Denoise diffusion-weighted images using higher-order singular value decomposition

Denoising complex-valued diffusion MR images using a two-step, nonlocal principal component analysis approach

PURPOSE

To propose a two-step, nonlocal principal component analysis (PCA) method and demonstrate its utility for denoising complex diffusion MR images with a few diffusion directions.

METHODS

A two-step denoising pipeline was implemented to ensure accurate patch selection even with high noise levels and was coupled with data preprocessing for g-factor normalization and phase stabilization before data denoising with a nonlocal PCA algorithm. At the heart of our proposed pipeline was the use of a data-driven optimal shrinkage algorithm to manipulate the singular values in a way that would optimally estimate the noise-free signal. Our approach's denoising performances were evaluated using simulation and in vivo human data experiments. The results were compared with those obtained with existing local PCA-based methods.

RESULTS

In both simulation and human data experiments, our approach substantially enhanced image quality relative to the noisy counterpart, yielding improved performances for estimation of relevant diffusion tensor imaging metrics. It also outperformed existing local PCA-based methods in reducing noise while preserving anatomic details. It also led to improved whole-brain tractography relative to the noisy counterpart.

CONCLUSION

The proposed denoising method has the utility for improving image quality for diffusion MRI with a few diffusion directions and is believed to benefit many applications, especially those aiming to achieve high-quality parametric mapping using only a few image volumes.

Navigator-free multi-shot diffusion MRI via non-local low-rank reconstruction

PURPOSE

To develop a non-local low-rank (NLLR) reconstruction method for multi-shot EPI (ms-EPI) in DWI, addressing phase inconsistencies and noise issues while maintaining high spatial resolution in clinically feasible scan times.

THEORY AND METHODS

Single-shot EPI (ss-EPI) is widely used for DWI but suffers from geometric distortions and T2* blurring. ms-EPI improves spatial resolution but introduces shot-to-shot phase variations requiring correction strategies. Traditional navigator-based approaches may increase acquisition time. Recent low-rank regularization reconstruction techniques, such as locally low-rank (LLR) methods, can estimate the phase errors but rely strictly on local neighborhood information along the shot dimension. The proposed NLLR method extends this framework by leveraging non-local patch matching by grouping similar image patches across spatially distant image locations, enhancing non-local redundancy exploitation for improved phase estimation and correction as well as noise suppression. The method was validated in simulations and in vivo experiments and compared to existing post-processing denoising and navigator-free approaches.

RESULTS

In simulation experiments, compared to post-processing denoising algorithms, NLLR demonstrated superior noise suppression and structural preservation across all metrics, even when reconstructing from a single diffusion direction. In the in-vivo experiments, NLLR outperformed conventional navigator-free approaches particularly regarding noise suppression. Fractional anisotropy maps reconstructed using NLLR exhibited improved visualization of fine structures with improved SNR, with performance differences becoming more pronounced at higher resolutions.

CONCLUSION

The proposed NLLR approach provides an efficient and good solution for high-resolution DWI reconstruction, improving image quality while mitigating phase variations and noise.

New method for diffusion-weighted images denoising based on patch-matching with higher-order singular value decomposition

BackgroundDiffusion-weighted imaging (DWI) is an important technique to study brain microstructure. However, diffusion-weighted (DW) images suffer from severe low signal-to-noise ratio (SNR) problem, affecting subsequent diffusion analysis.ObjectiveThe goal of this paper is to develop advanced DWI denoising technique to effectively reduce noise while improving the accuracy and reliability of subsequent diffusion model fitting and diffusion analysis, thereby facilitating the research and analysis of brain science.MethodsWe propose a new method for denoising DW images based on patch-matching with higher-order singular value decomposition (HOSVD) by combined with the variance-stabilizing transformation technique. It starts with introducing a novel non-local mean algorithm as a prefiltering stage, and then denoises the noisy data using a local HOSVD algorithm based on the HOSVD bases learned from prefiltered images.ResultsExperiments are performed on simulation, HCP and in vivo brain DWI datasets. Results show that the proposed method significantly reduces spatially invariant and variant noise, improving the most reliable diffusion analysis compared with the different denoising methods.ConclusionsThe proposed method achieves state-of-the-art performance which can improve image quality and enable accurate diffusion analysis.

