New denoising scheme for magnetic resonance spectroscopy signals

Denoising single MR spectra by deep learning: Miracle or mirage?

PURPOSE

The inherently poor SNR of MRS measurements presents a significant hurdle to its clinical application. Denoising by machine or deep learning (DL) was proposed as a remedy. It is investigated whether such denoising leads to lower estimate uncertainties or whether it essentially reduces noise in signal-free areas only.

METHODS

Noise removal based on supervised DL with U-nets was implemented using simulated 1 H MR spectra of human brain in two approaches: (1) via time-frequency domain spectrograms and (2) using 1D spectra as input. Quality of denoising was evaluated in three ways: (1) by an adapted fit quality score, (2) by traditional model fitting, and (3) by quantification via neural networks.

RESULTS

Visually appealing spectra were obtained; hinting that denoising is well-suited for MRS. However, an adapted denoising score showed that noise removal is inhomogeneous and more efficient for signal-free areas. This was confirmed by quantitative analysis of traditional fit results as well as DL quantitation following DL denoising. DL denoising, although apparently successful as judged by mean squared errors, led to substantially biased estimates in both implementations.

CONCLUSION

The implemented DL-based denoising techniques may be useful for display purposes, but do not help quantitative evaluations, confirming expectations based on estimation theory: Cramér Rao lower bounds defined by the original data and the appropriate fitting model cannot be circumvented in an unbiased way for single data sets, unless additional prior knowledge can be incurred in the form of parameter restrictions/relations or applicable substates.

Shifting-corrected regularized regression for 1H NMR metabolomics identification and quantification

The process of identifying and quantifying metabolites in complex mixtures plays a critical role in metabolomics studies to obtain an informative interpretation of underlying biological processes. Manual approaches are time-consuming and heavily reliant on the knowledge and assessment of nuclear magnetic resonance (NMR) experts. We propose a shifting-corrected regularized regression method, which identifies and quantifies metabolites in a mixture automatically. A detailed algorithm is also proposed to implement the proposed method. Using a novel weight function, the proposed method is able to detect and correct peak shifting errors caused by fluctuations in experimental procedures. Simulation studies show that the proposed method performs better with regard to the identification and quantification of metabolites in a complex mixture. We also demonstrate real data applications of our method using experimental and biological NMR mixtures.

Signal-to-Noise Ratio Enhancement of Single-Voxel In Vivo 31P and 1H Magnetic Resonance Spectroscopy in Mice Brain Data Using Low-Rank Denoising

Magnetic resonance spectroscopy (MRS) is a noninvasive technique for measuring metabolite concentration. It can be used for preclinical small animal brain studies using rodents to provide information about neurodegenerative diseases and metabolic disorders. However, data acquisition from small volumes in a limited scan time is technically challenging due to its inherently low sensitivity. To mitigate this problem, this study investigated the feasibility of a low-rank denoising method in enhancing the quality of single voxel multinuclei (³¹P and ¹H) MRS data at 9.4 T. Performance was evaluated using in vivo MRS data from a normal mouse brain (³¹P and ¹H) and stroke mouse model (¹H) by comparison with signal-to-noise ratios (SNRs), Cramer-Rao lower bounds (CRLBs), and metabolite concentrations of a linear combination of model analysis results. In ³¹P MRS data, low-rank denoising resulted in improved SNRs and reduced metabolite quantification uncertainty compared with the original data. In ¹H MRS data, the method also improved the SNRs, CRLBs, but it performed better for ³¹P MRS data with relatively simpler patterns compared to the ¹H MRS data. Therefore, we suggest that the low-rank denoising method can improve spectra SNR and metabolite quantification uncertainty in single-voxel in vivo ³¹P and ¹H MRS data, and it might be more effective for ³¹P MRS data. The main contribution of this study is that we demonstrated the effectiveness of the low-rank denoising method on small-volume single-voxel MRS data. We anticipate that our results will be useful for the precise quantification of low-concentration metabolites, further reducing data acquisition voxel size, and scan time in preclinical MRS studies.

