Real-time wavelet threshold denoising for laser speckle blood flow imaging

Abstract

We present a real-time denoising method for laser speckle contrast imaging (LSCI) that combines a logarithmic homomorphic transform with wavelet decomposition and adaptive thresholding. Experimental results on flow phantoms demonstrate improved linearity between the blood-flow index (BFI) and true velocity, while in vivo data show superior performance in enhancing image quality (higher Peak Signal-to-Noise Ratio/Mean Structural Similarity Index) and stabilizing BFI estimates, as well as reduced noise fluctuations compared to temporal-contrast, non-local means, Block-Matching and 3D Filtering, and variational mode decomposition. The method effectively suppresses high-frequency noise while preserving microvascular details, achieving higher PSNR/MSSIM and lower Root Mean Square Error. It processes a 4 K frame in 50 milliseconds with GPU acceleration, meeting real-time requirements. With fixed hyperparameters and adaptive thresholding, the method avoids the need for scene-specific tuning, offering robustness across varying noise levels and imaging conditions, making it a promising candidate for clinical LSCI applications.

Introduction

Laser Speckle Contrast Imaging (LSCI) is a technique that analyzes the time-averaged blur caused by the speckle contrast variation resulting from red blood cell movement. This is achieved by recording the speckle pattern formed after coherent light undergoes multiple scatterings within tissue, allowing for the acquisition of a large-field two-dimensional blood flow distribution under a single exposure. As a result, LSCI is widely used in fields such as neuroscience, skin transplantation, and microcirculation monitoring¹. However, the speckle noise commonly observed in LSCI images follows a multiplicative distribution, and its intensity fluctuations not only reduce the image contrast but also weaken the linear relationship between the blood flow index (BFI) and true flow velocity, which becomes a major bottleneck in LSCI-based quantitative analysis².

To address this issue, researchers have attempted to apply several common denoising algorithms to blood flow images. The BM3D (Block Matching and 3D Filtering) algorithm performs excellently in denoising natural images, achieving near-optimal PSNR. However, its complex computational process (such as multiple Fourier transforms and parameter adjustments) results in poor performance in real-time applications³. The Non-Local Means (NLM) algorithm denoises by utilizing the self-similarity of the image, which preserves details well. However, due to the need to traverse a large search window, it has a high computational cost and slower processing speed⁴. The Variational Mode Decomposition (VMD) algorithm, as an emerging signal decomposition method, decomposes the signal into a set of physically meaningful modes, which aids in denoising. However, VMD often suffers from instability in denoising results when handling images with strong multiplicative noise, as the number of modes and threshold settings during the decomposition process can significantly affect the outcome, making the denoising performance highly dependent on parameter choices⁵.

Although the aforementioned methods demonstrate strong denoising performance, they generally suffer from drawbacks such as complex parameter settings, high computa tional cost, and difficulty in achieving real-time processing, which limits their engineering applications in LSCI systems. To address these issues, this paper proposes a simplified scheme based on wavelet threshold denoising. The algorithm first applies a logarithmic homomorphic transform to approximate the conversion of multiplicative speckle noise into additive noise⁶. Experimental results on phantoms and in vivo data demonstrate that this algorithm, without requiring parameter adjustments, can achieve superior vascular structure preservation, image quality, and BFI stability​ comparable to or even better than BM3D and NLM, while improving processing speed by 5–10 times, thus meeting the requirements for real-time imaging.

Results and analysis

To compare denoisers under identical conditions, Fig. 1 plots BFI–velocity linear fits for raw phantom data processed by VMD, wavelet thresholding, and BM3D. All methods shared the same homomorphic log pre-processing and used recommended/optimized parameters. From Fig. 1, temporal-contrast (time-ratio) shows large fit fluctuations, indicating strong noise. Wavelet-thresholding and VMD give clearly tighter fits. BM3D improves over temporal-contrast but becomes unstable at high flows, trailing VMD and wavelet-thresholding. RMS analysis likewise favors wavelet-thresholding, indicating smaller post-denoising fluctuations.

Fig. 1.

