Denoising Magnetic Resonance Spectroscopy (MRS) Data Using Stacked Autoencoder for Improving Signal-to-Noise Ratio and Speed of MRS

Abstract

Background:

While magnetic resonance imaging (MRI) provides high resolution anatomical images with sharp soft tissue contrast, magnetic resonance spectroscopy (MRS) enables non-invasive detection and measurement of biochemicals and metabolites. However, MRS has low signal-to-noise ratio (SNR) when concentrations of metabolites are in the range of millimolar. Standard approach of using a high number of signal averaging (NSA) to achieve sufficient SNR comes at the cost of a long acquisition time.

Purpose:

We propose to use deep-learning approaches to denoise MRS data without increasing NSA. This method has potential to reduce the acquisition time as well as improve SNR and quality of spectra, which could enhance the diagnostic value and broaden the clinical applications of MRS.

Methods:

The study was conducted using data collected from the brain spectroscopy phantom and human subjects. We utilized a stack auto-encoder (SAE) network to train deep learning models for denoising low NSA data (NSA = 1, 2, 4, 8, and 16) randomly truncated from high SNR data collected with high NSA (NSA=192), which were also used to obtain the ground truth. We applied both self-supervised and fully-supervised training approaches and compared their performance of denoising low NSA data based on improvement in SNR. To prevent overfitting, the SAE network was trained in a patch-based manner. We then tested the denoising methods on noise-containing data collected from the phantom and human subjects, including data from brain tumor patients. We evaluated their performance by comparing the SNR levels and mean squared errors (MSEs) calculated for the whole spectra against high SNR “ground truth”, as well as the value of chemical shift of N-acetyl-aspartate (NAA) before and after denoising.

Results:

With the SAE model, the SNR of low NSA data (NSA = 1) obtained from the phantom increased by 28.5% and the MSE decreased by 42.9%. For low NSA data of the human parietal and temporal lobes, the SNR increased by 32.9% and the MSE decreased by 63.1%. In all cases, the chemical shift of NAA in the denoised spectra closely matched with the high SNR spectra without significant distortion to the spectra after denoising. Furthermore, the denoising performance of the SAE model was more effective in denoising spectra with higher noise levels.

Conclusions:

The reported SAE denoising method is a model-free approach to enhance the SNR of MRS data collected with low NSA. With the denoising capability, it is possible to acquire MRS data with a few NSA, shortening the scan time while maintaining adequate spectroscopic information for detecting and quantifying the metabolites of interest. This approach has the potential to improve the efficiency and effectiveness of clinical MRS data acquisition by reducing the scan time and increasing the quality of spectroscopic data.

1. INTRODUCTION

Magnetic resonance spectroscopy (MRS) is a clinically available non-invasive analytical tool to obtain biochemical and metabolic information of tissue in vivo^1–4. When combined with magnetic resonance imaging (MRI), it can be used to directly detect and measure concentrations of metabolites in the sampling volume well-defined by MRI^5,6. MRS has been shown to be applicable and beneficial in clinical radiological exams, particularly in the areas of characterizations of brain tumors^7,8, prostate^9,10 and breast cancers^11,12 as well as some neurological diseases, such as epilepsy^13,14. However, MRS signals from the metabolites of interest are usually orders of magnitude lower than the water signal used in conventional MRI^15,16. This intrinsic limitation of low signal-to-noise ratio (SNR) hinders the clinical applications of MRS¹⁷. Although SNR can be increased by acquiring data using a large sample volume or a high number of signal averages (NSA), these approaches have inevitable limitations in in vivo applications, such as poor spatial resolution and low specificity when sampling the heterogeneous tissue and long data acquisition time. Therefore, integrating MRS into clinical applications to gain metabolic information and biomarkers for improving individualized diagnosis has been largely overlooked¹⁸.

Given the increasing need in molecular and metabolic imaging and quantitative assessment of the diseases in precision medicine, there has been renewed interest in broadening and improving clinical applications of MRS. Efforts to accelerate MRS data acquisition include the development of ultrafast acquisition methods to obtain high-resolution MRS imaging¹⁹, utilization of ultra-high field systems or parallel data acquisition, and implementation of data-driven reconstructions²⁰. On the other hand, one of the strategies to improve the sensitivity of MRS with existing instrumentation and capabilities at the current clinical field strength (i.e., 3 Tesla) is to reduce or even completely remove noises while retaining the signal as a part of the post-processing step. Traditionally, noises can be mitigated by applying a specific form of filters, electronically or digitally, with the penalty of sacrificing portions of signals due to incomplete separation of signals and noise, especially when noises overlapping on signals. More advanced denoising approaches, such as the wavelet thresholding^21,22 and wavelet shrinkage^23,24 methods or most recently, machine-learning assisted wavelet feature analysis and classification methods^25,26, were developed to distinguish the signal from the noise before removing the noise components to improve the SNR. However, these denoising approaches are mostly based on the prior knowledge to describe the forms and features of the noise or signal, which may not capture all the noise patterns encountered in clinical settings.

