improves second-layer classification. This approach ensures that noisy pixels are replaced with more accurate values from architecturally comparable nearby regions.

TPDS in multi-layer networks may improve classification accuracy in medical imaging datasets with many pictures or complicated noise patterns. Multi-layer DNNs better classify structural components and noise at different scales by extracting hierarchical features from noisy pictures. CNNs and attention processes can help deep learning models distinguish proper anatomical features from noise aberrations. If this happened, denoising would be more exact without sacrificing information. DRL might be used to create an adaptive noise reduction model. This model uses real-world CT images to teach the network efficient denoising. This technique allows dynamic denoising parameter fine-tuning based on picture complexity. This would protect vital medical features while reducing noise. Deep learning models need large labelled datasets, computing resources, and intense training methods to minimize overfitting. Thus, a hybrid TPDS model using deep reinforcement learning and two-layer neural method should offer a complete solution. Combining the adaptive capabilities of deep learning with the border identification precision of TPDS might increase generalizability across medical imaging datasets.

The suggested model overcomes the blurring effect by combining median filtering with boundary detection methods and trans-pixel replacement. These methods ensure that the filter is only applied to noisy areas, while structural similarity analysis protects diagnostically important regions like edges and fine details. Image quality is improved without sacrificing diagnostic accuracy using this method. In addition, the two-layer neural network is used again to improve the picture further while keeping the diagnostically significant details. By elucidating this specific and limited usage of the median filter, the notion that it causes data loss in boundary-focused denoising is rendered less exceptional and more plausible. After the classification process, the noise between pixelated and non-pixelated boundaries is verified for precise boundary detection. Therefore, the boundary detected from the CT image is suggested for trans-pixel substitution through a two-layer neural network. Figure 1 presents the functional flow of the proposed scheme. Denoising CT scans while keeping diagnostic information is the Trans-Pixelate Denoising Scheme (TPDS) goal, as shown in Fig. 1. The initial phase is to get a noisy CT scan with aberrations at the pixel level, namely noise associated with borders and salt and pepper. First, make an educated guess as to how much noise is in the picture; specifically, find out how much noise is affecting the areas that border pixelated and non-pixelated. The denoising procedure relies on this estimate to direct its following stages. The plan continues by identifying ECPs, or Error Causing Pixels, the pixels that are mostly to blame for the picture’s noise. It is common around the edges of images, where background noise makes it difficult to diagnose accurately. To begin, locate the pixel boundaries or the borders between the noisy and non-pixelated areas. Using boundary detection, pinpoint the regions with the highest noise concentrations and eliminate them with little interference to structures crucial for diagnosis. The previously identified noisy border regions are the ones that receive the median filter. Without applying to the entire image, this filter successfully lowers salt-and-pepper noise, preventing the blurring of critical diagnostic features. The TPDS uses trans-pixel substitution after noise reduction. Replacing or removing noisy pixels with more precise pixel values derived from boundary classification is necessary to restore picture quality without sacrificing clarity. The outcome is a picture with less noise but with all the diagnostic data that quality metrics like PSNR (Peak Signal-to-Noise Ratio) have confirmed. Because of the improvements, the image is now more suitable for diagnostics.

Fig. 1.

Proposed TPD scheme.

The technique considers the noise issue in medical images by obtaining an image with noise and estimating the amount of noise. The proposed scheme uses Error Causing Pixels. to pinpoint noisy areas and implement a noise reduction technique that keeps picture structure intact while reducing Mean Squared Error . Pixel Boundary Analysis keeps essential picture borders intact, while Similarity Analysis of Structure ensures little distortion. To ensure that diagnostic features are preserved, the result is a noise-reduced image that quality measures like PSNR have confirmed. This process outlines the steps in obtaining a high-quality medical image, from identifying the problem to analyzing the image for noise and finally deciding on denoising procedures. In such cases, the variance between pixelate and non-pixelate boundaries is high; the Median filter rescues edges and high-frequency parts in an input CT image. Also, if the noise in each pixel level is stable power additive noise, namely salt and pepper noise, the Median filter classifies its boundaries better than other filters.

The Trans-Pixelate Denoising Scheme’s border detection method concentrates denoising rather than applying it randomly. TPDS reduces anatomical detail blurring by focusing on pixelated edges. Organ margins, malignancies, and vascular information are essential for appropriate medical diagnosis. Traditional denoising methods like median or Gaussian filters flatten images by eliminating noise and high-frequency data. Such behaviour may degrade diagnostic characteristics. In contrast, TPDS selectively denoises while keeping spatial and textural qualities crucial for clinical interpretation. This tailored technique increases diagnosis accuracy by 7.3% by eliminating noise only from image quality-degrading areas, leaving diagnostically relevant regions unaffected. Edge-preserving filters like the Bilateral Filter or Guided Filter improve boundary recognition. This would retain edge contrast and reduce noise. These filters reduce noise in homogenous regions while maintaining sharp edges by considering spatial proximity and intensity fluctuations. A hybrid TPDS technique that combines edge-preserving filtering and neural network-based boundary recognition can improve diagnostic accuracy. The increased noise in low-dose CT scans makes this useful for medical evaluations that need precise preservation of microscopic characteristics.