MP-PCA denoising for diffusion MRS data: promises and pitfalls

Diffusion-weighted (DW) magnetic resonance spectroscopy (MRS) suffers from a lower signal to noise ratio (SNR) compared to conventional MRS owing to the addition of diffusion attenuation. This technique can therefore strongly benefit from noise reduction strategies. In the present work, Marchenko-Pastur principal component analysis (MP-PCA) denoising is tested on Monte Carlo simulations and on in vivo DW-MRS data acquired at 9.4 T in rat brain and at 3 T in human brain. We provide a descriptive study of the effects observed following different MP-PCA denoising strategies (denoising the entire matrix versus using a sliding window), in terms of apparent SNR, rank selection, noise correlation within and across b-values and quantification of metabolite concentrations and fitted diffusion coefficients. MP-PCA denoising yielded an increased apparent SNR, a more accurate B0 drift correction between shots, and similar estimates of metabolite concentrations and diffusivities compared to the raw data. No spectral residuals on individual shots were observed but correlations in the noise level across shells were introduced, an effect which was mitigated using a sliding window, but which should be carefully considered.

Neuroinflammation in HIV-associated depression: evidence and future perspectives

People living with HIV face a high risk of mental illness, especially depression. We do not yet know the precise neurobiological mechanisms underlying HIV-associated depression. Depression severity in the general population has been linked to acute and chronic markers of systemic inflammation. Given the associations between depression and peripheral inflammation, and since HIV infection in the brain elicits a neuroinflammatory response, it is possible that neuroinflammation contributes to the high prevalence of depression amongst people living with HIV. The purpose of this review was to synthesise existing evidence for associations between inflammation, depression, and HIV. While there is strong evidence for independent associations between these three conditions, few preclinical or clinical studies have attempted to characterise their interrelationship, representing a major gap in the literature. This review identifies key areas of debate in the field and offers perspectives for future investigations of the pathophysiology of HIV-associated depression. Reproducing findings across diverse populations will be crucial in obtaining robust and generalisable results to elucidate the precise role of neuroinflammation in this pathophysiology.

Performance analysis of reshaped Gabor filter for removing the Rician distributed noise in brain MR images

Magnetic Resonance Imaging (MRI) is an essential clinical tool for detecting the abnormalities such as tumors and clots in the human brain. The brain MR images are contaminated by artifacts and noise that follow Rician distribution during the acquisition process. It causes the loss of fine details information, distortion, and a blurred vision of the image. A reshaped Gabor filter-based denoising technique is proposed to overcome these issues. To develop the reshaped Gabor filter, the range of reshaping parameters of the filter is initially obtained by a random search method. Further, to evaluate the better performance of the proposed filter, a manual search is used to find the optimal parametric values and tested on T1, T2, and PD weighted MR data sets one by one. Also, the proposed technique is compared with the existing state of the art filtering methods such as Wiener, Median, Partial differential equation (PDE), Anisotropic diffusion filter (ADF), Non-local means filter (NLM), Modified complex diffusion filter (MCD), Multichannel residual learning of CNN (MRL), Maximum a posteriori (MAP), Adaptive non-local means algorithm (ADNLM), and Advance NLM filtering with non-sub sampled (AVNLMNS) on the basic reference and no reference parameter. The parameters such as mean square error (MSE), peak signal to noise ratio (PSNR), structural similarity index metric (SSIM), perception-based image quality evaluator (PIQE), and blind/referenceless image spatial quality evaluator (BRISQE) are evaluated on T1, T2, and PD weighted MR images with different noise variances such as 1%, 3%, 5%, 7%, and 9%. The proposed method may be used as a better denoising scheme for Rician distributed noise, edge preservation, fine details restoration, and enhancement of abnormalities.

Are Cramér-Rao lower bounds an accurate estimate for standard deviations in in vivo magnetic resonance spectroscopy?