Here, we present a data-driven deep learning-based spectral denoise method for enhancing SNR of MRS data. The stacked autoencoder (SAE) network with feature learning and local denoising capabilities^27,28 was developed to denoise “spectrum-like” electrocardiogram (ECG) data^29–32. SAE uses an encoder to learn the higher-level hierarchical features and a decoder to reconstruct those features back to original-sized signals, while discarding the noisy components embedded in the original input. Like those of ECG data, noise peaks in MRS data have sparse representations in the feature vector domain. Thus, we can identify and characterize them using a patch-based SAE network. This approach has two distinctive strengths: 1) it uses a patch-based method to enlarge data variation when denoising the spectroscopic data, and 2) it is not dependent on the prior knowledge for the sparse representation. For applications in denoising MRS data, SAEs were trained in both fully-supervised and self-supervised manners. Our results demonstrated that this new approach can effectively reduce the noise level of spectra collected with low NSA and a short acquisition time (NSA = 4–8 and < 16 seconds), obtaining comparable metabolite signals to those from long scans, e.g., ~6–7 minutes or longer.

2. METHODS

2.1. Acquisition of MRS data

High SNR data were collected from a brain MRS phantom (Model 2152220, GE Healthcare, Chicago, IL) and healthy human subjects (N=3) using a 3T MR scanner (MAGNETOM Prisma, Siemens Healthcare, Erlangen, Germany). The phantom contains metabolites with known concentrations, including N-acetylaspartate (NAA, 12.5 mM), creatine (Cre, 10 mM), choline (Cho, 3 mM), lactate (Lac, 15 mM), glutamate (Glu, 12.5 mM) and myo-inositol (MI, 7.5 mM). Sagittal T₁-weighted magnetization-prepared rapid acquisition gradient echo (MPRAGE) images were recorded first with a repetition time (TR) of 2300 ms and echo time (TE) of 2.98 ms; time of inversion (TI) of 900 ms; flip angle of 9°, field of view (FOV) of 238×256 mm with the matrix size of 256×256, and 208–220 slices and slice thickness of 2 mm covering whole brain to generate T₁ weighted images that can be re-sliced to three different orthogonal directions for placing the MRS sampling volume. A single voxel of 20×20×20 mm³ then was placed at the position based on the images. For the data collected from the phantom, we selected 13 different locations to count for the location-dependent variations in the training dataset, including the anterior up (A_UP), anterior high (AH), anterior superior (AS), front left (FL), front right (FR), high (H), posterior up (P_UP), posterior down (P_DN), posterior high (PH), posterior left (PL), posterior right (PR), posterior superior (PS), and temporal (T) in reference to the isocenter, with examples shown in Figure 1 (a, b). For human subjects, we collected data from single voxels placed in the parietal and temporal brain regions, as depicted in Figure 1(c, d). Single-voxel proton (¹H) spectroscopy (SVS) data were collected using a point resolved spectroscopy sequence (PRESS) with a TE of 30 ms, TR of 2000 ms, an acquisition bandwidth of 1200 Hz and a vector size of 1024, with a standard shimming and chemical shift selective (CHESS) water suppression methods implemented on the scanner. The total MRS acquisition times, excluding pre-acquisition shimming and water suppression, were 6 minutes and 40 seconds for the high NSA spectra, including 8 pre-scans. Phase cycling of 4 was used for both phantom and human data acquisition. The data were saved individually at each acquisition, or NSA = 1, so that 192 individual spectra as well as an overall spectrum averaged from 192 individual ones were separately stored and can be retrieved for analysis. More details on the MRS data acquisition protocols can be found in our previous work³³. The human subject study was conducted in accordance with the institutional review board, and written consents were obtained from all participants.

Figure 1.

Examples of the locations used for collecting MRS data (NSA = 192) from a brain phantom at the center (a) and anterior high (b) locations, parietal (c) and temporal (d) regions of the human brain. Metabolite signals at different chemical shifts are labeled accordingly as Cre^#, MI, Cho, Cre, Glx, and NAA. Glx is composed of Glu and Gln that overlap at the field strength of 3 Tesla. Abbreviations: Cre^# and Cre, creatine; # indicates the methylene group from Cre; MI, myo-inositol; Cho, choline; NAA, N-acetylaspartate. Glu, glutamate and Gln, glutamine.

To test the developed method in a clinically relevant application, we retrospectively performed spectral denoising using low SNR data extracted from chemical shift spectroscopic images (CSI) acquired from four brain tumor patients using a clinical protocol with acquisition parameters, including TE of 36 ms, TR of 2000 ms, slice thickness of 20 mm. To match with the evaluation of single voxel spectra collected from healthy subjects and phantom, we extracted individual spectra from the multivoxel data of CSI with a FOV of 160×160 mm and the resolution of 1 ×12 voxels, giving the voxel size of 13.3×13. x20 mm. These CSI data were typically collected with low NSA (NSA=3) and a bandwidth of 1200 Hz using CHESS water suppression. The details of obtaining the low SNR dataset from CSI data have been reported in the previous study³³. Spectra extracted from the CSI have intrinsically low SNR due to low NSA. As these are low SNR data and no “ground truth” can be obtained through averaging, we evaluated the method qualitatively by visually inspecting individual spectra before and after denoising. In addition, we test denoising performance of the method in a patient data collected from one brain tumor patients using the SVS method. In this case, a single voxel with a size of 20 × 30 × 20 mm (x/y/z) was placed to cover the tumor. The SVS PRESS sequence was used with TE of 30 ms, TR of 1800 ms, and NSA of 96. All patient data were collected using a Siemens 3T scanner.