This proposed scheme is implemented on medical images to achieve high diagnosis accuracy. TPD scheme quickly defined the error-causing pixels . The noise-less medical image is represented as and the approximation of noise is represented as , the definition of can be expressed as

1

The peak signal-to-noise ratio (PSNR) in decibel DB is computed as,

2a

Otherwise,

2b

This PSNR ratio measures the maximum possible power value between the raw and compressed images. The signal (power) of vanishing/distorting noise in medical images raises problems in the quality of its pixel representation. The variable and denotes the maximum possible pixel value of the acquired input image and several features chosen from the images based on a filter. The similarity analysis of the structure is a process for identifying the similarity between the raw image and processed image to improve the traditional computing and . The similarity analysis is evaluated on different axes in an image, and it is validated between two planes and for average size :

3

where the variables and represent the average ratio of axis and axis, and is the observation of variance in and axis and means the observation of covariance in both and axis; And , Where the variable shows the robust range of pixel value. The role of concurrent layers in neural networks is to reduce the variance along the and axes, thereby improving the network’s precision and reducing the MSE. The concurrent layers achieve this by performing normalization and pixel differentiation, confining the maximum possible variance within a set boundary . As the layers work together, they reduce the influence of noise by identifying and processing the pixels contributing to variance, ultimately leading to a more refined and accurate output. This process is iterative, with each iteration progressively lowering the variance and enhancing the network’s performance.

In this scheme, the noise removal process is used to improve the accuracy of diagnosis from such images. The signals (power) value are computed for classifying pixelate and non-pixelate using concerning the boundary detected from an input CT image. The boundary classification output removes the noise occurrence through the denoising process. In this process of TPDS, the noisy images are removed or filtered. The processed image is represented as

4

where,

5a

And,

5b

where the variables and denote the mean squared error in both and for and planes for identifying trans-pixels. For this process, the rising and falling edges of and wavelets are observed for time interval . To separate the low-frequency components of a medical image from the high-frequency noise, wavelet processing decomposes the image into several frequency bands, isolates high-frequency noise, and identifies trans-pixels affected by this noise. This separation is critical for localizing them because trans-pixels are most impacted by high-frequency noise. This approach for targeted denoising improves overall medical image quality. Eq (5a) Eq (5b), defines the and for and planes for identifying trans-pixels using wavelet transformations. They quantify the error in the image reconstruction process by integrating the differences in frequency components, helping to identify and measure the noise at various scales. In this denoising process, the initial noise is vanished or distorted from the input image based on the transformation of and wavelets in different time intervals .By analyzing the and the wavelet transformation identifies the trans-pixels as those significantly affected by noise. These pixels, isolated in the detailed sub-bands of the wavelet transformation, are crucial for targeted noise reduction. With the calculation of noisy image process by incorporating the denoising technique based on the wavelet-transformed components and similarity analysis .

In this denoising process, the initial noise is vanished or distorted from the input image based on the transformation of and wavelets in different time intervals . Here, means the number of denoising images processed using the filter. Boundary detection using and is illustrated in Fig. 2. Figure 2 shows a complete diagram of the Trans-Pixelate Denoising Scheme’s (TPDS) boundary detection method, which uses spatial derivatives (σxQ.dx and σyQ.dy) to differentiate between regions in a CT image that is noisy and without noisy. One of the essential steps in improving medical picture diagnostic quality is accurately identifying pixelated (noisy) and non-pixelated (noise-free) borders—calculating the variation in pixel intensities across the x and y axes over time. In particular, σxQ.dx shows how pixel intensities vary along the x-axis, while σyQ.dy measures how intensities change along the y-axis. A standard noise indicator, especially near edges, these spatial derivatives aid in detecting areas with sharp changes in intensity. Applying wavelet modifications to the pixel data refines this detection by separating the picture into distinct frequency components. This process enables the algorithm to separate high-frequency noise from the image’s critical structural elements. The TPDS uses a trans-pixel replacement to fix the noisy pixels once these derivatives have discovered noisy borders. In this stage, more precise pixel values derived from the border classification are substituted for the noisy pixels (those with an enormous intensity variance). The trans-pixel replacement procedure is employed to decrease noise without distorting or obscuring diagnostically significant information like tiny edges or tissue structures. At each iteration, the procedure refines the difference between noisy and noise-free zones by recalculating ϜxQ.dx and σyQ.dy, as shown in the Fig. 2., thereby improving the accuracy of the boundary detection step by step. With each iteration, the procedure becomes better and better until the noise-free, diagnostically clear image is obtained by minimizing the Mean Squared Error (MSE) between the original noisy image and the corrected version. This methodical strategy for detecting boundaries and reducing noise is a significant step towards better CT pictures for medical diagnosis.

Fig. 2.

Boundary detection using and .

The TPDS pixel replacement approach uses a two-layer neural network to recognize and categorize noise-impacted areas, notably near pixel borders, to replace erroneous values with more exact ones. Trans-pixel replacement selectively removes high-frequency noise without distorting critical anatomical characteristics, a significant drawback of classic filtering approaches. This lets us remove noise without affecting picture quality. By replacing Error-Causing Pixels (ECPs) at pixel borders with architecturally identical values from surrounding regions, TPDS maintains spatial consistency and contrast. This approach improves image quality and vividly displays diagnostic information including lesion borders and tissue textures. A rise in diagnosis accuracy follows. Pixel substitution techniques like picture inpainting and contextual pixel replacement may enhance TPDS. Picture inpainting employs deep learning algorithms to restore missing or noisy pixels automatically. These approaches may boost spatial coherence, reducing distortions and making restored regions lifelike. Particularly beneficial when noise substantially modifies critical diagnostic characteristics. A hybrid substitution technique that employs TPDS and context-aware approaches to adapt pixel replacement methods depending on local picture attributes for optimal denoising. This will boost its noise-reducing efficiency for sophisticated medical imaging.