Due to inherent time constraints for in vivo experiments, it is infeasible to repeat multiple MRS scans to estimate standard deviations on the desired measured parameters. As such, the Cramér-Rao lower bounds (CRLBs) have become the routine method to approximate standard deviations for in vivo experiments. Cramér-Rao lower bounds, however, as the name suggests, are theoretically a lower bound on the standard deviation and it is not clear if and under what circumstances this approximation is valid. Realistic synthetic 3 T spectra were used to investigate the relationship between estimated CRLBs, true CRLBs and standard deviations. Here we demonstrate that, although the CRLBs are theoretically truly a lower bound on the standard deviation (not an equality) for the problem typically encountered in quantification, they are still an adequate approximation to standard deviation as long as the model perfectly characterizes the data. In the case when the macromolecule basis deviates from the measured macromolecules it was shown that the CRLBs can deviate from standard deviations by approximately 50% for N-acetylaspartic acid, creatine and glutamate and of the order of 100% or more for myo-inositol and γ-aminobutyric acid. In the case when the model perfectly reflects the data the CRLBs are within approximately 10% of standard deviations for all metabolites. The result of the CRLB being within 10% of standard deviations means that, for an accurate model, novel quantification methods such as machine learning or deep learning will not be able to obtain substantially more precise estimates for the desired parameters than traditional maximum-likelihood estimation.

PCA denoising and Wiener deconvolution of 31 P 3D CSI data to enhance effective SNR and improve point spread function

Purpose

This study evaluates the performance of 2 processing methods, that is, principal component analysis‐based denoising and Wiener deconvolution, to enhance the quality of phosphorus 3D chemical shift imaging data.

Methods

Principal component analysis‐based denoising increases the SNR while maintaining spectral information. Wiener deconvolution reduces the FWHM of the voxel point spread function, which is increased by Hamming filtering or Hamming‐weighted acquisition. The proposed methods are evaluated using simulated and in vivo 3D phosphorus chemical shift imaging data by 1) visual inspection of the spatial signal distribution; 2) SNR calculation of the PCr peak; and 3) fitting of metabolite basis functions.

Results

With the optimal order of processing steps, we show that the effective SNR of in vivo phosphorus 3D chemical shift imaging data can be increased. In simulations, we show we can preserve phosphorus‐containing metabolite peaks that had an SNR < 1 before denoising. Furthermore, using Wiener deconvolution, we were able to reduce the FWHM of the voxel point spread function with only partially reintroducing Gibb‐ringing artifacts while maintaining the SNR. After data processing, fitting of the phosphorus‐containing metabolite signals improved.

Conclusion

In this study, we have shown that principal component analysis‐based denoising in combination with regularized Wiener deconvolution allows increasing the effective spectral SNR of in vivo phosphorus 3D chemical shift imaging data, with reduction of the FWHM of the voxel point spread function. Processing increased the effective SNR by at least threefold compared to Hamming weighted acquired data and minimized voxel bleeding. With these methods, fitting of metabolite amplitudes became more robust with decreased fitting residuals.

Improved Low-Rank Filtering of MR Spectroscopic Imaging Data With Pre-Learnt Subspace and Spatial Constraints

OBJECTIVE

To investigate the use of pre-learnt subspace and spatial constraints for denoising magnetic resonance spectroscopic imaging (MRSI) data.

METHOD

We exploit the partial separability or subspace structures of high-dimensional MRSI data for denoising. More specifically, we incorporate a subspace model with pre-learnt spectral basis into the low-rank approximation (LORA) method. Spectral basis is determined based on empirical prior distributions of the spectral parameters variations learnt from auxiliary training data; spatial priors are also incorporated as is done in LORA to further improve denoising performance.

RESULTS

The effects of the explicit subspace and spatial constraints in reducing estimation bias and variance have been analyzed using Cramér-Rao Lower bound analysis, Monte-Carlo study, and experimental study.

CONCLUSION

The denoising effectiveness of LORA can be significantly improved by incorporating pre-learnt spectral basis and spatial priors into LORA.

SIGNIFICANCE

This study provides an effective method for denoising MRSI data along with comprehensive analyses of its performance. The proposed method is expected to be useful for a wide range of studies using MRSI.