2.2. Pre-processing of MRS data

Raw MRS data were pre-processed with following steps before being prepared as direct input patches and learning targets for SAEs. First, the raw time domain free induction decay (FID) data were transformed to the frequency domain spectra by applying Fourier transformation using in-house MATLAB routine or Linear Combination of Model spectra (LCModel, version 6.3–1H)³⁴, which is a widely used software package for MRS data process and analysis. Using a set of pre-computed model spectra that contain signals from different metabolites rising from different chemical shifts, LCModel can find the best linear combination of these model spectra that matches the experimental MRS spectrum. Therefore, it is a prior-knowledge-based approach in contrast to the proposed deep-learning denoising method. We used LCModel to process the raw spectral data in only three steps/processes: 1) applying Fourier transformation to covert signals of FID data to individual spectra; 2) performing phase correction, and 3) assigning the proper frequency or chemical shifts to signals from the metabolites of interest based on the model spectra in LCModel^35–37, We then used an in-house MATLAB program with a “polyfit” function, a polynomial fitting method, for baseline correction. Briefly, the baseline points were estimated across the entire frequency range of the spectrum (i.e., chemical shift or x-axis), the polyval function takes the obtained polynomial coefficients and the corresponding values in the x-axis as inputs and returns the corresponding values in the y-axis to reach the estimated baseline.

After pre-processing the high NSA data (NSA = 192) collected at each location, we randomly selected 160 out of 192 individual spectra from each high NSA data and averaged them to generate the high SNR “ground truth” data. For generating noise-containing input data, we randomly selected 1, 2, 4, 8, or 16 spectra from the 160 individual spectra to make low NSA and low SNR data equivalent to those NSA of 1, 2, 4, 8, or 16 without actually acquiring them. This process was repeated 100 times for each location to obtain 100 pairs of high SNR “pure signal” ground truth and noise-containing inputs for training or evaluation purposes. The rationale and process of generating training and testing MRS dataset, e.g., NSA = 8, from high SNR data is presented in Figure S-1 in supplement materials. However, for the low SNR data (CSI data) collected from brain tumor patients, individual spectra were obtained based on the actual NSA used in the clinical exam, typically 1 or 4. In these cases, there was no corresponding “ground truth” data available.

2.3. Denoising workflow

Among the eight selected locations on the brain phantom, we used the high SNR data collected at nine locations (i.e., AH, A_UP, AS, P_DN, P_UP, PS, PH, H, and T) for model training, while the high SNR data collected at the rest four locations (FL, FR, PL, and PR) from the phantom, as well as those from the temporal and parietal lobes of healthy subjects (the third subject only had temporal data), were used as the sampling data for quantitatively evaluating the reported method. Voxel-wised low NSA spectral data extracted from clinical CSI of brain tumor patients collected previously were used to test the spectral improvement after denoising.

The main denoising workflow, as illustrated in Figure 2, consists of training and testing phases. In the training phase (Figure 2(a)), low NSA spectra and their corresponding noise-free “ground truth” were paired as the noise-containing spectra and pure signals to train the SAE models. In the testing phase (Figure 2(b)), the trained SAE models were applied to the input noise-containing data. The denoising performance of the method was assessed by comparing the similarity between denoised and noise-free “ground truth” signals. Metrics for quantifying the denoising performance include SNR, mean squared error (MSE), and the chemical shift value of the selected metabolite, i.e., NAA. The feed forward SAE network is depicted in Figure 2(c), and the network parameters were optimized through the backward path via minimizing the loss function defined between the input and learning target.

Figure 2.

The workflows of (a) training and (b) testing phases, and the sketched architecture of SAEs (c) used for denoising MRS spectra.

During the training phase, we utilized both self-supervised and fully-supervised learning to update the learning parameters for SAEs. Self-supervised learning, as commonly used in the literature^27,38, involves reconstructing the input noise-containing data with a denoised reconstruction net without referencing the “ground truth” noise-free signals, but using the input itself as the learning target. On the other hand, the fully-supervised training approach employs the noise-free “ground truth” as the learning target. The two approaches thus define different loss functions for training.

In the current study, we only used section of the data from the spectral or chemical shift range of 0.2 to 4.0 ppm, given this part of brain MRS data covering most brain metabolites that are investigated in most studies and clinically cases. To overcome the potential overfitting problem and simplify the involved SAEs, we used the patch-based training method to augment our dataset as well as to shorten the input segments. Since we only had limited learning patterns in data collected from the brain phantom and human subjects, this approach allowed us to increase the amount of available training data. We chose a patch size covering 0.29 ppm with an origin shifting of 0.02 ppm. As a result of the augmentation process, the size of the training dataset has increased significantly with 109,200 pairs of short patches comparing to the original dataset with only 600 pairs of full-scale noise-containing and noise-free spectra. For each pair of noise-free “ground truth” and noise-containing patches, both were further scaled to [0,1] linearly before being fed into the SAE networks for training or testing.