The TPDS framework identifies high-noise pixels, especially those near the borders, as Error-Causing Pixels (ECPs), which reduce image quality. MSE, SSI, and spatial derivatives are used to detect these pixels. These methods identify intensity differences between pixelated and non-pixelated areas. Prioritizing ECPs by contrast deviation and frequency distribution lets the two-layer neural network substitute high-impact noise. Trans-pixel replacement restores pixel values while respecting anatomical features. An adaptive ECP detection technique can improve resilience by monitoring CT scan quality changes including noise and structural variations. This is achieved by responding quickly to changes. Context-aware filtering and deep learning-based ECP prediction can increase generalizability across imaging locales. This method improves CT image denoising for artifact-prone, low-dose, or motion-prone pictures.

The noisy CT image is utilized for extraction from which identified. This is computed based on two factors and . The and that differentiates PSNR from (both x and y) for precise (x and y) detection. In this process, structural similarity is performed for and for and exceeding for detection. This refers to the boundary space between and and and . The (if possible) is used to extract any new pixels (leftover) (Fig. 2).

Step-by-step process of pixelate and non-pixelate boundary classification and trans-pixel substitution

Boundary detection

The purpose of boundary detection is to identify and regions in the image for target denoising. This involves detecting the edges within the image where pixel characteristics change significantly, and the analysis is done through Eq. (14a) using wavelet transformation.

Trainig and classification

The training and classification process classifies the pixel boundaries using a two-layer network for accurate noise targeting based on the detected boundaries. Layer 1 involves initial pixel classification derived in Eq. (14b), and layer 2 validates and refines the classification process as derived in Eq. (14c).

Trans-pixel substitution

Replace or remove any noisy trans-pixels based on the classification and boundary detection from the previous steps and to improve image quality by reducing noise. The process substitutes trans-pixels with more accurate pixel values to restore image quality.

Normalization and refinement

Minimizing the MSE and reducing variance variables and to ensure consistent pixel values and effective noise removal. This step ensures that noise is effectively removed and that the image’s pixel values are consistent.

Final output

The final step proceeded with the denoised image production, minimal noise, and accurate boundaries. The process ensures that the all-necessary pixel substitutions and removals have been made and the images have been fully denoised. These steps provide a systematic approach to reducing noise and improving image quality.

Medical images undergo filtering to lessen the amount of background noise. The normalized initialization and intermediate normalization layers for trans-pixel substitution and trans-pixel removal that is denoted as follows in Eq. 6, in which the integrals are performed over the variables dx and dy, indicating that we are integrating concerning x and y, respectively:

6

The formula for trans-pixel substitution, if , where and then . Spatial derivatives (dx, dy) and their relationships in pixel substitution are simplified in the Eq. (7) which assures accuracy and clarity. This article aims to provide a comprehensive explanation of pixel replacement, which simplifies the trans-pixel substitution process to simple mathematical ideas.

7

The goal of the Eq. (8) is to show the logarithmic adjustment of pixels in relation to spatial coordinates is represented as follows.

8

In Eq. (7 and 8), the factors and are the substitution and removal of pixels based on pixelate and non-pixelate boundary classification. Based on the presence of noise in and planes from an input CT image, it is suggested for either of the conditions using a two-layer neural network. The variable represents the capacity of the filters to reduce noise occurrence used in both situations. Now, the normalized denoising image process based on is defined as

9

And,

10

The normalized noise-free medical image is represented as after applying filters that are observed. From this , the two features, such as mean squared error and degree of loss in the compression process are extracted for further verification. Equations (11) and (12) are used to compute and

11

And,

12

where, and shows pixelate and non-pixelate boundaries observed from such images. The log normalization of generates based on and as in Eq. (13)

13

These normalized initialization and intermediate normalization layers are analyzed for trans-pixel substitution and removal conditions with different time intervals. The estimation process is diagrammatically given in Fig. 3. In Fig. 3, the estimation process is illustrated using input. This input is extracted from and process using verification. Therefore, the substitution/removal is defined based on the and derivatives. If either of or requires a trans-pixel for or suppression, then the and takes place. Contrarily, if (or) is not required then and and are performed. Based on the that suppresses the pixel distribution is required for noise removal. Using a two-layer neural network, the classification process is based on pixelate and non-pixelate boundaries.

Fig. 3.

Estimation process.