Fitting Analysis and RMS Comparison of Denoising Algorithms. (A) Shows the fitting analysis of Time Ratio with the experimental data. The scatter plot depicts the relationship between Time Ratio and the relevant parameter; the fitted line has a slope of 0.7034 with R² = 0.9793. (B) Shows the fitting analysis for VMD (Variational Mode Decomposition). The fitted line has a slope of 0.9969 and R² = 0.9964, demonstrating very high correlation and the effectiveness of VMD. (C) Shows the fitting analysis for Wavelet Threshold. The fitted line has a slope of 0.9991 with R² = 0.9971, indicating an excellent fit. (D) Shows the fitting analysis for BM3D (Block Matching and 3D Filtering). The fitted line has a slope of 0.9835 with R² = 0.9962, indicating high accuracy on the experimental data. (E) Shows the RMS comparison across denoising methods—Time Ratio, Wavelet Threshold, BM3D, and VMD. Time Ratio has the highest RMS (9.07), while Wavelet Threshold has the lowest (8.01), suggesting that, in terms of RMS as the performance metric, the proposed wavelet method yields the most favorable outcome among the evaluated algorithms. BM3D and VMD have RMS values of 8.56 and 8.74, respectively, falling between the two.

Figure 2 compares denoisers on 3-frame LSCI (rabbit mesentery). The raw frame (A) shows heavy speckle and blurred vessels. TC (B) lowers noise but leaves blocky artifacts; NLM (C) under-suppresses multiplicative noise. BM3D (E) preserves vessels and cleans background but is the slowest in our setup, missing real-time needs. Wavelet (D) offers a superior quality–speed trade-off, closely matching the 100-frame high-SNR reference (F). Quantitatively, Among the methods compared, Wavelet yields the highest PSNR/MSSIM and the lowest BFI RMS across ROIs, with markedly lower latency than BM3D/NLM, supporting real-time LSCI. We use the Birgé–Massart strategy for adaptive thresholding without manual tuning; impacts of wavelet basis/levels and hard vs. soft rules were evaluated via PSNR/MSSIM.

Fig. 2.

Pseudo-color Visualization and Run Time Comparison of Denoising Algorithms. (A) Original Image: Displays baseline pseudocolor with evident speckle noise and moderate small-vessel visibility; P and M values set the reference. Scale: 20 mm. (B) Time-Ratio Result: Improves trunk-vessel edge clarity and contrast but retains grainy background; P and M increase slightly. (C) NLM Denoising: Reduces noise significantly and maintains vessel continuity, yet smooths local textures, leading to minor detail loss. (D) Wavelet Thresholding: Balances noise suppression and detail preservation, enhancing microvessel texture clarity and contrast; yields superior visual and metric outcomes. (E) BM3D Denoising: Achieves strong noise reduction and a cleaner appearance but risks over-smoothing in bright areas, potentially flattening fine structures; P and M improve. (F) Reference Image: Serves as an approximate ground truth from 100-frame averaging for qualitative and quantitative benchmarking. (G) Runtime Comparison: Plots algorithm speed (in milliseconds); wavelet thresholding is fastest (50ms), BM3D slowest (1500ms), with time-ratio (250ms) and NLM (300ms) intermediate.

To assess quantitative effects, we computed the mean BFI within a matched ROI for the raw image and four denoisers. As shown in Fig. 3, the raw image exhibits strong speckle that blurs fine vessels and compromises perfusion depiction. NLM suppresses high-frequency noise but softens small-vessel edges, reducing boundary sharpness. BM3D yields the smoothest background yet risks over-smoothing, erasing fine details and affecting structural fidelity.Wavelet achieves a favorable balance: it suppresses background fluctuation while preserving small-vessel continuity, improving readability and quantitative accuracy of flow estimates.The savg.tLSCI result maintains clear major vessels but shows weak stripe-like undulations along the flow direction under local velocity changes, suggesting room for refinement. Overall, all methods reduce noise, but their trade-offs differ; Wavelet provides the most favorable quality–accuracy compromise for quantitative blood-flow analysis.

Fig. 3.

Comparative Analysis of Denoising Algorithm Performance and ROI-BFI. (A) Provides a comparative visualization of the denoising effects achieved by different algorithms on the original laser speckle image. The original, unprocessed image exhibits poor quality with significant speckle noise. Application of the savg.tLSCI (smoothed time-local speckle contrast imaging) method yields effective noise reduction and clearer structural details. The NLM (Non-Local Means) algorithm demonstrates competent denoising performance, albeit with a potential risk of detail loss. In contrast, the BM3D method achieves marked noise suppression but may over-smooth fine features. The proposed wavelet-based method effectively suppresses noise while demonstrating a superior capability in preserving vascular details, despite slight over-smoothing in some homogeneous regions. Scale bars, 2 mm.(B) Magnified view of a selected region highlighting vessel details. This subfigure is extracted from (A) to more clearly show how each algorithm affects vascular structures. Red arrows indicate specific vessel areas, and the zoom facilitates comparison of algorithmic impacts on vessel morphology. (C) Comparison of the mean ROI BFI and differences from the original. The blue curve shows the mean ROI BFI after each method; the red curve shows each methods deviation from the original image. The data indicate that the original image has the highest ROI BFI, while denoised results (e.g., NLM, Wavelet, etc.) exhibit lower differences and more consistent ROI BFI values. This comparison illustrates the balance between image-quality improvement and deviation from the original achieved by each denoising method.