MRI at low field: A review of software solutions for improving SNR

Low magnetic field magnetic resonance imaging (MRI) (B 0 $$ {B}_0 $$  < 1 T) is regaining interest in the magnetic resonance (MR) community as a complementary, more flexible, and cost-effective approach to MRI diagnosis. Yet, the impaired signal-to-noise ratio (SNR) per square root of time, or SNR efficiency, leading in turn to prolonged acquisition times, still challenges its relevance at the clinical level. To address this, researchers investigate various hardware and software solutions to improve SNR efficiency at low field, including the leveraging of latest advances in computing hardware. However, there may not be a single recipe for improving SNR at low field, and it is key to embrace the challenges and limitations of each proposed solution. In other words, suitable solutions depend on the final objective or application envisioned for a low-field scanner and, more importantly, on the characteristics of a specific lowB 0 $$ {B}_0 $$ field. In this review, we aim to provide an overview on software solutions to improve SNR efficiency at low field. First, we cover techniques for efficient k-space sampling and reconstruction. Then, we present post-acquisition techniques that enhance MR images such as denoising and super-resolution. In addition, we summarize recently introduced electromagnetic interference cancellation approaches showing great promises when operating in shielding-free environments. Finally, we discuss the advantages and limitations of these approaches that could provide directions for future applications.

Spherical Harmonics-Based Deep Learning Achieves Generalized and Accurate Diffusion Tensor Imaging

Diffusion tensor imaging (DTI) is a prevalent magnetic resonance imaging (MRI) technique, widely used in clinical and neuroscience research. However, the reliability of DTI is affected by the low signal-to-noise ratio inherent in diffusion-weighted (DW) images. Deep learning (DL) has shown promise in improving the quality of DTI, but its limited generalization to variable acquisition schemes hinders practical applications. This study aims to develop a generalized, accurate, and efficient DL-based DTI method. By leveraging the representation of voxel-wise diffusion MRI (dMRI) signals on the sphere using spherical harmonics (SH), we propose a novel approach that utilizes SH coefficient maps as input to a network for predicting the diffusion tensor (DT) field, enabling improved generalization. Extensive experiments were conducted on simulated and in-vivo datasets, covering various DTI application scenarios. The results demonstrate that the proposed SH-DTI method achieves advanced performance in both quantitative and qualitative analyses of DTI. Moreover, it exhibits remarkable generalization capabilities across different acquisition schemes, centers, and scanners, ensuring its broad applicability in diverse settings.

Improved Diffusion-Weighted Hyperpolarized 129Xe Lung MRI with Patch-Based Higher-Order, Singular Value Decomposition Denoising

RATIONALE AND OBJECTIVES

Hyperpolarized xenon (129Xe) MRI is a noninvasive method to assess pulmonary structure and function. To measure lung microstructure, diffusion-weighted imaging-commonly the apparent diffusion coefficient (ADC)-can be employed to map changes in alveolar-airspace size resulting from normal aging and pulmonary disease. However, low signal-to-noise ratio (SNR) decreases ADC measurement certainty, and biases ADC to spuriously low values. Further, these challenges are most severe in regions of the lung where alveolar simplification or emphysematous remodeling generate abnormally high ADCs. Here, we apply Global Local Higher Order Singular Value Decomposition (GLHOSVD) denoising to enhance image SNR, thereby reducing uncertainty and bias in diffusion measurements.

MATERIALS AND METHODS

GLHOSVD denoising was employed in simulated images and gas phantoms with known diffusion coefficients to validate its effectiveness and optimize parameters for analysis of diffusion-weighted 129Xe MRI. GLHOSVD was applied to data from 120 subjects (34 control, 39 cystic fibrosis (CF), 27 lymphangioleiomyomatosis (LAM), and 20 asthma). Image SNR, ADC, and distributed diffusivity coefficient (DDC) were compared before and after denoising using Wilcoxon signed-rank analysis for all images.

RESULTS

Denoising significantly increased SNR in simulated, phantom, and in-vivo images, showing a greater than 2-fold increase (p < 0.001) across diffusion-weighted images. Although mean ADC and DDC remained unchanged (p > 0.05), ADC and DDC standard deviation decreased significantly in denoised images (p < 0.001).

CONCLUSION

When applied to diffusion-weighted 129Xe images, GLHOSVD improved image quality and allowed airspace size to be quantified in high-diffusion regions of the lungs that were previously inaccessible to measurement due to prohibitively low SNR, thus providing insights into disease pathology.

Denoising complex-valued diffusion MR images using a two-step non-local principal component analysis approach

Purpose

to propose a two-step non-local principal component analysis (PCA) method and demonstrate its utility for denoising diffusion tensor MRI (DTI) with a few diffusion directions.

Methods

A two-step denoising pipeline was implemented to ensure accurate patch selection even with high noise levels and was coupled with data preprocessing for g-factor normalization and phase stabilization before data denoising with a non-local PCA algorithm. At the heart of our proposed pipeline was the use of a data-driven optimal shrinkage algorithm to manipulate the singular values in a way that would optimally estimate the noise-free signal. Our approach's denoising performances were evaluated using simulation and in-vivo human data experiments. The results were compared to those obtained with existing local-PCA-based methods.