This classification output helps to differentiate the mean squared error and degree of loss in the compressed image that satisfies either of the conditions. In this classification, the features are independently analyzed at each level. The input CT, image and training sets, are determined for the pixel substitution, and removal is validated as

14a

In Eq. (14a), represents the pixel boundary for both pixelate and non-pixelate detected from the image, and is the initial training set at different time instances. Similarly, the classification output and training sets for is computed as

14b

And,

14c

The Equation mentioned above represents the neural network’s input, output, and hidden layers in a way that allows the training recurrence to be pursued under either of the circumstances. This helps reduce the noisy pixels with maximum diagnosis accuracy and the maximum possible classification instances. The output and hidden layer of the neural network process rely on for and wavelets. The case of achieves a boundary of that indirectly shows . Based on the neural network, the pixel substitution or removal is performed in the order of , , partial and partial . The 2-layer neural process is illustrated in Fig below. Figure 4 shows the TPDS’s two-layer neural network in great detail. As shown in the picture, the network uses two separate layers to identify and categorize noisy pixels in the input CT image, emphasizing the image’s noisy edges. Classifying pixels into pixelated (noisy) or non-pixelated (noise-free) regions is the primary function of the first layer, which is dependent on the strength of the noise. Spatial derivatives (σxQ.dx and σyQ.dy) and techniques for detecting boundaries direct this categorization. Normalization helps the layer distinguish between background noise and diagnostically significant information. The second layer takes this categorization further by checking the detected borders and, if required, replacing or removing pixels in the trans-pixel image. Improving the diagnostic quality of the picture, this iterative approach replaces noisy pixels with precise values while preserving the borders.

Fig. 4.

2-Layer neural process illustration.

The graphic further highlights the interaction of layers. The second layer employs structural similarity analysis (xy) to minimize noise while preserving the image’s structural integrity after obtaining the output from the first layer. The network’s denoised picture keeps all the essential diagnostic details, such as edges and small structures, vital for medical interpretation. Improved diagnostic accuracy is a direct result of the combined efforts of the two layers to reduce the mean squared error (MSE) and increase the peak signal-to-noise ratio (PSNR). The two-layer neural network process requires and for processing. This is obtained for intervals validated for and (layer 1) and and (layer 2).

Two-Layer neural network process

Input and hidden layers

An input layer accepts pixel values from the image, including boundary conditions for and and prepares for data processing. Processes the input data to identify noisy pixels based on their boundaries and conditions. It uses for wavelet transformations to manage pixel classification.

Layer 1

The normalization involves and to normalize the pixel data and differentiate between and regions where pixel substitution determines values for handling pixel boundaries and noise.

Layer 2

This layer ensures accurate pixel classification and performs structural similarity analysis based on results from layer 1. The accuracy verification substitutes and removes pixels based on boundary detection and training data. These requirements are obtained through iterative processing in the neural network layers, where layer 1 focuses on normalizing and preparing the data, layer 2 validates and refines the results for accurate pixel classification and noise reduction.

In both process and are the normalization ( reduced) output for assessment. Therefore, the layer 1 analysis of the condition for and . This differentiation is performed to identify any (for trans-substitution) to avoid noise suppression. Layer 2 is responsible for validating obtained from layer 1 to perform with Of the input and training image. Therefore, the output is verified for and and any in the missing and (Refer to Fig. 4). Hence, the further accuracy verification is done. The pixels are substituted to complete the boundary, and if that pixel is set to the current boundary, then pixel removal is performed. Hence, the outcome of the hidden layer sequence depends on the input layer and output layer.

Table 2 describes the list of notations and its description involved in this research.

Table 2.

List of notations.

Variables	Definition
	Noise-less medical image after applying the Trans-Pixelate Denoising (TPD)
	Approximation of noise in the image
	Error Causing Pixels
	Peak Signal-to-Noise Ratio
	Maximum possible pixel value of the acquired input image
	Number of features
	Structural analysis of similarity along x and y axis
x, y	Spatial co-ordinates in the 2D image plane
	Average values on the co-ordinates,
	Variance on the co-ordinates,
	Covariance between the co-ordinates
	Constants used in similarity analysis calculations
	Robust range of pixel values for boundary detection
	Processed image after noise removal
	Mean squared error in the x and y planes for identifying trans-pixels
	Spatial derivatives of x and y over time, capturing intensity changes along x and y co-ordinates
	Number of denoising images processed using the filter
	Combined mean squared error in both x and y directions
and	Variances along x and y co-ordinates
,	Substitution process for pixels in the x and y directions
,	Removal process for pixels in the x and y directions
	Capacity of the filters to reduce noise occurrence in both condition
	Mean Squared Error, representing the error between and
	Degree of Loss
	Pixelate boundaries
	Non-pixelate boundaries
	Neural network output for non-pixelate boundaries after classification
	Initial training set for , , and .
	Pixel boundary for both and based on , , and
	Neural network’s hidden layer processes for reducing noisy pixels with maximum diagnosis accuracy

Results and Discussion

Experimental results

The proposed scheme is experimentally analyzed using the "cilia denoising dataset" acquired from⁴¹. The dataset provides training and testing images for reference, masking, and exposure. This dataset presents 40 short and long-exposure cilia images for testing. The training is pursued using 1K + images. The noise is reduced using a Gaussian filter after differentiating and . Based on this input, a MATLAB experiment is conducted to validate TPDS. The model uses multiple rounds to fine-tune pixel categorisation and denoising. Each cycle recalculates spatial derivatives and employs trans-pixel substitution to improve boundary detection. The two-layer neural network initialises weight assignments with random integers to avoid local minima and ensure non-deterministic starting positions. Most tests use random seed initialisation to assure consistency. Input the dataset’s training and testing pictures into MATLAB. Get the photos resized and normalized as part of the first pre-processing round to ensure the dataset is uniform. Optimize the filtering process by specifying parameters like filter size and standard deviation and then using a Gaussian filter to decrease noise. Try out different things in MATLAB on a standalone machine that has 16 GB of RAM (2 × 8 GB) and a 2.4 GHz dual-core CPU.