2.4. Training the stack auto-encoder (SAE)

The architecture of the SAEs as shown in Figure 2(c) consists of a compressing encoder branch to extract the sparse deep features from the input noise-containing MRS patch $\widehat{x}$ via encoding $\widehat{x}$ to principle MRS features $\widehat{h}$ in the hidden layers. In the feature domain, the informative part of MRS data can be expressed by a few components compared to the entire feature vectors. The noise, typically represented as bias, may be related to non-sparse feature vectors. Sparsity can help removing the noise. An expanded decoding branch is used to reconstruct the denoised spectral patch $\widehat{x}\text{'}$, while the paired “ground truth” noise-free patch $\widehat{y}$ was already prepared. By stacking the hidden layers, the original input $\widehat{x}$ is encoded to higher-level abstractions. Through the sparsity of hidden layers, only the principle components in feature domain are kept and used for reconstruction, while the noisy components are removed without prior knowledge³⁹. The objective of SAEs is to minimize the defined reconstruction error either between $\widehat{x}\text{'}$ and $\widehat{y}$ for fully-supervised learning, or between $\widehat{x}\text{'}$ and $\widehat{x}$ for self-supervised training strategy.

Let ${\theta }_i=\left\{w_i,b_i\right\}$ be the weighting and bias learnable parameters for the $i_{th}$ layer and $A\left(x\right)=1/\left(1+\mathit{\text{exp}}\left(-x\right)\right)$ is a sigmoid activation function between stacking layers, the hidden layer can then be represented as

$${\widehat{h}}_1=A\left(w_1\widehat{x}+b_1\right),$$ ( 1 )

$${\widehat{h}}_i=A\left(w_i\text{'}{\widehat{h}}_{i-1}+b_i\right),\hspace{1em}i=2,3,4.$$ ( 2 )

We define the decoder’s output as follows:

$$\widehat{x}\text{'}=A\left(w_{\mathit{\text{out}}}{\widehat{h}}_4+b_{\mathit{\text{out}}}\right)$$ ( 3 )

in which ${\theta }^{\text{'}}=\left\{w_{\mathit{\text{out}}},b_{\mathit{\text{out}}}\right\}$ is denoted as the weighting and bias parameters for the last output decoder layer.

For each denoised patch $\widehat{x}\text{'}$, it is reconstructed form the noise-containing patch $\widehat{x}$, and is expected to resemble either the noise-free signal patch $\widehat{y}$ (fully-supervised learning) or the input $\widehat{x}$ itself (self-supervised learning). Thus, for fully-supervised learning the learnable parameters are optimized by minimizing the reconstruction error:

$${\theta }_i,{\theta }^{\text{'}}=\mathit{\text{arg}}\underset{{\theta }_i,{\theta }^{\text{'}}}{\text{min}}{‖\widehat{x}\text{'}-\widehat{y}‖}_2^2,$$ ( 4 )

or for self-supervised learning the learnable parameters are optimized by minimizing the reconstruction error:

$${\theta }_i,{\theta }^{\text{'}}=\mathit{\text{arg}}\underset{{\theta }_i,{\theta }^{\text{'}}}{\text{min}}{‖\widehat{x}\text{'}-\widehat{x}‖}_2^2.$$ ( 5 )

where the L2 norm is the mean square error aiming to minimize the difference between $\widehat{x}\text{'}$ and the learning target. Both the fully-supervised and self-supervised learning approaches were used in the training process, and the results of both approaches will be presented. The training process used an Adam gradient descent optimizer with a learning rate of 0.002. The batch size was set to 50. The training dataset was split into training and validation sets using a 2:1 ratio with 2/3 of the data used for training and 1/3 used for validation.

Once the patch-based SAE network was fully trained, we tested the model with MRS data collected from FR and PR locations of the phantom as well as those from the parietal and temporal lobes of the human subjects. Similar to the processes used in the training phase, the testing spectra were also split into patches to predict denoised patches with the trained SAE models. The denoised patches were then assembled to form the full-scale denoised spectra.

2.5. Evaluation of denoising performance

Denoised spectra were compared with the “ground truth” spectra to evaluate the performance of the SAE model. SNR and MSE were used as metrics for evaluation of similarity between the noise-containing/denoised spectra and “ground truth”:

$$\mathit{\text{SNR}}=10{\mathit{\text{log}}}_{10}\frac{\sum _{i=1}^n{x_i}^2}{\sum _{i=1}^n{(s_i-x_i)}^2},$$ ( 6 )

$$\mathit{\text{MSE}}=\frac{1}{n}\sum _{i=1}^n{\left(s_i-x_i\right)}^2,$$ ( 7 )

where $x_i$ denotes the noise-containing or denoised MRS spectra, and $s_i$ is the noise-free “ground truth.” Since SNR and MSE were computed for both noise-containing and denoised spectrum, we can evaluate the denoising performance of SAEs by comparing the metrics before and after denoising.

The calculation of SNR of one single noise-containing spectrum involves both the spectrum itself and the corresponding ground truth (average of high NSA data) spectrum. In our application, the two spectra are considered to have the same width ($n$ data points). In equation (6), $x_i$ is the $i$th data point on the noise-containing spectrum while $s_i$ is the $i$th data point on the ground truth spectrum ($i=1,2,\dots ,n$). By following equation (6), we can then calculate the SNR of this single noise-containing spectrum. Since for each NSA (NSA = 1, 2, 4, 8, and 16), we performed multiple measurements with randomly selected noise-containing spectra, the mean of the SNRs of each noise-containing spectrum was then used as the SNR before denoising. Similarly, both denoised and corresponding ground truth spectra were used to calculate the SNR of a single denoised spectrum. In this case, $x_i$ in equation (6) is the $i$th data point on the denoised spectrum while $s_i$ is still the $i$th data point on the ground truth spectrum ($i=1,2,\dots ,n$). The mean of SNRs of multiple denoised spectra was then reported. The difference in SNR before and after denoising can be measured to present the performance of the deployed denoising tool.