For medical image denoising, considering image size and the similarity of approximation coefficients, we compare the performance of two wavelet bases—sym4 and Haar—under different decomposition levels and thresholding strategies.

In Fig. 4(A), PSNR for sym4 is stable at 3–5 levels, whereas Haar fluctuates with depth. In Fig. 4(B), MSSIM increases with depth for both bases, indicating stronger structural preservation. Despite the higher metrics at deeper decompositions, Fig. 4(C) reveals over-smoothing at 5 levels (sym4/Haar), which is undesirable for vessel observation. Thus, 3 levels provide a favorable balance between speckle suppression and vessel fidelity while keeping runtime practical. Across low/high noise, wavelet thresholding remains stable; PSNR/MSSIM vary little, showing good adaptability. Compared with BM3D and NLM, wavelet is more robust in high-noise, complex flow: BM3D denoises well but is too slow for real time; NLM keeps detail yet leaves heavy noise. With a simplified pipeline, the default sym4/3-level/hard/Birgé–Massart setting performs consistently without tuning, offering better adaptivity and a superior quality–speed trade-off for real-time LSCI. Parameter-sensitivity and robustness analyses support this balance.

Fig. 4.

PSNR/MSSIM Comparison of Wavelet Bases and 5-Level Decomposition Visualization. (A) PSNR comparison of the Sym4 and Haar wavelet bases at different decomposition levels. Overall trend: as the number of levels increases, PSNR rises initially; Haar peaks at a moderate depth (≈ 3 levels) and then slightly declines, whereas Sym4 maintains or slightly improves at higher depths, showing better overall stability. (B) MSSIM comparison at different decomposition levels. For both bases, MSSIM generally increases with depth; at higher levels, Sym4 yields slightly higher MSSIM than Haar, indicating better preservation of structural similarity. (C) Pseudocolor results after 5-level decomposition using Sym4 vs. Haar. Sym4 provides more continuous details and textures—especially in fine vessels—with smoother noise; Haar shows stronger contrast but somewhat blocky edges and slightly inferior detail retention. Scale bars, 5 mm.

Discussion

This study demonstrates that a streamlined wavelet-threshold denoising method enhances Laser Speckle Contrast Imaging (LSCI) by combining a homomorphic logarithmic transform, 3-level wavelet decomposition, and adaptive Birgé-Massart thresholding. The approach simplifies the processing pipeline, avoids complex parameter tuning, and reduces computational complexity, enabling real-time denoising of 4 K frames within 50 ms-a valuable feature for clinical monitoring.

Experimental validation addressed different performance aspects. Phantom experiments with gravimetric flow calibration showed improved linearity between the Blood Flow Index (BFI) and true flow velocity, supported by lower RMS error compared to other methods (Fig. 1). For in vivo data, where no independent velocity ground-truth was available, evaluation using a high-frame-average image as a pseudo-reference confirmed the method’s effectiveness in enhancing image quality (PSNR, MSSIM) and stabilizing BFI estimates over time (Figs. 2 and 3), making it suitable for longitudinal monitoring.

The method’s performance stems from its theoretical basis: wavelet sparsity separates structural details from noise, while the homomorphic transform converts multiplicative speckle into additive noise. A 3-level decomposition balanced speed and denoising quality, avoiding over-smoothing seen at deeper levels (Fig. 4).

Despite these strengths, limitations include potential detail loss in high dynamic-range images. Future work will focus on adaptive transforms for non-Gaussian noise and broader clinical validation to promote practical adoption.

Methods

Speckle from coherent scattering is multiplicative and concentrates at high frequencies, reducing contrast and biasing BFI–velocity relations in LSCI^7–10. We therefore apply a log-homomorphic transform followed by three-level wavelet hard-thresholding to suppress high-frequency speckle while preserving low-frequency vascular structure. Compared with BM3D, NLM, and VMD—each of which is either hyperparameter-heavy, computationally expensive, or parameter-sensitive—our method uses few fixed parameters, is readily GPU-acceleratable, and achieves a superior quality–speed trade-off for real-time LSCI^11–17.

