Denoise magnitude diffusion magnetic resonance images via variance-stabilizing transformation and optimal singular-value manipulation

Main Paths of Brain Fibers in Diffusion Images Mixed with a Noise to Improve Performance of Tractography Algorithm-Evaluation in Phantom

Background

Some voxels may alter the tractography results due to unintentional alteration of noises and other unwanted factors.

Objective

This study aimed to investigate the effect of local phase features on tractography results providing data are mixed by a Gaussian or random distribution noise.

Material and Methods

In this simulation study, a mask was firstly designed based on the local phase features to decrease false-negative and -positive tractography results. The local phase features are calculated according to the local structures of images, which can be zero-dimensional, meaning just one point (equivalent to noise in tractography algorithm), a line (equivalent to a simple fiber), or an edge (equivalent to structures more complex than a simple fiber). A digital phantom evaluated the feasibility current model with the maximum complexities of configurations in fibers, including crossing fibers. In this paper, the diffusion images were mixed separately by a Gaussian or random distribution noise in 2 forms a zero-mean noise and a noise with a mean of data.

Results

The local mask eliminates the pixels of unfitted values with the main structures of images, due to noise or other interferer factors.

Conclusion

The local phase features of diffusion images are an innovative solution to determine principal diffusion directions.

Tensor denoising of quantitative multi-parameter mapping

PURPOSE

Quantitative multi-parameter mapping (MPM) provides maps of physical quantities representing physiologically meaningful tissue characteristics, which allows to investigate microstructure-function relationships reflecting normal or pathologic processes in the brain. However, the achievable spatial resolution and stability of MPM for basic research or clinical applications is severely constrained by SNR limits of the MR acquisition process, resulting in relatively long acquisition times. To increase SNR, we denoise MPM acquisitions using principal component analysis along tensors exploiting the Marchenko-Pastur law (tMPPCA).

METHODS

tMPPCA denoising was applied to three sets of MPM raw data before the quantification of maps of proton density, magnetization transfer saturation, R1, and R2*. The regional SNR gain for high-resolution MPM was investigated as well as reproducibility gains for clinically optimized protocols with moderate and high acceleration factors at different image resolutions.

RESULTS

Substantial noise reduction in raw data was achieved, resulting in reduced noise for quantitative mapping up to sixfold without introducing bias of mean values (below 1%). Scan-rescan fluctuations were reduced up to threefold. Denoising allowed to decrease the voxel volume fourfold at the same scan time or reduce the scan time twofold at same voxel volume without loss of sensitivity.

CONCLUSIONS

tMPPCA denoising can (a) improve of fine spatial and temporal patterns, (b) considerably reduce scan time for clinical applications, or (c) increase resolution to potentially push cutting-edge MPM protocols from the upper to the lower limit of the mesoscopic scale.

Optimal shrinkage denoising breaks the noise floor in high-resolution diffusion MRI

The spatial resolution attainable in diffusion magnetic resonance (MR) imaging is inherently limited by noise. The weaker signal associated with a smaller voxel size, especially at a high level of diffusion sensitization, is often buried under the noise floor owing to the non-Gaussian nature of the MR magnitude signal. Here, we show how the noise floor can be suppressed remarkably via optimal shrinkage of singular values associated with noise in complex-valued k-space data from multiple receiver channels. We explore and compare different low-rank signal matrix recovery strategies to utilize the inherently redundant information from multiple channels. In combination with background phase removal, the optimal strategy reduces the noise floor by 11 times. Our framework enables imaging with substantially improved resolution for precise characterization of tissue microstructure and white matter pathways without relying on expensive hardware upgrades and time-consuming acquisition repetitions, outperforming other related denoising methods.