The proposed model utilizes one more dataset of CT medical images³⁷. The dataset aims to provide a platform for evaluating various techniques to understand CT image data patterns tied to contrast and patient age. The goal is to find statistical patterns, visual textures, and traits that correlate well with these features. Suppose these photos have been incorrectly categorized or there are outliers, such as suspicious instances, wrong measurements, or uncalibrated devices. In that case, the goal is to develop simple tools to classify these images automatically. The data are a small sample of cancer imaging database photos. Valid age, modality, and contrast tags are on these CT images. They have a centre slice. This yields 475 series from 69 patients. The image-based results are charted in Tables 3, 4, 5, and 6.

Table 3.

Boundary detection.

Input image

Table 4.

Pixelate differentiation.

Input image			Normalized output

Table 5.

Substitution and removal.

Input image

Table 6.

Noise reduction.

Input image		Denoised output

The two-layer neural network and trans-pixel replacement process that make up TPDS impact its computational efficiency. These two components necessitate substantial CPU resources when used in real-time. The method is more computationally intensive than standard filtering algorithms since it uses boundary detection, classification, and pixel replacement. Teraflop processors (TPUs) or high-performance graphics processing units (GPUs) that can quickly analyze large medical images would be necessary for TPDS to provide real-time diagnosis. To run well, a PC with at least 16 GB of RAM, a multi-core CPU (such as an Intel i7 or AMD Ryzen 9), and a dedicated graphics processing unit (like an NVIDIA RTX 3090 or A100). Modifying the model for edge devices by adding quantization and trimming the model could optimize TPDS for broad deployment. In doing so, the neural network’s complexity might decrease without compromising accuracy. Another option is for hospitals with limited computer resources to transfer processing to remote servers through a cloud-based deployment using simplified frameworks such as TensorFlow Lite or ONNX. Hospitals could perform real-time analyses without needing to invest heavily in on-site technology.

Apart from the experimental analysis, the following observations are used for graphical assessments. First the for the woo iterations for , and are analyzed. The suppression is the first step for reducing MSE for any range of pixel distribution observed. The and are the capable normalization outputs to improve precision. Considerably the neural network’s two layers are concurrent in reducing and provided the maximum and are confined in . As the reduction pursues the training for normalization and pixel differentiation, the is reduced. Simply, the causing pixels to be identified from and in the Sa separation post and processes. These constructive processes are responsible for reducing for the increasing iterations (Fig. 5).

Fig. 5.

Analyses for different iterations.

Different from the above discussion, the ratio observed in the input and its corresponding and is graphically presented in Fig. 6. The above representation in Fig. 6 presents various assessments based on rate. The second layer of the neural network is responsible for analyzing and based on . This condition trains new inputs for reducing in the newly distributed pixel representations. Therefore, as and extractions are performed, the training is highest for maximum validation. In this process, the testing-based improvements are pursued across the highest possible with .

Fig. 6.

and analyses.

Medical imaging data for deep learning model training presents ethical considerations about patient privacy, data security, and informed consent. Medical images must be anonymized before being used in teaching. Thus, HIPAA and GDPR compliance requires removing all personally identifiable information (PII), including patient names, identification numbers, and metadata. Since it uses public datasets like the Cilia Denoising Dataset and the CT Medical Images Dataset, which are pre-processed to remove sensitive data, it likely meets data anonymization standards. The Institutional Review Board (IRB) and patient approval must also be obtained to use private hospital data ethically. Encrypted storage and restricted access safeguard patient data. Medical image-trained models must not blur diagnosis or erode patient trust in AI-driven healthcare. Open data use is necessary for ethical AI activities.

Comparison with existing findings

The comparative analysis uses diagnosis accuracy, noisy pixel detection, error factor, detection time, and diagnosis precision. The number of boundaries varies from 1 to 12, and the trans-pixel rate/ boundary vary from 0.05 to 0.4 for analysis. Similarly, prevailing methods CNN-FTV²⁷, SN2N³³, CNCL²⁰, LDCT³⁵, and MDFTN³⁶ are used along with the proposed TPDS in this comparative analysis.

Diagnosis accuracy

This proposed system is used to detect noisy pixels from an input CT image to improve diagnosis accuracy based on boundary classification output (Refer to Fig. 7). In medical image denoising, “diagnostic accuracy” refers to the algorithm’s ability to preserve diagnostic information like edges, delicate features, and structural components that healthcare providers need to interpret the image. It is calculated based on Eq. 15.

Fig. 7.

Diagnosis accuracy.

The pixelate and non-pixelate boundaries are classified under either of the conditions to satisfy high diagnosis accuracy. A two-layer neural network mitigates the detected noisy pixels in both pixelate and non-pixelate borders. Noise approximation and error-causing pixel (ECP) removal are tested using this network’s initial, hidden, and output layers. The objective is to generate noise-free images from the medical fields and sequentially analyze them to achieve the maximum possible diagnosis accuracy with less detection time. The neural network output trains the noisy inputs to satisfy either substitution or removal to prevent noises. To reduce the noise, the proposed scheme differentiates the raw and processed images based on the edges of the pixel and high-frequency parts. If the non-pixelated boundary is identified in the denoising process, the trans-pixel substitution is performed, and accuracy is verified using 2LNN. The error-causing factors are confined to the proposed scheme, which achieves high diagnosis accuracy.