The speckle noise in LSCI follows a multiplicative model , where R is the ideal reflected signal and N is the speckle noise.

1

A log-homomorphic transform converts multiplicative speckle to approximately additive noise, stabilizing variance and meeting linear-denoising assumptions; this strategy is effective in SAR, ultrasound, and LSCI¹⁸. We then perform a 3-level DWT in the log domain to obtain approximation and detail coefficients at each scale. For adaptive thresholds, the noise SD is estimated from the level-1 high-frequency band using:

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Subsequently, Birgé–Massart thresholds are computed per scale and applied to the corresponding wavelet coefficients¹⁹. This suppresses high-frequency speckle while preserving low-frequency structure. After thresholding, we invert the log to recover intensity, keeping values within the expected range. A final linear stretch and a mild continuous-shrinkage refinement reduce residual noise and compress dark tones.

3

(,)are fixed upper and lower limits, which can enhance the contrast between the blood vessels and the background, making the small blood vessels more prominent.

The following hyperparameters were fixed throughout the study: the Sym4 wavelet base, 3-level decomposition, hard thresholding strategy, the Birgé-Massart criterion for threshold selection, and a linear intensity stretch based on the 1st to 99th percentile range. Thresholds are adaptively estimated from image statistics, yielding stable denoising and structural fidelity across noise levels without retuning. The discrete wavelet transform (DWT) and the subsequent shrinkage step were implemented using vectorized operations and GPU acceleration, which is crucial for supporting real-time processing.

Evaluation. We compare Wavelet with BM3D, NLM, and TC using four metric classes: (i) BFI quantification—BFI–velocity linearity and residual RMS; (ii) Efficiency—per-frame latency, FPS, pixel throughput; (iii) Quality—PSNR, MSSIM; (iv) BFI level—mean BFI over matched ROIs. Unless noted, metrics are computed in the linear domain (after inverse log).

Phantom setup. A custom agar + fat-emulsion phantom is tested at multiple flow rates. For each frame we compute spatial speckle contrast, derive BFI, fit BFI to calibrated flow, and analyze residuals. We also summarize each methods residual RMS in a bar chart.

(1) Spatial speckle contrast:²⁰

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Whereandrepresent the standard deviation and mean of the local window’s intensity, respectively. As the relative blood flow indicator in LSCI, this is used to define the BFI:^21,22

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(2) Correlation with linearity: Taking V as the independent variable and as the dependent variable, perform linear regression:

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The coefficient of determination:²³

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And the Root Mean Square Error (RMSE, or RMS):²⁴.

RMS comparison. For each algorithm, we compute the RMSE of BFI residuals across all flow rates and report a single scalar in a bar chart; lower RMS indicates better consistency with the linear model.

All procedures involving live vertebrate animals (New Zealand white rabbits) were reviewed and approved by the Institutional Animal Care and Use Committee of the Shaanxi Medical Device Testing Institute (Approval No.: SXQJ-IACUC-2025-001V1.0). All experimental operations complied with applicable national and international animal welfare guidelines, including GB 14,925 − 2023 and GB/T 16886.2–2011.All animal experiments in this study were conducted and reported in accordance with the ARRIVE guidelines.This study employed one male New Zealand white rabbit (body weight: 3.72 kg), housed individually in a standard laboratory cage under controlled environmental conditions (temperature 18–25 °C; relative humidity 30–50%; 12 h/12 h light–dark cycle). Each cage was equipped with a bottom tray and an integrated feeder, and the rabbit had free access to water.Before imaging, anesthesia was induced via intravenous administration of Sumianxin (0.24 mL) combined with Zoletil 50 (0.24 mL). The depth of anesthesia was continuously monitored through peripheral nerve reflex assessment and respiratory observation. A midline abdominal incision was subsequently performed to access the abdominal cavity. The mesentery was gently exteriorized and positioned on a custom observation platform to reduce motion artifacts during laser speckle contrast imaging. Warm saline was intermittently applied to the exposed tissue to maintain physiological conditions throughout the procedure.After all imaging experiments were completed, the rabbit was euthanized using a carbon dioxide chamber (SMQ-Ⅱ-Q, Shanghai Mingli Test Technology Development Co., Ltd.) with a CO₂ concentration of 90% and a flow rate of 15 L/min. Euthanasia was confirmed by the absence of respiratory and cardiac activity for at least 5 min.For the same rabbit–mesentery dataset, each denoising algorithm was applied to blood-flow images, while a high-frame time-domain averaged image (same scene and exposure, high SNR) was used as a pseudo-reference. Performance was evaluated using PSNR, MSSIM, and per-frame runtime.(1) PSNR: First, calculate the Mean Squared Error (MSE):