Evaluating the effect of denoising submillimeter auditory fMRI data with NORDIC

Functional magnetic resonance imaging (fMRI) has emerged as an essential tool for exploring human brain function. Submillimeter fMRI, in particular, has emerged as a tool to study mesoscopic computations. The inherently low signal-to-noise ratio (SNR) at submillimeter resolutions warrants the use of denoising approaches tailored at reducing thermal noise - the dominant contributing noise component in high resolution fMRI. NORDIC PCA is one of such approaches, and has been benchmarked against other approaches in several applications. Here, we investigate the effects that two versions of NORDIC denoising have on auditory submillimeter data. As investigating auditory functional responses poses unique challenges, we anticipated that the benefit of this technique would be especially pronounced. Our results show that NORDIC denoising improves the detection sensitivity and the reliability of estimates in submillimeter auditory fMRI data. These effects can be explained by the reduction of the noise-induced signal variability. However, we also observed a reduction in the average response amplitude (percent signal), which may suggest that a small amount of signal was also removed. We conclude that, while evaluating the effects of the signal reduction induced by NORDIC may be necessary for each application, using NORDIC in high resolution auditory fMRI studies may be advantageous because of the large reduction in variability of the estimated responses.

Locally low-rank denoising in transform domains

Purpose

To develop an extension to locally low rank (LLR) denoising techniques based on transform domain processing that reduces the number of images required in the MR image series for high-quality denoising.

Theory and Methods

LLR methods with random matrix theory-based thresholds are successfully used in the denoising of MR image series in a number of applications. The performance of these methods depend on how well the LLR assumption is satisfied, which deteriorates with few numbers of images, as is commonly encountered in quantitative MRI applications. We propose a transform-domain approach for denoising of MR image series to represent the underlying signal with higher fidelity when using a locally low rank approximation. The efficacy of the method is demonstrated for fully-sampled k-space, undersampled k-space, DICOM images, and complex-valued SENSE-1 images in quantitative MRI applications with as few as 4 images.

Results

For both MSK and brain applications, the transform domain denoising preserves local subtle variability, whereas the quantitative maps based on image domain LLR methods tend to be locally more homogeneous.

Conclusion

A transform domain extension to LLR denoising produces high quality images and is compatible with both raw k-space data and vendor reconstructed data. This allows for improved imaging and more accurate quantitative analyses and parameters obtained therefrom.

DENOISING DIFFUSION MRI: CONSIDERATIONS AND IMPLICATIONS FOR ANALYSIS

Development of diffusion MRI (dMRI) denoising approaches has experienced considerable growth over the last years. As noise can inherently reduce accuracy and precision in measurements, its effects have been well characterised both in terms of uncertainty increase in dMRI-derived features and in terms of biases caused by the noise floor, the smallest measurable signal given the noise level. However, gaps in our knowledge still exist in objectively characterising dMRI denoising approaches in terms of both of these effects and assessing their efficacy. In this work, we reconsider what a denoising method should and should not do and we accordingly define criteria to characterise the performance. We propose a comprehensive set of evaluations, including i) benefits in improving signal quality and reducing noise variance, ii) gains in reducing biases and the noise floor and improving, iii) preservation of spatial resolution, iv) agreement of denoised data against a gold standard, v) gains in downstream parameter estimation (precision and accuracy), vi) efficacy in enabling noise-prone applications, such as ultra-high-resolution imaging. We further provide newly acquired complex datasets (magnitude and phase) with multiple repeats that sample different SNR regimes to highlight performance differences under different scenarios. Without loss of generality, we subsequently apply a number of exemplar patch-based denoising algorithms to these datasets, including Non-Local Means, Marchenko-Pastur PCA (MPPCA) in the magnitude and complex domain and NORDIC, and compare them with respect to the above criteria and against a gold standard complex average of multiple repeats. We demonstrate that all tested denoising approaches reduce noise-related variance, but not always biases from the elevated noise floor. They all induce a spatial resolution penalty, but its extent can vary depending on the method and the implementation. Some denoising approaches agree with the gold standard more than others and we demonstrate challenges in even defining such a standard. Overall, we show that dMRI denoising performed in the complex domain is advantageous to magnitude domain denoising with respect to all the above criteria.