15

Noisy pixel detection

In this proposed scheme using a two-layer neural network to satisfy highly noisy pixel detection for the variance between pixelate and non-pixelate boundaries at each pixel layer in different instances is represented as in (Refer to Fig. 8). Based on the transformation of and wavelet, the presence of noise is identified from the input CT images using classification output is to improve noisy pixel detection. The filter is applied to reduce salt and pepper noises from the acquired image, but not both. Sequential pixel availability is monitored to identify the missing pixel in a particular boundary, and this process accurately detects the noisy pixel to prevent error factors. In this article, the noisy inputs are trained using a two-layer neural network to generate new compressed images and improve diagnosis accuracy. The TPDS is used to tamper or distort the acquired images by using unnecessary noise at each pixel level. Both conditions are validated using the proposed scheme and neural network to satisfy high diagnosis accuracy. Therefore, high noisy pixel detection is achieved using boundary classification.

Fig. 8.

Noisy pixel detection.

Error factor

In this article, the proposed scheme is used to classify pixelate precisely. Non-pixelate boundaries are high, and the boundary-detected input images are suggested for trans-pixel substitution through the two-layer neural network with noise-free images (Refer to Fig. 9). In this manuscript, the average and variance between pixelate and non-pixelate boundaries are evaluated to identify noisy pixels. The input CT image’s high-frequency components and pixel edges are preserved using a median filter. The missing pixels are replaced with other pixels, and if the substituted pixel fits that place, it is verified for further processing. Therefore, the noisy pixels are identified to improve diagnosis accuracy and avoid non-fitted pixels from the instance. The diagnosis accuracy verification is performed based on the PSNR ratio measurement. The maximum possible signal value between the raw and compressed images is to prevent error-causing pixels. The structural similarity analysis is performed to observe the similarity between the input and processed images to reduce the error factor at different instances. Fewer error factors are achievable using the proposed scheme and two-layer neural network.

Fig. 9.

Error factor.

Detection time

This proposed scheme achieves high noisy pixel detection and diagnosis accuracy using similarity analysis. The classification output in each layer reduces detection time with the best solution (Refer to Fig. 10). In pixelated boundaries, the continuous pixel availability is verified. In contrast, the missing pixel is identified in non-pixelated boundaries to remove noise occurrence. The pixel substitution may vary for each pixel level based on satisfying the conditions; the images acquired with less radiation dose preserve the damage to patients. Hence, the noise in medical images can affect the diagnosis. The denoising process is based on classification output and pixel availability to reduce noisy pixels from such images and generate new images.

Fig. 10.

Detection time.

In this article, the training recurrence is performed until maximum diagnosis accuracy with a noise-free image is achieved through a substitution process or trans-pixel removal. If the alternate pixel is not fitted to that boundary, the process is halted. In this scenario, the boundary detection for accurate pixel substitution reduces the noisy pixels and improves diagnosis accuracy. Hence, the proposed scheme achieves less detection time.

Diagnosis precision

The proposed scheme achieves high diagnosis precision with less error factor and detection time than the other factors, as represented in Fig. 11. The pixelate and non-pixelate boundaries are independently processed for noise reduction. The trans-pixel substitution and removal are performed based on either of the conditions to improve diagnosis accuracy without any noisy pixel occurrence. This proposed TPDS using a two-layer neural network identifies the error-causing pixels in each layer to enhance diagnosis precision and accuracy. This scheme effectively improves the prediction, reduction, and training accuracy of denoising process. The classification of pixelate and non-pixelate boundaries output based on velocity and position between the images will lead to noisy pixels or other impacts. The two-layer neural network notices the error-causing pixel from the input images to increase noise removal. Therefore, the fitness functions of substitution and removal are directly proportional to these values. The consistent denoising procedure obtains the previous knowledge of the noise; this process is performed to identify the noise variance. Therefore, the proposed scheme satisfies less diagnosis precision.

Fig. 11.

Diagnosis Precision.

Structural Similarity Index (SSI)

Assess the recommended Trans-Pixelate Denoising Scheme (TPDS) performance measures using CT medical images and the cilia denoising dataset shown in Table 7. SSI evaluates brightness, contrast, and structure to determine how well the denoised picture retains the structure and essential aspects of the original image. Comparing the denoised picture to the original image using SSI assesses structural information preservation. More structural similarity means better SSIM scores. The SSI assesses how well structural information is retained after denoising. Lower SSI values indicate simplification, whereas higher values indicate a precise structural match to the original image.

Table 7.

SSI comparison.

Model	SSI (cilia denoising dataset)	SSI (CT medical images)
CNN-FTV27	0.81	0.84
SN2N33	0.85	0.88
CNCL20	0.87	0.89
LDCT35	0.84	0.86
MDFTN36	0.82	0.86
TPDS (Proposed)	0.89	0.92

TPDS has the highest SSI values in both datasets: 0.89 in Cilia Denoising and 0.92 in CT Medical Images. TPDS retains more structural information than the other models; therefore, denoising preserves important visual properties like textures and edges. This is crucial in medical imaging because CT scan accuracy determines diagnosis reliability. Traditional models like CNN-FTV and LDCT have lower SSI values: 0.81–0.84 and 0.82–0.85. This suggests these models may distort or obfuscate essential structural information during denoising, reducing diagnostic reliability. SN2N and CNCL outperform models with SSI values between 0.85 and 0.89; however, they are still below TPDS norms. They minimize noise well, but TPDS maintains more of the building’s structural integrity. The SSI findings show that TPDS outperforms standard models and stays structurally close to the original picture. It is crucial in CT medical imaging because correct diagnosis depends on minute details. A significant advantage of the TPDS system over traditional denoising methods is that controlled trans-pixel substitution reduces noise without compromising structural information.