To assess the ability of the denoising method to preserve metabolic information, the distinct chemical shift value of NAA peak at 2.02 ppm were identified and used to examine any distortion in the noise-containing and denoised spectra comparing to that of the “ground truth” spectra. The position change of the chemical shift of NAA in reference to the “ground truth” spectra before and after denoising can be used to evaluate whether the reported denoising method cause any displacement in the chemical shift of NAA signal.

$${\text{Shift-error}}_{\mathit{\text{noise-containing}}}=\left|\mathit{\text{argmax}}\left(\widehat{x}\right)-\mathit{\text{argmax}}\left(\widehat{y}\right)\right|,$$ ( 8 )

$${\text{Shift-error}}_{\mathit{\text{denoised}}}=\left|\mathit{\text{argmax}}\left(\widehat{x}\text{'}\right)-\mathit{\text{argmax}}\left(\widehat{y}\right)\right|$$ ( 9 )

where $\mathit{\text{argmax}}\left(\widehat{x}\right),\mathit{\text{argmax}}\left(\widehat{x}\text{'}\right)$ and $\mathit{\text{argmax}}\left(\widehat{y}\right)$ are the NAA peak positions of noise-containing inputs, denoised spectra and noise-free (“ground truth”) spectra, respectively. By comparing Shift-error_{noise-containing} and Shift-error_denoised we can estimate the “drift” of NAA peaks, which is the chemical shift difference between the ground truth the noise-containing and denoised spectra.

In addition to quantitative evaluation, the reported denoising methods were also tested to denoise low NSA CSI data collected from the brain tumor patients. Since no “ground truth” can be obtained from these CSI data, numerical metrics such as SNR or MSE were not feasible for evaluating denoising efficacy. Instead, the effectiveness of denoising on these low SNR data was evaluated qualitatively through visual comparison between the noise-containing and denoised spectra.

2.6. Comparison to other denoising methods

The wavelet-based transformation (WT)^40,41 and lowpass filters⁴², such as Gaussian lowpass filters, are effective and widely available denoising techniques used in various fields of signal and image processing^26,40,43. To demonstrate the better performance of the reported SAEs, we compared the denoising performance of the reported method with both WT and Gaussian lowpass filters on the same training/testing datasets based on the SNRs and MSEs of resulting denoised spectra.

The WT provides multi-resolution analysis. We employed the Daubechies 4 (db4) wavelets for multilevel one-dimensional decomposition and reconstruction of the long MRS spectra using the “PyWavelets (pywt)” package⁴⁴ in Python (Python version 3.9.12)⁴⁵. On the training dataset, we iteratively eliminated various levels (level = 1 to 7) of the decomposed coefficients until we achieved optimal SNRs after denoising. Then we use the optimal level cut off to denoise the test datasets.

The Gaussian low-pass filter convolves the input spectrum with a one-dimensional Gaussian kernel (a discrete approximation of the Gaussian function), and then reconstructs a smoother spectrum. We used the “scipy.ndimage” package in the SciPy library⁴⁶ to perform Gaussian lowpass filtering on the training and testing data. The Gaussian kernels with multiple standard deviations (sigma = 0.1, 0.2, 0.5, 1, 2, 5, 10, and 20) and various truncation (0.1, 0.2, 0.5, 1, 2, 5, 10, and 20) were used and optimized on the training dataset, and then applied to the test datasets.

3. RESULTS

3.1. Denoising baseline corrected spectra with SAEs

Multiple experiments were conducted to denoise low SNR spectra with varying NSA values of 1, 2, 4, 8, and 16. The results showed that the reported network was effective in removing noise from low NSA MRS data while preserving the primary metabolite signals for quantification. Table 1 summarizes the results from quantitative evaluation of the fully-supervised learning approach based on the measurements of SNR and MSE before and after denoising data collected from the phantom (FL location). The SNR increased and MSE decreased after denoising, demonstrating SNR enhancement. Moreover, the SNR improvement is more significant with data from lower NSA. For example, SNR increase is the greatest for NSA = 1, with 35.4% better while the MSE decreased 48.4%. In comparison, only 5.1% increase in SNR and only 22.7% MSE decrease were observed in denoising less noisy data from NSA = 16. This difference in performance may be because the input spectra with NSA = 16 are averaged over collection of “single shot” (NSA=1) of spectra with cancellation of random noise from individual spectra.

Table 1.

Comparison of SNR and MSE values of spectra from the phantom MRS spectra before and after denoising using the fully-supervised learning strategy.