Results

In both simulation and human data experiments, our approach substantially enhanced image quality relative to the noisy counterpart, yielding improved performances for estimation of relevant DTI metrics. It also outperformed existing local-PCA-based methods in reducing noise while preserving anatomic details. It also led to improved whole-brain tractography relative to the noisy counterpart.

Conclusion

The proposed denoising method has the utility for improving image quality for DTI with reduced diffusion directions and is believed to benefit many applications especially those aiming to achieve quality parametric mapping using only a few image volumes.

Tensor Methods in Biomedical Image Analysis

In the past decade, tensors have become increasingly attractive in different aspects of signal and image processing areas. The main reason is the inefficiency of matrices in representing and analyzing multimodal and multidimensional datasets. Matrices cannot preserve the multidimensional correlation of elements in higher-order datasets and this highly reduces the effectiveness of matrix-based approaches in analyzing multidimensional datasets. Besides this, tensor-based approaches have demonstrated promising performances. These together, encouraged researchers to move from matrices to tensors. Among different signal and image processing applications, analyzing biomedical signals and images is of particular importance. This is due to the need for extracting accurate information from biomedical datasets which directly affects patient's health. In addition, in many cases, several datasets have been recorded simultaneously from a patient. A common example is recording electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) of a patient with schizophrenia. In such a situation, tensors seem to be among the most effective methods for the simultaneous exploitation of two (or more) datasets. Therefore, several tensor-based methods have been developed for analyzing biomedical datasets. Considering this reality, in this paper, we aim to have a comprehensive review on tensor-based methods in biomedical image analysis. The presented study and classification between different methods and applications can show the importance of tensors in biomedical image enhancement and open new ways for future studies.

Hyperpolarized 13 C metabolic imaging of the human abdomen with spatiotemporal denoising

PURPOSE

Improving the quality and maintaining the fidelity of large coverage abdominal hyperpolarized (HP) 13 C MRI studies with a patch based global-local higher-order singular value decomposition (GL-HOVSD) spatiotemporal denoising approach.

METHODS

Denoising performance was first evaluated using the simulated [1-13 C]pyruvate dynamics at different noise levels to determine optimal kglobal and klocal parameters. The GL-HOSVD spatiotemporal denoising method with the optimized parameters was then applied to two HP [1-13 C]pyruvate EPI abdominal human cohorts (n = 7 healthy volunteers and n = 8 pancreatic cancer patients).

RESULTS

The parameterization of kglobal  = 0.2 and klocal  = 0.9 denoises abdominal HP data while retaining image fidelity when evaluated by RMSE. The kPX (conversion rate of pyruvate-to-metabolite, X = lactate or alanine) difference was shown to be <20% with respect to ground-truth metabolic conversion rates when there is adequate SNR (SNRAUC  > 5) for downstream metabolites. In both human cohorts, there was a greater than nine-fold gain in peak [1-13 C]pyruvate, [1-13 C]lactate, and [1-13 C]alanine apparent SNRAUC . The improvement in metabolite SNR enabled a more robust quantification of kPL and kPA . After denoising, we observed a 2.1 ± 0.4 and 4.8 ± 2.5-fold increase in the number of voxels reliably fit across abdominal FOVs for kPL and kPA quantification maps.

CONCLUSION

Spatiotemporal denoising greatly improves visualization of low SNR metabolites particularly [1-13 C]alanine and quantification of [1-13 C]pyruvate metabolism in large FOV HP 13 C MRI studies of the human abdomen.

Brain fiber structure estimation based on principal component analysis and RINLM filter

Diffusion magnetic resonance imaging is a technique for non-invasive detection of microstructure in the white matter of the human brain, which is widely used in neuroscience research of the brain. However, diffusion-weighted images(DWI) are sensitive to noise, which affects the subsequent reconstruction of fiber orientation direction, microstructural parameter estimation and fiber tracking. In order to better eliminate the noise in diffusion-weighted images, this study proposes a noise reduction method combining Marchenko-Pastur principal component analysis(MPPCA) and rotation-invariant non-local means filter(RINLM) to further remove residual noise and preserve the image texture detail information. In this study, the algorithm is applied to the fiber structure and the prevailing microstructural models within the human brain voxels based on simulated and real human brain datasets. Experimental comparisons between the proposed method and the state-of-the-art methods are performed in single-fiber, multi-fiber, crossed and curved-fiber regions as well as in different microstructure estimation models. Results demonstrated the superior performance of the proposed method in denoising DWI data, which can reduce the angular error in fiber orientation reconstruction to obtain more valid fiber structure estimation and enable more complete fiber tracking trajectories with higher coverage. Meanwhile, the method reduces the estimation errors of various white matter microstructural parameters and verifies the performance of the method in white matter microstructure estimation.