Feasibility of free-breathing 19 F MRI image acquisition to characterize ventilation defects in CF and healthy volunteers at wash-in

PURPOSE

To explore the feasibility of measuring ventilation defect percentage (VDP) using 19 F MRI during free-breathing wash-in of fluorinated gas mixture with postacquisition denoising and to compare these results with those obtained through traditional Cartesian breath-hold acquisitions.

METHODS

Eight adults with cystic fibrosis and 5 healthy volunteers completed a single MR session on a Siemens 3T Prisma. 1 H Ultrashort-TE MRI sequences were used for registration and masking, and ventilation images with 19 F MRI were obtained while the subjects breathed a normoxic mixture of 79% perfluoropropane and 21% oxygen (O2 ). 19 F MRI was performed during breath holds and while free breathing with one overlapping spiral scan at breath hold for VDP value comparison. The 19 F spiral data were denoised using a low-rank matrix recovery approach.

RESULTS

VDP measured using 19 F VIBE and 19 F spiral images were highly correlated (r = 0.84) at 10 wash-in breaths. Second-breath VDPs were also highly correlated (r = 0.88). Denoising greatly increased SNR (pre-denoising spiral SNR, 2.46 ± 0.21; post-denoising spiral SNR, 33.91 ± 6.12; and breath-hold SNR, 17.52 ± 2.08).

CONCLUSION

Free-breathing 19 F lung MRI VDP analysis was feasible and highly correlated with breath-hold measurements. Free-breathing methods are expected to increase patient comfort and extend ventilation MRI use to patients who are unable to perform breath holds, including younger subjects and those with more severe lung disease.

Tensor denoising of multidimensional MRI data

PURPOSE

To develop a denoising strategy leveraging redundancy in high-dimensional data.

THEORY AND METHODS

The SNR fundamentally limits the information accessible by MRI. This limitation has been addressed by a host of denoising techniques, recently including the so-called MPPCA: principal component analysis of the signal followed by automated rank estimation, exploiting the Marchenko-Pastur distribution of noise singular values. Operating on matrices comprised of data patches, this popular approach objectively identifies noise components and, ideally, allows noise to be removed without introducing artifacts such as image blurring, or nonlocal averaging. The MPPCA rank estimation, however, relies on a large number of noise singular values relative to the number of signal components to avoid such ill effects. This condition is unlikely to be met when data patches and therefore matrices are small, for example due to spatially varying noise. Here, we introduce tensor MPPCA (tMPPCA) for the purpose of denoising multidimensional data, such as from multicontrast acquisitions. Rather than combining dimensions in matrices, tMPPCA uses each dimension of the multidimensional data's inherent tensor-structure to better characterize noise, and to recursively estimate signal components.

RESULTS

Relative to matrix-based MPPCA, tMPPCA requires no additional assumptions, and comparing the two in a numerical phantom and a multi-TE diffusion MRI data set, tMPPCA dramatically improves denoising performance. This is particularly true for small data patches, suggesting that tMPPCA can be especially beneficial in such cases.

CONCLUSIONS

The MPPCA denoising technique can be extended to high-dimensional data with improved performance for smaller patch sizes.

Axial and radial axonal diffusivities and radii from single encoding strongly diffusion-weighted MRI

We enable the estimation of the per-axon axial diffusivity from single encoding, strongly diffusion-weighted, pulsed gradient spin echo data. Additionally, we improve the estimation of the per-axon radial diffusivity compared to estimates based on spherical averaging. The use of strong diffusion weightings in magnetic resonance imaging (MRI) allows to approximate the signal in white matter as the sum of the contributions from only axons. At the same time, spherical averaging leads to a major simplification of the modeling by removing the need to explicitly account for the unknown distribution of axonal orientations. However, the spherically averaged signal acquired at strong diffusion weightings is not sensitive to the axial diffusivity, which cannot therefore be estimated although needed for modeling axons - especially in the context of multi-compartmental modeling. We introduce a new general method for the estimation of both the axial and radial axonal diffusivities at strong diffusion weightings based on kernel zonal modeling. The method could lead to estimates that are free from partial volume bias with gray matter or other isotropic compartments. The method is tested on publicly available data from the MGH Adult Diffusion Human Connectome project. We report reference values of axonal diffusivities based on 34 subjects, and derive estimates of axonal radii from only two shells. The estimation problem is also addressed from the angle of the required data preprocessing, the presence of biases related to modeling assumptions, current limitations, and future possibilities.