Low Rank Enhanced Matrix Recovery of Hybrid Time and Frequency Data in Fast Magnetic Resonance Spectroscopy

GOAL

The two dimensional magnetic resonance spectroscopy (MRS) possesses many important applications in bioengineering but suffers from long acquisition duration. Non-uniform sampling has been applied to the spatiotemporally encoded ultrafast MRS, but results in missing data in the hybrid time and frequency plane. An approach is proposed to recover this missing signal, of which enables high quality spectrum reconstruction. M ethods: The natural exponential characteristic of MRS is exploited to recover the hybrid time and frequency signal. The reconstruction issue is formulated as a low rank enhanced Hankel matrix completion problem and is solved by a fast numerical algorithm.

RESULTS

Experiments on synthetic and real MRS data show that the proposed method provides faithful spectrum reconstruction, and outperforms the state-of-the-art compressed sensing approach on recovering low-intensity spectral peaks and robustness to different sampling patterns. C onclusion: The exponential signal property serves as an useful tool to model the time-domain MRS signals and even allows missing data recovery. The proposed method has been shown to reconstruct high quality MRS spectra from non-uniformly sampled data in the hybrid time and frequency plane.

SIGNIFICANCE

Low-intensity signal reconstruction is generally challenging in biological MRS and we provide a solution to this problem. The proposed method may be extended to recover signals that generally can be modeled as a sum of exponential functions in biomedical engineering applications, e.g., signal enhancement, feature extraction, and fast sampling.

Considerations in applying compressed sensing to in vivo phosphorus MR spectroscopic imaging of human brain at 3T

The purpose of this study was to apply compressed sensing method for accelerated phosphorus MR spectroscopic imaging (³¹P-MRSI) of human brain in vivo at 3T. Fast ³¹P-MRSI data of five volunteers were acquired on a 3T clinical MR scanner using pulse-acquire sequence with a pseudorandom undersampling pattern for a data reduction factor of 5.33 and were reconstructed using compressed sensing. Additionally, simulated ³¹P-MRSI human brain tumor datasets were created to analyze the effects of k-space sampling pattern, data matrix size, regularization parameters of the reconstruction, and noise on the compressed sensing accelerated ³¹P-MRSI data. The ³¹P metabolite peak ratios of the full and compressed sensing accelerated datasets of healthy volunteers in vivo were similar according to the results of a Bland-Altman test. The estimated effective spatial resolution increased with reduction factor and sampling more at the k-space center. A lower regularization parameter for both total variation and L1-norm penalties resulted in a better compressed sensing reconstruction of ³¹P-MRSI. Although the root-mean-square error increased with noise levels, the compressed sensing reconstruction was robust for up to a reduction factor of 10 for the simulated data that had sharply defined tumor borders. As a result, compressed sensing was successfully applied to accelerate ³¹P-MRSI of human brain in vivo at 3T.

Spectral data de-noising using semi-classical signal analysis: application to localized MRS

In this paper, we propose a new post-processing technique called semi-classical signal analysis (SCSA) for MRS data de-noising. Similar to Fourier transformation, SCSA decomposes the input real positive MR spectrum into a set of linear combinations of squared eigenfunctions equivalently represented by localized functions with shape derived from the potential function of the Schrödinger operator. In this manner, the MRS spectral peaks represented as a sum of these 'shaped like' functions are efficiently separated from noise and accurately analyzed. The performance of the method is tested by analyzing simulated and real MRS data. The results obtained demonstrate that the SCSA method is highly efficient in localized MRS data de-noising and allows for an accurate data quantification.

Denoising of MR spectroscopic imaging data using statistical selection of principal components

OBJECTIVES

To evaluate a new denoising method for MR spectroscopic imaging (MRSI) data based on selection of signal-related principal components (SSPCs) from principal components analysis (PCA).

MATERIALS AND METHODS

A PCA-based method was implemented for selection of signal-related PCs and denoising achieved by reconstructing the original data set utilizing only these PCs. Performance was evaluated using simulated MRSI data and two volumetric in vivo MRSIs of human brain, from a normal subject and a patient with a brain tumor, using variable signal-to-noise ratios (SNRs), metabolite peak areas, Cramer-Rao bounds (CRBs) of fitted metabolite peak areas and metabolite linewidth.