Boosting quantification accuracy of chemical exchange saturation transfer MRI with a spatial-spectral redundancy-based denoising method

Chemical exchange saturation transfer (CEST) is a versatile technique that enables noninvasive detections of endogenous metabolites present in low concentrations in living tissue. However, CEST imaging suffers from an inherently low signal-to-noise ratio (SNR) due to the decreased water signal caused by the transfer of saturated spins. This limitation challenges the accuracy and reliability of quantification in CEST imaging. In this study, a novel spatial-spectral denoising method, called BOOST (suBspace denoising with nOnlocal lOw-rank constraint and Spectral local-smooThness regularization), was proposed to enhance the SNR of CEST images and boost quantification accuracy. More precisely, our method initially decomposes the noisy CEST images into a low-dimensional subspace by leveraging the global spectral low-rank prior. Subsequently, a spatial nonlocal self-similarity prior is applied to the subspace-based images. Simultaneously, the spectral local-smoothness property of Z-spectra is incorporated by imposing a weighted spectral total variation constraint. The efficiency and robustness of BOOST were validated in various scenarios, including numerical simulations and preclinical and clinical conditions, spanning magnetic field strengths from 3.0 to 11.7 T. The results demonstrated that BOOST outperforms state-of-the-art algorithms in terms of noise elimination. As a cost-effective and widely available post-processing method, BOOST can be easily integrated into existing CEST protocols, consequently promoting accuracy and reliability in detecting subtle CEST effects.

A user independent denoising method for x-nuclei MRI and MRS

PURPOSE

X-nuclei (also called non-proton MRI) MRI and spectroscopy are limited by the intrinsic low SNR as compared to conventional proton imaging. Clinical translation of x-nuclei examination warrants the need of a robust and versatile tool improving image quality for diagnostic use. In this work, we compare a novel denoising method with fewer inputs to the current state-of-the-art denoising method.

METHODS

Denoising approaches were compared on human acquisitions of sodium (23 Na) brain, deuterium (2 H) brain, carbon (13 C) heart and brain, and simulated dynamic hyperpolarized 13 C brain scans, with and without additional noise. The current state-of-the-art denoising method Global-local higher order singular value decomposition (GL-HOSVD) was compared to the few-input method tensor Marchenko-Pastur principal component analysis (tMPPCA). Noise-removal was quantified by residual distributions, and statistical analyses evaluated the differences in mean-square-error and Bland-Altman analysis to quantify agreement between original and denoised results of noise-added data.

RESULTS

GL-HOSVD and tMPPCA showed similar performance for the variety of x-nuclei data analyzed in this work, with tMPPCA removing ˜5% more noise on average over GL-HOSVD. The mean ratio between noise-added and denoising reproducibility coefficients of the Bland-Altman analysis when compared to the original are also similar for the two methods with 3.09 ± 1.03 and 2.83 ± 0.79 for GL-HOSVD and tMPPCA, respectively.

CONCLUSION

The strength of tMPPCA lies in the few-input approach, which generalizes well to different data sources. This makes the use of tMPPCA denoising a robust and versatile tool in x-nuclei imaging improvements and the preferred denoising method.

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.

Denoise ultra-low-field 3D magnetic resonance images using a joint signal-image domain filter

Ultra-low-field magnetic resonance imaging (MRI) could suffer from heavy uncorrelated noise, and its removal could be a critical post-processing task. As a primary source of interference, Gaussian noise could corrupt the sampled MR signal (k-space data), especially at lower B₀ field strength. For this reason, we consider both signal and image domains by proposing a new joint filter characterized by a Kalman filter with linear prediction and a nonlocal mean filter with higher-order singular value decomposition (HOSVD) for denoising 3D MR data. The Kalman filter first attenuates the noise in k-space, and then its reconstruction images are used to guide HOSVD denoising process with exploring self-similarity among 3D structures. The clearer prefiltered images could also generate improved HOSVD learned bases used to transform the noise corrupted patch groups in the original MR data. The flexibility of proposed method is also demonstrated by integrating other k-space filters into the algorithm scheme. Experimental data includes simulated MR images with the varying noise level and real MR images obtained from our 50 mT MRI scanner. The results reveal that our method has a better noise-removal ability and introduces lesser unexpected artifacts than other related MRI denoising approaches.