NSAa	SNR (dB)			MSE
	Before	After	Change (%)	Before	After	Change (%)
1	12.7±2.9	17.2±5.0	35.4	1.2±0.7E-02	6.1±6.6E-03	−48.4
2	16.6±2.1	20.3±3.6	22.4	5.0±2.4E-03	2.6±2.1E-03	−48.6
4	19.1±2.4	22.5±3.8	17.4	2.9±2.1E-03	1.7±2.0E-03	−40.5
8	22.7±2.6	25.2±3.4	11.1	1.3±1.0E-03	8.5±9.4E-04	−35.1
16	25.7±2.2	27.0±2.6	5.1	6.4±4.1E-04	4.9±3.8E-04	−22.7

The data were preprocessed with LCModel and baseline corrected with an in-house MATLAB program.

Note: The data were collected from the FL location of the phantom.

^aNumber of signal averaging (NSA).

From the plotted noise-containing, “ground truth”, and denoised spectra, we observed improved SNR and quality of denoised spectra. Figure 3 depicts the quality of denoising noise-containing spectra with NSA of 2 and 8 collected from the phantom (FL location) using both fully-supervised and self-supervised training approaches. In both cases, the denoised spectra are significantly smoother compared to the original noise-containing inputs, and are very close to the “ground truth”. As noisy components were removed, signals from low concentration metabolites emerged at distinctive chemical shifts and became detectable. Additionally, the SAE denoising models exhibited a greater smoothing effect on the noise-containing data collected with NSA = 2 compared to those with NSA = 8, despite the input data having a worse SNR.

Figure 3.

Examples of MRS spectra before and after being denoised with different training approaches. Spectra were collected from the FL location of brain phantom with NSA of 2 or 8. (a, b): Spectra denoised with self-supervised learning, and (c, d): with fully-supervised learning. High SNR “ground truth” spectra collected with high NSA are presented in solid blue line with noisy spectra and corresponding denoised spectra shown in dotted red line and solid green line, respectively. The raw spectral data were preprocessed with LCModel and baseline corrected with an in-house MATLAB tool.

When we compared the effectiveness of denoising using different training approaches, i.e., self-supervised or fully-supervised SAEs, both training approaches achieved substantial SNR improvement and MSE reduction, yielding high quality denoised spectra. As summarized in Table 2, the fully-supervised learning approach outperformed the self-supervised method. In the phantom experiments of denoising low SNR spectra with NSA = 1, 2, and 4, and the human experiments of NSA = 1, 2, 4, and 8, the fully-supervised models yielded a greater improvement in SNR and decrease in MSE, compared to their self-supervised counterparts. For example, training with fully-supervised SAEs resulted in 32.9% SNR increase and in 63.1% MSE reduction in the denoised low SNR spectra collected from the healthy subjects with NSA of 1. When using the self-supervised approach to denoise the same data, we observed 29.6% SNR improvement with 52.3% MSE reduction. Overall, both self-supervised and fully-supervised denoising approaches are more effective in denoising noisier and lower NSA data than less noisy and high NSA spectra.

Table 2.

The denoising performance of self- and fully-supervised learning as measured by SNR and MSE changes after denoising the data with different noise level and NSA.

Phantom
NSA	SNR change (%)		MSE change (%)		Signal “Drift” (10−3 ppm)
	Self-super-vised	Fully-super-vised	Self-super-vised	Fully-super-vised	Self-supervised		Fully-supervised
					Before	After	Before	After
1	18.2	28.5	−32.4	−42.9	140.3 ± 487.6	8.1 ± 95.1	140.3 ± 487.6	2.2 ± 4.1
2	14.4	19.3	−31.5	−39.9	21.7 ± 188.9	2.4 ± 4.0	21.7 ± 188.9	2.1 ± 3.9
4	11.5	13.3	−30.7	−34.5	7.1 ± 95.1	1.9 ± 3.8	7.1 ± 95.1	1.6 ± 3.5
8	8.5	8.1	−28.2	−28.4	1.0 ± 2.9	1.5± 3.4	1.0 ± 2.9	1.2 ± 3.0
16	3.6	2.7	−16.5	−14.5	0.5 ± 2.0	1.3 ± 3.2	0.5 ± 2.0	1.0 ± 3.2
Healthy subjects
1	29.6	32.9	−52.3	−63.1	132.8 ± 421.6	33.6 ± 162.1	132.8 ± 421.6	19.2 ± 93.7
2	23.8	31.1	−51.1	−64.1	15.2 ± 103.1	7.2 ± 41.1	15.2 ± 103.1	4.0 ± 5.1
4	18.9	22.3	−49.2	−56.3	4.5 ± 5.5	3.2 ± 5.0	4.5 ± 5.5	3.3 ± 4.8
8	14.1	14.8	−46.8	−50.0	4.5 ± 4.9	2.3 ± 4.0	4.5 ± 4.9	2.3 ± 4.1
16	8.3	7.8	−36.7	−36.1	2.8 ± 4.5	2.0 ± 3.8	2.8 ± 4.5	1.7 ± 3.5

The comparison of the spectral distortion caused by denoising is based on “drift” of the NAA peak at 2.02 ppm along the chemical shift axis. The data have been pre-processed using LCModel and then baseline corrected.