8

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(2) MSSIM: Using the proposed Structural Similarity Index:

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Experimental setup. A 785 nm single-mode diode laser (linewidth < 0.1 nm) provides stable, high-contrast speckle under 5 ms exposure, avoiding thermal loading²⁵. The beam is delivered via a 3 mm optical fiber and expanded with a Galilean beam expander to a 25 mm × 25 mm top-hat illumination. Scattered light is collected by a 5× telecentric objective (NA 0.09, WD 110 mm) and imaged onto a 12-bit CMOS camera (3840 × 2160). The camera and laser are synchronized by a 10 MHz clock at 5 ms exposure, 60 fps, ensuring LSCI accuracy and temporal resolution. All frames are saved in RAW linear intensity for normalization before log-homomorphic and wavelet-threshold processing.Our method achieves a processing time of 50 ms per 4 K frame, which, while not matching the 60 fps (16.7 ms per frame) acquisition rate in a strict one-to-one manner, enables real-time visualization in a pipelined system. In such a setup, the display shows processed frames with a minimal latency, suitable for intraoperative monitoring where rapid feedback is critical. The overall experimental layout is shown in Fig. 5.

Fig. 5.

Schematic diagram of the overall experimental optical setup. (A) Depicts the main optical layout. A 785 nm laser beam is split: one illuminates the experimental platform, while the other is directed to a CMOS camera for image acquisition. A GPU module and display unit handle processing and visualization. Additional components (e.g., pump, control panel) are indicated to show full system integration. (B) Shows the physical arrangement of the setup. Key elements include the imaging camera, phantom sample tray, laser head bracket, rubber tubing, control panel, and pump. Labels clarify the role and interaction of each component, providing an intuitive overview of the operational workflow.

(1) Tissue-mimicking medium fabrication: Agar gel mixed with Intralipid is used to build a bulk scattering medium with tunable absorption and scattering properties. Prior studies provide a reproducible protocol for standardized preparation of agar-based optical phantoms and rapid characterization of the scattering coefficient of Intralipid–gel layers, which can be directly used as a reference for formulations and procedures²⁶. During gel casting, rubber tubing is embedded to form “vessel” channels at specified depths, as shown in Fig. 6(A); this matches flow phantoms with customized tube diameters and burial depths, facilitating control of geometric and optical boundaries.

Fig. 6.

Phantom vessel structure and flow calibration. (A) Schematic of the phantom vessel cross-section. A thin top cover is used; a 785-nm laser illuminates from above and is focused with a 1× telecentric lens. The scattering medium consists of an agar–Intralipid gel to mimic blood-like flow. The model contains a tube of inner diameter carrying the working fluid (blood surrogate), enclosed by the rubber wall. Adjustable parameters indicated beneath the figure include the tube inner diameter and burial depth, providing experimental details. (B) Flow-rate calibration curve obtained by a gravimetric method (120 s, repeated 3 times). The plot shows the linear fit versus the ideal line y = x and the deviation between the measured and set values. The “Synthetic Flow Correction” label indicates the calibration procedure. Measured flow (y-axis) versus set flow (x-axis) is shown with mean values and SD error bars, illustrating the agreement with the nominal flow.

(2) Flow control and calibration: A peristaltic pump drives the working fluid through the tubing, circulating in a closed loop from the reservoir cup → phantom dish → peristaltic pump → return line. Six preset flow rates are set²⁷:,Where is used as the “quiet” baseline to calculate the BFI deviation. This minimizes the effects of small oscillations or disturbances, and ensures that the connection between the sample and the long connecting tube is at a gentle slope, which helps ensure that each measurement is completed over multiple cycles.

(3) To obtain the true flow rate, each is standardized by performing a 120s calibration procedure, repeated three times. The flow rate is then calculated by adjusting for the fluid density . Figure 6(B) presents the resulting flow-rate calibration curve, which includes the mean standard deviation () error bars, the ideal reference line, the fitted equation, and the coefficient of determination (). All subsequent analyses use the corrected flow rates.