Single-cell phenotypic profiling to identify a set of immune cell protein biomarkers for relapsed and refractory diffuse large B cell lymphoma: A single-center study

Diffuse large B-cell lymphoma (DLBCL) is the most common invasive type of non-Hodgkin lymphoma. Cell-of-origin (COO) classification is related to patients' prognoses. Primary drug resistance in treatment for DLBCL has been observed. The specific serum biomarkers in these patients who suffer from relapsed and refractory (R/R)-DLBCL remains unclear. In the current study, using single-cell RNA sequencing (scRNA-seq) and mass cytometry (CyTOF), we determined and verified immune cell biomarkers at the mRNA and protein levels in single-cell resolution from 18 diagnostic PBMC specimens collected from patients with R/R DLBCL. As controls, 5 PBMC specimens from healthy volunteers were obtained. We identified a panel of 35 surface marker genes for the features of R/R DLBCL unique cell cluster by scRNA-seq of 8 R/R DLBCL patient samples and validated its efficiency in an external cohort consisting of 10 R/R DLBCL patients by CyTOF. The cell clustering and dimension reduction were compared among R/R DLBCL samples in CyTOF Space with COO as well as the C-MYC expression designation. Immune cells from each patient occupied unique regions in the 32-dimensional phenotypic space with no apparent clustering of samples into discrete subtypes. Significant heterogeneity observed in subgroups was mainly attributed to individual differences among samples and not to expression differences in a single, homogeneous immune cell subpopulation. The marker panel showed reliability in labeling R/R DLBCL without any influence from COO stratification and C-MYC expression designation. Furthermore, we compared all the markers between R/R DLBCL and normal samples. A total of 12 biomarkers were significantly overexpressed in R/R DLBCL relative to the normal samples. Therefore, we further optimized the diagnostic biomarker panel of R/R DLBCL comprising CD82, CD55, CD36, CD63, CD59, IKZF1, CD69, CD163, CD14, CD226, CD84, and CD31. In summary, we developed a novel set of biomarkers for the diagnoses of patients with R/R DLBCL. Detections procedures at single-cell resolution provide precise biomarkers, which may substantially overcome intertumoral and intratumoral heterogeneity among primary samples. The findings confirmed that each case was unique and may comprise multiple, genetically distinct subclones.

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.

Denoise Functional Magnetic Resonance Imaging With Random Matrix Theory Based Principal Component Analysis

High-resolution functional MRI (fMRI) is largely hindered by random thermal noise. Random matrix theory (RMT)-based principal component analysis (PCA) is promising to reduce such noise in fMRI data. However, there is no consensus about the optimal strategy and practice in implementation. In this work, we propose a comprehensive RMT-based denoising method that consists of 1) rank and noise estimation based on a set of newly derived multiple criteria, and 2) optimal singular value shrinkage, with each module explained and implemented based on the RMT. By incorporating the variance stabilizing approach, the denoising method can deal with low signal-to-noise ratio (SNR) (such as <5) magnitude fMRI data with favorable performance compared to other state-of-the-art methods. Results from both simulation and in-vivo high-resolution fMRI data show that the proposed denoising method dramatically improves image restoration quality, promoting functional sensitivity at the same level of functional mapping blurring compared to existing denoising methods. Moreover, the denoising method can serve as a drop-in step in data preprocessing pipelines along with other procedures aimed at removal of structured physiological noises. We expect that the proposed denoising method will play an important role in leveraging high-quality, high-resolution task fMRI, which is desirable in many neuroscience and clinical applications.