RESULTS

In simulated data, SSPC determined the correct number of signal-related PCs. For in vivo studies, the SSPC denoising resulted in improved SNRs and reduced metabolite quantification uncertainty compared to the original data and two other methods for denoising. The method also performed very well in preserving the spectral linewidth and peak areas. However, this method performs better for regions that have larger numbers of similar spectra.

CONCLUSION

The proposed SSPC denoising improved the SNR and metabolite quantification uncertainty in MRSI, with minimal compromise of the spectral information, and can result in increased accuracy.

Lorentzian sparsity based spectroscopic reconstruction for fast high-dimensional magnetic resonance spectroscopy

Two-dimensional magnetic resonance spectroscopy (2D MRS) is challenging, even with state-of-art compressive sensing methods, such as L1-sparsity method. In this work, using the prior that the 2D MRS can be regarded as a series of Lorentzian functions, we aim to develop a robust Lorentzian-sparsity based spectroscopy reconstruction method for high-dimensional MRS. The proposed method sparsifies 2D MRS in Lorentzian functions. Instead of thousands of pixel-wise variables, this Lorentzian-sparsity method significantly reduces the number of unknowns to several geometric variables, such as the center, magnitude and shape parameters for each Lorentzian function. The spectroscopy reconstruction is formulated as a nonlinear and nonconvex optimization problem, and the simulated annealing algorithm is developed to solve the problem. The proposed method was compared with inverse FFT method and L1-sparsity method, under various undersampling factors. While FFT and L1 results contained severe artifacts, the Lorentzian-sparsity results provided significantly improved spectroscopy. A new 2D MRS reconstruction method is proposed using the Lorentzian sparsity, with significantly improved MRS reconstruction quality, in comparison with standard inverse FFT method or state-of-art L1-sparsity method.

Hybrid sparse regularization for magnetic resonance spectroscopy

Magnetic resonance spectroscopy imaging (MRSI) is a powerful non-invasive tool for characterising markers of biological processes. This technique extends conventional MRI by providing an additional dimension of spectral information describing the abnormal presence or concentration of metabolites of interest. Unfortunately, in vivo MRSI suffers from poor signal-to-noise ratio limiting its clinical use for treatment purposes. This is due to the combination of a weak MR signal and low metabolite concentrations, in addition to the acquisition noise. We propose a new method that handles this challenge by efficiently denoising MRSI signals without constraining the spectral or spatial profiles. The proposed denoising approach is based on wavelet transforms and exploits the sparsity of the MRSI signals both in the spatial and frequency domains. A fast proximal optimization algorithm is then used to recover the optimal solution. Experiments on synthetic and real MRSI data showed that the proposed scheme achieves superior noise suppression (SNR increase up to 60%). In addition, this method is computationally efficient and preserves data features better than existing methods.

On the Expectation-Maximization Algorithm for Rice-Rayleigh Mixtures With Application to Noise Parameter Estimation in Magnitude MR Datasets

Magnitude magnetic resonance (MR) images are noise-contaminated measurements of the true signal, and it is important to assess the noise in many applications. A recently introduced approach models the magnitude MR datum at each voxel in terms of a mixture of upto one Rayleigh and an a priori unspecified number of Rice components, all with a common noise parameter. The Expectation-Maximization (EM) algorithm was developed for parameter estimation, with the mixing component membership of each voxel as the missing observation. This paper revisits the EM algorithm by introducing more missing observations into the estimation problem such that the complete (observed and missing parts) dataset can be modeled in terms of a regular exponential family. Both the EM algorithm and variance estimation are then fairly straightforward without any need for potentially unstable numerical optimization methods. Compared to local neighborhood- and wavelet-based noise-parameter estimation methods, the new EM-based approach is seen to perform well not only on simulation datasets but also on physical phantom and clinical imaging data.

Denoising MR spectroscopic imaging data with low-rank approximations

This paper addresses the denoising problem associated with magnetic resonance spectroscopic imaging (MRSI), where signal-to-noise ratio (SNR) has been a critical problem. A new scheme is proposed, which exploits two low-rank structures that exist in MRSI data, one due to partial separability and the other due to linear predictability. Denoising is performed by arranging the measured data in appropriate matrix forms (i.e., Casorati and Hankel) and applying low-rank approximations by singular value decomposition (SVD). The proposed method has been validated using simulated and experimental data, producing encouraging results. Specifically, the method can effectively denoise MRSI data in a wide range of SNR values while preserving spatial-spectral features. The method could prove useful for denoising MRSI data and other spatial-spectral and spatial-temporal imaging data as well.