RMSE

The Cilia Denoising Dataset and CT Medical Images show that TPDS obtains the lowest RMSE values, at 0.032 and 0.029, respectively, as shown in Table 8. Because of its little distortion and good noise removal, TPDS produces denoised pictures far closer to the original, noise-free images than other models. The more significant root-mean-squared errors (RMSEs) of more traditional models, such as CNN-FTV and LDCT, suggest that the denoising procedures used by these models produce more residual noise or more detail loss, leading to a more noticeable departure from the source picture. Even if they outperform CNN-FTV and LDCT, models such as SN2N and CNCL still have larger RMSE values than TPDS. This means they aren’t as accurate as TPDS when preserving the original picture quality after denoising. Both datasets demonstrate that TPDS outperforms traditional models in noise removal while maintaining the original image’s pixel values, thanks to its reduced RMSE values. This improves the dependability of TPDS in fields such as medical imaging, where the accurate storage of picture data is essential for diagnosis.

Table 8.

RMSE.

Model	SSI (cilia denoising dataset)	SSI (CT medical images)
CNN-FTV27	0.045	0.039
SN2N33	0.037	0.034
CNCL20	0.041	0.043
LDCT35	0.039	0.046
MDFTN36	0.040	0.036
TPDS (Proposed)	0.032	0.029

Peak-to-Average Signal-to-Noise Ratio (PASN)

In medical imaging, especially CT scans, the Peak-to-Average Signal-to-Noise Ratio (PASN) is used to evaluate noise reduction procedures. PASN measures how well a denoising procedure preserves high-intensity areas while reducing noise by comparing the highest peak signal power to the average noise power. If the PASN value is high, the technique can keep high-detail regions like organ borders, lesions, and minute anatomical traits without smoothing them. Since PASN evaluates noise suppression locally, it is especially crucial for CT scans, where minute details must be preserved for diagnosis.

The proposed TPDS method outperforms CNN-FTV, SN2N, CNCL, LDCT, and MDFTN in PASN scores. It uses targeted trans-pixel substitution to remove noisy pixels while preserving edge structures. CNN-FTV and LDCT models also hide essential information, lowering PASN values. This is because they over-smooth photographs. Even though SN2N and CNCL perform better, they cannot distinguish structural noise and crucial diagnostic textures. This improves PASN somewhat. Despite the network’s robustness, MDFTN’s more excellent false positive rates cause slight signal distortions in essential regions. TPDS had the highest PASN score of all the procedures studied. This is because the two-layer neural network technique targets noise-rich areas. Table 9 shows that TPDS reduces noise while preserving image quality. It removes PASN from all other techniques. The TPDS’s PASN score of 31.3 dB for CT Medical Images shows its ability to record anatomical features for accurate diagnosis. Because of this, TPDS is a great candidate for medical picture denoising, and adaptive pixel replacement and hybrid learning models may improve PASN functionality in the future.

Table 9.

Peak-to-average signal-to-noise ratio (PASN).

Model	PASN (cilia denoising dataset)	PASN (CT medical images)
CNN-FTV	22.5 dB	24.8 dB
SN2N	25.3 dB	27.1 dB
CNCL	26.7 dB	28.5 dB
LDCT	24.2 dB	25.9 dB
MDFTN	25.9 dB	27.6 dB
Proposed TPDS	29.1 dB	31.3 dB

The main TPDS measures are PSNR, SSIM, and RMSE. All these metrics show how effectively TPDS enhances CT scan quality while keeping diagnostic information. PSNR measures total noise reduction, RMSE measures error between original and denoised pictures, and SSIM measures structural integrity and sensory quality. An RMSE measure is a relative mean square error. These three steps, known as TPDS, guarantee that denoising does not create artefacts or affect the picture’s integrity, improving diagnostic accuracy over conventional approaches. PSNR compares a picture’s maximum signal intensity to its noise level in db. The processed image retained more original elements and had less distortion. PSNR emphasises pixel intensity fluctuations, which is insufficient to describe perceptual quality. PSNR focuses on these variances. SSIM evaluates structural consistency, contrast, and brightness in denoised and original pictures. This helps alleviate this drawback. CT scans with SSIM values closer to 1 maintain anatomical features better. Reducing RMSEs means fewer pixels are out of focus than in the original image. Since they minimize noise without distorting less visible medical information, these metrics justify TPDS.

Research discussion

The proposed system significantly improves the analyzed result performance metrics: diagnosis accuracy rises by 7.3%, noisy pixel detection increases by 13.05%, and error reduction falls by 11.15% compared to earlier approaches. Additionally, the system shows a decrease of 9.03% in detection time. Utilizing a two-layer neural network for accurate pixel classification and noise management, these enhancements align with the research goal of creating a more effective denoising scheme for medical images. The scheme has improved diagnostic accuracy and efficiency, as the significant percentage differences show.