Denoising diffusion weighted imaging data using convolutional neural networks

Diffusion weighted imaging (DWI) with multiple, high b-values is critical for extracting tissue microstructure measurements; however, high b-value DWI images contain high noise levels that can overwhelm the signal of interest and bias microstructural measurements. Here, we propose a simple denoising method that can be applied to any dataset, provided a low-noise, single-subject dataset is acquired using the same DWI sequence. The denoising method uses a one-dimensional convolutional neural network (1D-CNN) and deep learning to learn from a low-noise dataset, voxel-by-voxel. The trained model can then be applied to high-noise datasets from other subjects. We validated the 1D-CNN denoising method by first demonstrating that 1D-CNN denoising resulted in DWI images that were more similar to the noise-free ground truth than comparable denoising methods, e.g., MP-PCA, using simulated DWI data. Using the same DWI acquisition but reconstructed with two common reconstruction methods, i.e. SENSE1 and sum-of-square, to generate a pair of low-noise and high-noise datasets, we then demonstrated that 1D-CNN denoising of high-noise DWI data collected from human subjects showed promising results in three domains: DWI images, diffusion metrics, and tractography. In particular, the denoised images were very similar to a low-noise reference image of that subject, more than the similarity between repeated low-noise images (i.e. computational reproducibility). Finally, we demonstrated the use of the 1D-CNN method in two practical examples to reduce noise from parallel imaging and simultaneous multi-slice acquisition. We conclude that the 1D-CNN denoising method is a simple, effective denoising method for DWI images that overcomes some of the limitations of current state-of-the-art denoising methods, such as the need for a large number of training subjects and the need to account for the rectified noise floor.

What's new and what's next in diffusion MRI preprocessing

Diffusion MRI (dMRI) provides invaluable information for the study of tissue microstructure and brain connectivity, but suffers from a range of imaging artifacts that greatly challenge the analysis of results and their interpretability if not appropriately accounted for. This review will cover dMRI artifacts and preprocessing steps, some of which have not typically been considered in existing pipelines or reviews, or have only gained attention in recent years: brain/skull extraction, B-matrix incompatibilities w.r.t the imaging data, signal drift, Gibbs ringing, noise distribution bias, denoising, between- and within-volumes motion, eddy currents, outliers, susceptibility distortions, EPI Nyquist ghosts, gradient deviations, B1 bias fields, and spatial normalization. The focus will be on "what's new" since the notable advances prior to and brought by the Human Connectome Project (HCP), as presented in the predecessing issue on "Mapping the Connectome" in 2013. In addition to the development of novel strategies for dMRI preprocessing, exciting progress has been made in the availability of open source tools and reproducible pipelines, databases and simulation tools for the evaluation of preprocessing steps, and automated quality control frameworks, amongst others. Finally, this review will consider practical considerations and our view on "what's next" in dMRI preprocessing.

Axonal T2 estimation using the spherical variance of the strongly diffusion-weighted MRI signal

In magnetic resonance imaging, the application of a strong diffusion weighting suppresses the signal contributions from the less diffusion-restricted constituents of the brain's white matter, thus enabling the estimation of the transverse relaxation time T₂ that arises from the more diffusion-restricted constituents such as the axons. However, the presence of cell nuclei and vacuoles can confound the estimation of the axonal T₂, as diffusion within those structures is also restricted, causing the corresponding signal to survive the strong diffusion weighting. We devise an estimator of the axonal T₂ based on the directional spherical variance of the strongly diffusion-weighted signal. The spherical variance T₂ estimates are insensitive to the presence of isotropic contributions to the signal like those provided by cell nuclei and vacuoles. We show that with a strong diffusion weighting these estimates differ from those obtained using the directional spherical mean of the signal which contains both axonal and isotropically-restricted contributions. Our findings hint at the presence of an MRI-visible isotropically-restricted contribution to the signal in the white matter ex vivo fixed tissue (monkey) at 7T, and do not allow us to discard such a possibility also for in vivo human data collected with a clinical 3T system.