Noise estimation in magnitude MR datasets

Estimating the noise parameter in magnitude magnetic resonance (MR) images is important in a wide range of applications. We propose an automatic noise estimation method that does not rely on a substantial proportion of voxels being from the background. Specifically, we model the magnitude of the observed signal as a mixture of Rice distributions with common noise parameter. The expectation-maximization (EM) algorithm is used to estimate all parameters, including the common noise parameter. The algorithm needs initializing values for which we provide some strategies that work well. The number of components in the mixture model also needs to be estimated en route to noise estimation and we provide a novel approach to doing so. Our methodology performs very well on a range of simulation experiments and physical phantom data. Finally, the methodology is demonstrated on four clinical datasets.

Compressed sensing for resolution enhancement of hyperpolarized 13C flyback 3D-MRSI

High polarization of nuclear spins in liquid state through dynamic nuclear polarization has enabled the direct monitoring of 13C metabolites in vivo at very high signal-to-noise, allowing for rapid assessment of tissue metabolism. The abundant SNR afforded by this hyperpolarization technique makes high-resolution 13C 3D-MRSI feasible. However, the number of phase encodes that can be fit into the short acquisition time for hyperpolarized imaging limits spatial coverage and resolution. To take advantage of the high SNR available from hyperpolarization, we have applied compressed sensing to achieve a factor of 2 enhancement in spatial resolution without increasing acquisition time or decreasing coverage. In this paper, the design and testing of compressed sensing suited for a flyback 13C 3D-MRSI sequence are presented. The key to this design was the undersampling of spectral k-space using a novel blipped scheme, thus taking advantage of the considerable sparsity in typical hyperpolarized 13C spectra. Phantom tests validated the accuracy of the compressed sensing approach and initial mouse experiments demonstrated in vivo feasibility.

NMR data processing using iterative thresholding and minimum l(1)-norm reconstruction

Iterative thresholding algorithms have a long history of application to signal processing. Although they are intuitive and easy to implement, their development was heuristic and mainly ad hoc. Using a special form of the thresholding operation, called soft thresholding, we show that the fixed point of iterative thresholding is equivalent to minimum l(1)-norm reconstruction. We illustrate the method for spectrum analysis of a time series. This result helps to explain the success of these methods and illuminates connections with maximum entropy and minimum area methods, while also showing that there are more efficient routes to the same result. The power of the l(1)-norm and related functionals as regularizers of solutions to underdetermined systems will likely find numerous useful applications in NMR.

Automatic estimation of the noise variance from the histogram of a magnetic resonance image

Estimation of the noise variance of a magnetic resonance (MR) image is important for various post-processing tasks. In the literature, various methods for noise variance estimation from MR images are available, most of which however require user interaction and/or multiple (perfectly aligned) images. In this paper, we focus on automatic histogram-based noise variance estimation techniques. Previously described methods are reviewed and a new method based on the maximum likelihood (ML) principle is presented. Using Monte Carlo simulation experiments as well as experimental MR data sets, the noise variance estimation methods are compared in terms of the root mean squared error (RMSE). The results show that the newly proposed method is superior in terms of the RMSE.

Frequency-selective quantification of short-echo time magnetic resonance spectra

Short-echo time magnetic resonance (MR) spectra contain large nuisance components which should be removed in order to improve quantification of the underlying metabolite concentrations. This paper shows that powerful filtering techniques such as the maximum-phase FIR filter or HLSVD-PRO proposed by Sundin et al. and Laudadio et al., respectively, as used in long-echo time MR spectral quantification, can be applied to their more complex short-echo time spectral counterparts. Both filters are extensively studied in the presence of various unwanted components. In most of the cases the maximum-phase FIR filter outperforms HLSVD-PRO. The potential and limitations of both filters are reported.