Worth noting, fully-supervised learning also resulted in less error (“drift”) or distortion to the chemical shift of the metabolites, as indicated by the position of the NAA peak in comparison with that of “ground truth” spectra. As shown in Table 2, the spectra with lower NSA appear to have higher chemical shift “drift” comparing to the high NSA spectra before and after denoising. For example, before denoising data from healthy human, differences in the chemical shift (shift “drift”) of NAA between “ground truth” spectra and NSA = 1 and NSA = 8 are 0.13 ± 0.42 ppm and 0.0045 ± 0.0049 ppm, respectively. After fully-supervised denoising, the signal “drift” in chemical shift decrease to 0.02 ± 0.09 ppm for the spectra with NSA = 1 and 0.0023 ± 0.0041 ppm with NSA = 8. This is because the low NSA spectra contain less information and may result in less accurate quantification of chemical shifts for the designated metabolites. Both fully-supervised and self-supervised denoising approaches yielded almost negligible “drift” in chemical shift of NAA (~ 10⁻³ ppm) when applied to most phantom data (NSA = 2 to 16 randomly selected from high SNR data) and many of the healthy subject data (NSA = 4 to 16 randomly selected from high SNR data). In the case of the data with NSA = 1 collected from human subjects, the chemical shift error decreased from about 0.13 to 0.03 ppm with self-supervised denoising, and it decreased from about 0.13 to 0.02 ppm with fully-supervised denoising. Both approaches showing a noticeable improvement of shift “drift” after denoising for the spectra with lower NSA. These results demonstrate that denoising with the reported deep learning methods do not cause distortion to the chemical shift of the metabolites.

In addition to the quantitative evaluations, we tested the SAEs to denoise the real-world clinical data from two brain tumor patients, retrospectively. The voxel-wise MRS data extracted from CSI were considered as low NSA noisy input data, while SAEs were trained with the phantom data. As the examples presented in Figure S-2 in supplement materials, the reported SAEs improved SNR of the spectra extracted from both tumor and normal regions.

3.2. Denoising non-baseline corrected spectra with SAEs

To further test the robustness of our reported denoising SAEs, we also trained and tested deep learning networks to denoise raw data with less pre-processing steps. In this case, we performed additional investigations on the effect of baseline correction by denoising spectra/data without baseline correction by LCModel and evaluating the performance of the reported denoising methods. Using the same training and testing strategies on these spectral data, the denoising method demonstrated similar performance and effectiveness of denoising non-baseline corrected data (Table S-1 in supplement materials) as we observed in the results on the corrected data reported in Table 2.

3.3. Comparison with lowpass filter and WT methods

To compare the performance of our reported SAEs and the conventional denoising methods, we also trained and tested the spectral denoising using the Gaussian lowpass filter and WT. Table S-2 in supplement materials summarizes the performances in SNR and MSE for all four methods (the self- and fully-supervised SAE, lowpass filter, and WT). The results showed that the both SAEs outperformed the conventional WT and the lowpass filter in terms of SNR and MSE enhancement across all experiments, with the fully-supervised SAEs perform the best for data with lower NSAs. For the self-supervised SAE, it outperformed the WT and lowpass filter methods in almost all cases.

4. DISCUSSION

In this study, we have shown a highly effective deep learning technique for denoising MRS data without compromising the sensitivity to metabolites. Reported SAEs denoising method performed well across diverse testing datasets, including those from the standard spectroscopy phantom, healthy human brain and brain tumors in patients, demonstrating the robustness and generalizability of the models. These findings highlight the potential of SAEs as a promising tool for enhancing SNR and quality of MRS data through denoising, which can potentially impact clinical MRS applications through improving accuracy and reliability of MRS data, accelerating MRS data acquisition and streamlining clinical workflows of MRS protocols.

We have presented and evaluated both fully-supervised and self-supervised learning approaches. Interestingly, both approaches are more effective in enhancing the noisier data collected with lower NSA, especially NSA = 1, compared to less noisy and averaged data collected with higher NSA (e.g., NSA = 16). It is likely that less noisy data were obtained by averaging multiple spectra in which noise cancellation takes place to those random noise components when data are averaged. While signal averaging is a classic approach to improve the SNR, it requires a longer acquisition time. Thus, high NSA data acquisition is prohibitive to MRS applications when fast data acquisition is needed in clinical situations when limited time is allowed to collect data from patients, such as patients with stroke or pediatric patients, or data collection in the regions is motion-sensitive, such as liver or heart or even lung. Therefore, the robustness of the reported denoising method to improve the SNR of extremely low NSA data, e.g., NSA = 4 or even 1, is potentially “game-changing” in clinical settings, enabling MRS applications in clinical problems that need to obtain additional molecular and metabolic information.

Our study has shown that, in general, fully-supervised SAEs outperforms conventional self-supervised SAEs, particularly when denoising low NSA data. This difference in denoising effectiveness may be explained by the fact that the two methods have different training targets. SAEs are commonly used in self-supervised mode, without the need for extra labeling effort^27,47–49. They take in the noise-containing input to learn high-level abstract features and then reconstruct a denoised spectrum that resembles the input itself. In other words, self-supervised SAEs have no knowledge of what a “true” spectrum should look like, but can only estimate it from the noise-containing input. For data with a higher level of noise, the estimation by the network can be substantially distracted by the embedded noise, causing errors and large deviations from the ground truth. In comparison, our proposed fully-supervised SAEs learned the “ground truth” spectra of high SNR, thus the denoising method was guided with much more information to generate the output spectra. Therefore, fully-supervised SAEs performed better in most cases. For NSA = 8 or 16 spectra, where the input itself has enough signals or features to process from multiple averages, the output spectrum is easier to reconstruct, and thus both training strategies showed comparable performance.