Noise Mapping and Removal in Complex-Valued Multi-Channel MRI via Optimal Shrinkage of Singular Values

In magnetic resonance imaging (MRI), noise is a limiting factor for higher spatial resolution and a major cause of prolonged scan time, owing to the need for repeated scans. Improving the signal-to-noise ratio is therefore key to faster and higher-resolution MRI. Here we propose a method for mapping and reducing noise in MRI by leveraging the inherent redundancy in complex-valued multi-channel MRI data. Our method leverages a provably optimal strategy for shrinking the singular values of a data matrix, allowing it to outperform state-of-the-art methods such as Marchenko-Pastur PCA in noise reduction. Our method reduces the noise floor in brain diffusion MRI by 5-fold and remarkably improves the contrast of spiral lung ¹⁹F MRI. Our framework is fast and does not require training and hyper-parameter tuning, therefore providing a convenient means for improving SNR in MRI.

[A diffusion-weighted image denoising algorithm using HOSVD combined with Rician noise corrected model]

OBJECTIVE

To propose a novel diffusion-weighted (DW) image denoising algorithm based on HOSVD to improve the signal-to-noise ratio (SNR) of DW images and the accuracy of subsequent quantization parameters.

METHODS

This HOSVDbased denoising method incorporated the sparse constraint and noise-correction model. The signal expectations with Rician noise were integrated into the traditional HOSVD denoising framework for direct denoising of the DW images with Rician noise. HOSVD denoising was performed directly on each local DW image block to avoid the stripe artifacts. We compared the proposed method with 4 image denoising algorithms (LR + Edge, GL-HOSVD, BM3D and NLM) to verify the effect of the proposed method.

RESULTS

The experimental results showed that the proposed method effectively reduced the noise of DW images while preserving the image details and edge structure information. The proposed algorithm was significantly better than LR +Edge, BM3D and NLM in terms of quantitative metrics of PSNR, SSIM and FA-RMSE and in visual evaluation of denoising images and FA images. GL-HOSVD obtained good denoising results but introduced stripe artifacts at a high noise level during the denoising process. In contrast, the proposed method achieved good denoising results without causing stripe artifacts.

CONCLUSION

This HOSVD-based denoising method allows direct processing of DW images with Rician noise without introducing artifacts and can provide accurate quantitative parameters for diagnostic purposes.

ULTRAHIGH FIELD and ULTRAHIGH RESOLUTION fMRI

Functional magnetic resonance imaging (fMRI) has become one of the most powerful tools for investigating the human brain. Ultrahigh magnetic field (UHF) of 7 Tesla has played a critical role in enabling higher resolution and more accurate (relative to the neuronal activity) functional maps. However, even with these gains, the fMRI approach is challenged relative to the spatial scale over which brain function is organized. Therefore, going forward, significant advances in fMRI are still needed. Such advances will predominantly come from magnetic fields significantly higher than 7 Tesla, which is the most commonly used UHF platform today, and additional technologies that will include developments in pulse sequences, image reconstruction, noise suppression, and image analysis in order to further enhance and augment the gains than can be realized by going to higher magnetic fields.

NOise reduction with DIstribution Corrected (NORDIC) PCA in dMRI with complex-valued parameter-free locally low-rank processing

Diffusion-weighted magnetic resonance imaging (dMRI) has found great utility for a wide range of neuroscientific and clinical applications. However, high-resolution dMRI, which is required for improved delineation of fine brain structures and connectomics, is hampered by its low signal-to-noise ratio (SNR). Since dMRI relies on the acquisition of multiple different diffusion weighted images of the same anatomy, it is well-suited for denoising methods that utilize correlations across the image series to improve the apparent SNR and the subsequent data analysis. In this work, we introduce and quantitatively evaluate a comprehensive framework, NOise Reduction with DIstribution Corrected (NORDIC) PCA method for processing dMRI. NORDIC uses low-rank modeling of g-factor-corrected complex dMRI reconstruction and non-asymptotic random matrix distributions to remove signal components which cannot be distinguished from thermal noise. The utility of the proposed framework for denoising dMRI is demonstrated on both simulations and experimental data obtained at 3 Tesla with different resolutions using human connectome project style acquisitions. The proposed framework leads to substantially enhanced quantitative performance for estimating diffusion tractography related measures and for resolving crossing fibers as compared to a conventional/state-of-the-art dMRI denoising method.