Research challenges

The TPDS faces limitations in handling diverse noise types and computational complexity. Additionally, it may struggle with generalizability across various medical image types and risks overfitting to training data.

TPDS is effective in denoising CT images, however, it cannot handle medical imaging noise. MRI pictures have Gaussian and Rician noise, unlike X-ray images, which have quantum mottling or structural anomalies. Poisson noise—caused by photon counting errors—significantly affects computed tomography (CT) images. TPDS was initially designed for CT pictures; thus, it’s unclear if it can reduce pixel border noise in X-ray or MRI images without modification. In some imaging techniques, the two-layer neural network struggles with structural changes and noise distributions. Transfer learning can educate TPDS to modify its parameters to other imaging modalities, making it more generalizable. With adaptive filtering, performance may be improved across several datasets. Pictures’ noise characteristics lead these systems to shift dynamically with the kind of picture. A multi-modal training strategy employing a colossal dataset of medical images from various sources would ensure that TPDS can learn noise patterns outside CT scans and provide robust denoising across numerous imaging scenarios.

Inability to manage border noise between pixelated and non-pixelated regions causes current denoising algorithms to overlook critical diagnostic characteristics. Median and Gaussian filtering utilize uniform noise reduction, which can distort biologically essential small structures and blur edges. CNNs and GANs increase noise suppression but struggle with boundary noise, which causes data structure mistakes. Due to their inability to distinguish ECPs from diagnostically relevant characteristics, several methods smooth or reduce noise too much. Overcoming these limits, TPDS uses a two-layer neural network to recognize and replace noisy border pixels to improve diagnostic accuracy, clarity, and structural integrity.

Implications of future research

Future enhancements of this research could integrate advanced noise models and adaptive filtering techniques to enhance performance across various TPDS imaging modalities. Additionally, evaluating the scalability of the two-layer neural network with more extensive and diverse datasets could further optimize denoising accuracy and computational efficiency.

The proposed TPDS methodically deleted or changed different parts of the model to see how they affected the overall performance. The main points of the study were the two-layer neural network, median filter, and trans-pixel replacement technique. The filter is vital for early noise reduction because the model exhibited a considerable increase in noise retention when the median filter was removed, resulting in a 7% decrease in SSIM and a 10% rise in RMSE. With a 12% rise in RMSE, it is clear that removing the trans-pixel replacement degraded the picture quality, affecting boundary features and sharp edges. Last but not least, reducing the two-layer neural network to a single layer decreased the model’s capacity to distinguish between noisy and non-noisy pixels accurately, lowering diagnostic accuracy and producing a 5% decrease in SSIM. The ablation findings show that TPDS’s outstanding denoising performance is due to the combined efforts of all of its components, particularly in increasing diagnostic clarity and preserving structural features in CT medical pictures.

TPDS integration with hospital PACS or telemedicine systems can enhance automated CT scan processing for real-time diagnosis. When radiologists integrate TPDS into their processes, noisy CT images are automatically assessed before they reach them. This improves diagnostic accuracy and reduces manual intervention. Combining TPDS with AI-driven CAD systems helps identify suspicious spots and preserve structural information in denoised pictures. TPDS on cloud platforms provide remote CT scan processing in telemedicine settings with limited computational resources. Remote or low-income healthcare institutions would profit significantly from this because they rarely access high-tech imaging equipment. Real-time API connectivity with cloud PACS allows radiologists to access improved CT images anywhere. Visual noise would be reduced, enabling more accurate remote diagnosis.

Conclusion

The article introduced the Trans-pixelate denoising scheme using the two-layer neural network. This model performs a denoising process for extracting the noise-free image through pixel substitution or trans-pixel removal. This relies on different types of filters to ensure the best noise-free image and high noise is removed. TPDS is an optimization scheme that finds all kinds of output to find the best answer at each pixel level. The Trans-pixelate substitution and removal using the two-layer neural network are used as a computing medium to identify the noisy inputs under either of the conditions. The proposed scheme is an optimization method that searches for noise presence in the entire pixel to remove the noises in each level. From the comparative analysis, the following conclusions are derived: this TPDS improves diagnosis accuracy, precision, and pixel detection by 7.3%, 8.14%, and 13.05%, respectively, under different trans-pixel rates/boundaries. Under the same variant, this scheme reduces error and detection time by 11.15% and 9.03%, respectively.

Author contributions

1.Fengjun Hu :Writing–original draft, Writing–review and editing 2.Hanjie Gu: Writing–review and editing, Supervision 3.Fan Wu: Conceptualization, Methodology 4.Chahira Lhioui: Data curation, Writing–original draft, 5.Salwa Othmen: Validation, Writing–review and editing 6.Ayman Alfahid: Writing–original draft, Writing–review and editing 7.Amr Yousef: Writing–review and editing, Supervision 8.Paolo Mercorelli: Formal Analysis, Validation.

Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 82011530399), the Zhejiang Province Key Research and Development Program (Grant No. 2021C01189), Leading talents of Science and Technology Innovation in Zhejiang Province (Grant No. 2020R52042), Zhejiang-Netherlands Joint Laboratory for Digital Diagnosis and Treatment of oral diseases, and Major Scientific Research Innovation (team) Project “Research and Application of Multi-objective Collaborative Intelligent Control Method”.

Data availability

Data will be made available on request to the Corresponding Author.

Declarations

Competing interests

The authors declare no competing interests.