We found that reported learning-based SAEs have better denoising performance comparing to conventional denoising approaches, such as WT and lowpass filters. The self-/fully- supervised SAEs outperformed both classic spectral denoising methods in terms of SNR and MSE improvement for most of the cases, demonstrating the robustness and effectiveness of SAEs in denoising MRS data signals. Such ability may come from the basic structures of SAEs. SAEs are layered networks that use hidden neurons to encode inputs. Each hidden neuron in the next layer is a linear combination of multiple neurons in the previous layer. The nonlinear connections between layers further enhance their ability to extract high-level complex features. The large number of hidden neurons and nonlinearity between layers in an SAE allows it to learn complicated features with great flexibility and complexity, whereas WT and lowpass filter methods only use limited numbers of handcrafted basis to decompose the inputs. This is a significant advantage of SAEs over classical methods for denoising MRS data.

As a proof-of concept study, this work is limited by the data size and sources, which is a common issue in deep learning methods. In the study, we only used one type of brain phantom that contains a limited number of metabolites, leading to less diverse and complicated MRS patterns compared to those in humans. For healthy brain data, we only collected two sampling regions, i.e., the parietal and temporal lobes, while we understand that the brain tissue is heterogeneous in different areas and structures. Therefore, the representations of MRS patterns are limited in our datasets. To overcome these limitations, we employed a patch-based method that treated the full-scale spectra within a chemical shift range of 0.2–4 ppm as 182 short patches of size 0.29 ppm. By covering such a narrow spectral range, the model’s complexity needed to learn high-level abstractions is largely reduced. Additionally, we augmented the dataset by generating 109,200 short patch pairs from 600 full-scale spectra pairs, thereby avoiding potential overfitting problem.

While using the spectroscopic phantom allow us to obtain “ground truth” as close as possible as we showed in our previous work³³, it is almost impossible to obtain similar “ground truth” data from human brains and patient data at this point. To overcome this challenge, we adopted a method in our study where we used high SNR spectra as the noise-free “ground truth” for both training and evaluation. Previous experiments^50,51 have used the average of 128 repeated single measurements as the “true” information, while in our work, we opted for NSA = 160 to generate the high SNR “ground truth”, which involved more averages than those experiments.

While our study did not involve metabolite quantification of human subjects as a form of training information, we found that the high NSA spectra used as the “ground truth” already contained embedded metabolite quantification information. Specifically, chemical shift peaks of NAA, MI, Cre, Cre#, Cho, and Glx were present in the “ground truth” spectra. Therefore, a denoised spectra that is identical to the “ground truth” would naturally embed the correct metabolite quantification information. Consequently, the MSE calculated relative to the “ground truth” can serve as a metric to measure the similarity between the low SNR data (before or after denoising) and the “ground truth”, which implicitly reflects the accuracy of the extracted metabolite quantification information.

5. CONCLUSIONS

This work developed and demonstrated SAE networks that enable the model-free denoising of MRS spectra without need of the prior knowledge. In addition, reported deep-learning denoising approaches outperformed traditional spectral denoising methods, for example, WT and lowpass filters. Using the averaged high NSA spectra as “ground truth”, we also showed that the fully-supervised learning achieved better results to self-supervised training strategy. Furthermore, SNR and spectral quality improvements are more pronounced when deep-learning denoising methods were applied to input spectra with higher noise levels. Therefore, the reported deep learning denoising methods can potentially obtain digitally enhanced high-quality spectra from the noisy data collected using much lower NSA, thereby shortening the data acquisition time. Future investigation on the diagnostic value of deep-learning enhanced spectra and subsequent development and optimization of the reported methods could lead to clinical translation of the deep-learning approaches in improving and broadening clinical applications of MRS.

Supplementary Material

Fig S1

The schematic presentation of the workflow used for creating 100 pairs of “ground truth” and noise-containing spectra from the high SNR data for training or testing purposes. The raw data of 192 individual spectra with NSA of 1 were pre-processed first using LCModel and in-house MATLAB program for baseline correction and [0,1] normalization. Then the noise-free “ground truth” spectra were obtained by averaging randomly selected 160 out of 192 individual spectra, while the noise-containing spectra only averaged over 1, 2, 4, or 8 individual spectra. This process was repeated 100 times for each dataset to obtain a diverse set of training and testing data.

Fig S2

Examples of denoising the low SNR spectra (NSA = 3) extracted from chemical shift images (CSI) obtained from three brain tumor patients (a-c) and single-voxel MRS from one patient (d). The regions of interest (ROIs) in tumors are outlined in white, while the yellow ROIs indicate voxels selected from the normal regions. For each ROI, we present individual spectra extracted from selected voxels of CSI. The original (dotted grey lines) and denoised spectra from the tumor region (e, g, I, k) and the normal region (f, h, j), respectively. Both fully-supervised (solid blue lines) and self-supervised learning (dashed orange lines) SAEs were employed for denoising. The data were preprocessed with LCModel and baseline correction. The patient was examined by the single-voxel MRI method (d) only had MRS data (NSA = 64) from the tumor.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.