(4) Convert the volumetric flow rate to the cross-sectional mean velocity inside the tube. To evaluate the algorithm’s applicability to real tissue, we followed the protocol for constructing customized tissue phantoms and implementing a polarization-enhanced scheme, assessing the ability of polarization states to suppress surface reflections and LSCI detection performance under different vessel diameters and depths²⁸.

For the animal study (Fig. 7) we compared four denoisers: speckle-contrast (TC), BM3D, Non-Local Means (NLM) and our wavelet hard-thresholding. All methods were implemented in the same MATLAB environment and executed on identical hardware (Intel Core i5-14600KF CPU, NVIDIA RTX 4060 Ti GPU), using GPU/BLAS acceleration where applicable to ensure fair runtime comparisons²⁹.Speckle in LSCI is multiplicative and commonly modeled by Gamma-type statistics. We therefore applied a log-homomorphic transform to the raw linear-intensity frames before denoising so that methods assuming additive Gaussian noise (e.g., BM3D, NLM) operate under comparable conditions; data were normalized after the log step and inverse-transformed for metric computation³⁰. Method specifics and key settings used in this study:

Fig. 7.

Schematic Diagram of Animal Experiment System. (A) Lists key hardware parts (e.g., locking clip, optical filter, eyepiece, C-mount connector) that ensure clear imaging for blood-flow analysis through a modular design. (B) Shows a schematic of the platform with labeled components (e.g., camera, endoscope, oscilloscope, animal stage), used for acquiring blood-flow data and physiological information. (C) Demonstrates real-time use in animal studies, highlighting speckle patterns and pseudocolor images for intuitive visualization of dynamic blood-flow changes. (D) Displays the workflow from imaging to data acquisition, including speckle-pattern conversion, pseudocolor analysis, and enhancement functions; scale bars indicate 5 mm for reference. (E) Outlines the end-to-end process from animal selection/anesthesia to data capture, incorporating nonsurgical/surgical approaches and metrics (PSNR, MSSIM, BFI) for evaluation.

BM3D: patch grouping + 3D collaborative filtering. We set the noise parameter ≈ 0.3 (log-domain σ) after preliminary tuning to achieve near-optimal performance on our datasets; BM3D is sensitive to block and threshold settings and is computationally heavy³¹.

NLM: implemented via MATLAB imnlmfilt with a 21 × 21 search window, 7 × 7 comparison window; smoothing factor h selected automatically from noise estimate. Standard NLM is not speckle-specific, so log preprocessing was applied; GPU acceleration was used for similarity computations³².

Wavelet (this work): 3-level DWT (sym4), hard thresholding with Birgé–Massart scale-wise thresholds estimated from the level-1 detail band (MAD→σ̂), followed by inverse log and linear stretch. These defaults were chosen because they provide a good quality–speed tradeoff at LSCI resolutions³³.

All algorithms were run with recommended/near-optimal parameters (see SI) and compared by: (i) BFI–velocity linearity and residual RMS; (ii) computational efficiency (per-frame latency, FPS, pixel throughput); (iii) image quality (PSNR, MSSIM); and (iv) mean BFI over matched ROIs. Metrics are reported in the linear intensity domain after inverse log.

Author contributions

Lei Zhang 1,4 , Xiang Gao 1 : Conceptualization; Methodology; Software; Validation; Formal analysis; Investigation; Data curation; Visualization; Writing – original draft.Chen Yang 2,4 : Resources; Supervision; Project administration; Writing – review & editing.Xiaodong Wang 3,* , Zhaoyang Zuo 1,** , Zhen’an He 2,5,*** : Methodology; Validation; Formal analysis; Writing – review & editing.Dongming Liu 3 , Ze Li 2 : Funding acquisition; Project administration; Supervision.

Funding

This work was supported by the Key Core Technology Research Project of Shaanxi Province (No. 2024SF2-GJHX-25), the Qin Chuang Yuan “Scientist + Engineer” Teams of Shaanxi Province (No. 2025QCY-KXJ-179), the Key Research and Development Program of Shaanxi Province (No. 2024SF-YBXM-436), and the Key Industrial Chain Technology Research Project of Xi’an City (No. 2025JH-ZDLYB-0009), along with the Xi’an Science and Technology Plan Project (Grant No. 23ZDCYJSGG0026-2023).

Data availability

The data reported in this study are available from the lead contact upon reasonable request for the purpose of verifying the findings or for further academic research. Applicants must outline the intended use of the data. This paper does not report original code. Any additional information required to reanalyze the data will also be provided upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.