SENSE EPI reconstruction with 2D phase error correction and channel-wise noise removal

PURPOSE

To develop a robust reconstruction pipeline for EPI data that enables 2D Nyquist phase error correction using sensitivity encoding without incurring major noise artifacts in low SNR data.

METHODS

SENSE with 2D phase error correction (PEC-SENSE) was combined with channel-wise noise removal using Marcenko-Pastur principal component analysis (MPPCA) to simultaneously eliminate Nyquist ghost artifacts in EPI data and mitigate the noise amplification associated with phase correction using parallel imaging. The proposed pipeline (coined SPECTRE) was validated in phantom DW-EPI data using the accuracy and precision of diffusion metrics; ground truth values were obtained from data acquired with a spin echo readout. Results from the SPECTRE pipeline were compared against PEC-SENSE reconstructions with three alternate denoising strategies: (i) no denoising; (ii) denoising of magnitude data after image formation; (iii) denoising of complex data after image formation. SPECTRE was then tested using highb $$ b $$ -value (i.e., low SNR) diffusion data (up tob = 3000 $$ b=3000 $$  s/mm2 $$ {}^2 $$ ) in four healthy subjects.

RESULTS

Noise amplification associated with phase error correction incurred a 23% bias in phantom mean diffusivity (MD) measurements. Phantom MD estimates using the SPECTRE pipeline were within 8% of the ground truth value. In healthy volunteers, the SPECTRE pipeline visibly corrected Nyquist ghost artifacts and reduced associated noise amplification in highb $$ b $$ -value data.

CONCLUSION

The proposed reconstruction pipeline is effective in correcting low SNR data, and improves the accuracy and precision of derived diffusion metrics.

Assessment of higher-order singular value decomposition denoising methods on dynamic hyperpolarized [1-13C]pyruvate MRI data from patients with glioma

BACKGROUND

Real-time metabolic conversion of intravenously-injected hyperpolarized [1-13C]pyruvate to [1-13C]lactate and [13C]bicarbonate in the brain can be measured using dynamic hyperpolarized carbon-13 (HP-13C) MRI. However, voxel-wise evaluation of metabolism in patients with glioma is challenged by the limited signal-to-noise ratio (SNR) of downstream 13C metabolites, especially within lesions. The purpose of this study was to evaluate the ability of higher-order singular value decomposition (HOSVD) denoising methods to enhance dynamic HP [1-13C]pyruvate MRI data acquired from patients with glioma.

METHODS

Dynamic HP-13C MRI were acquired from 14 patients with glioma. The effects of two HOSVD denoising techniques, tensor rank truncation-image enhancement (TRI) and global-local HOSVD (GL-HOSVD), on the SNR and kinetic modeling were analyzed in [1-13C]lactate data with simulated noise that matched the levels of [13C]bicarbonate signals. Both methods were then evaluated in patient data based on their ability to improve [1-13C]pyruvate, [1-13C]lactate and [13C]bicarbonate SNR. The effects of denoising on voxel-wise kinetic modeling of kPL and kPB was also evaluated. The number of voxels with reliable kinetic modeling of pyruvate-to-lactate (kPL) and pyruvate-to-bicarbonate (kPB) conversion rates within regions of interest (ROIs) before and after denoising was then compared.

RESULTS

Both denoising methods improved metabolite SNR and regional signal coverage. In patient data, the average increase in peak dynamic metabolite SNR was 2-fold using TRI and 4-5 folds using GL-HOSVD denoising compared to acquired data. Denoising reduced kPL modeling errors from a native average of 23% to 16% (TRI) and 15% (GL-HOSVD); and kPB error from 42% to 34% (TRI) and 37% (GL-HOSVD) (values were averaged voxelwise over all datasets). In contrast-enhancing lesions, the average number of voxels demonstrating within-tolerance kPL modeling error relative to the total voxels increased from 48% in the original data to 84% (TRI) and 90% (GL-HOSVD), while the number of voxels showing within-tolerance kPB modeling error increased from 0% to 15% (TRI) and 8% (GL-HOSVD).

CONCLUSION

Post-processing denoising methods significantly improved the SNR of dynamic HP-13C imaging data, resulting in a greater number of voxels satisfying minimum SNR criteria and maximum kinetic modeling errors in tumor lesions. This enhancement can aid in the voxel-wise analysis of HP-13C data and thereby improve monitoring of metabolic changes in patients with glioma following treatment.

Deep Learning-Based Diffusion-Weighted Magnetic Resonance Imaging in the Diagnosis of Ischemic Penumbra in Early Cerebral Infarction

The prefiltered image was imported into the local higher-order singular value decomposition (HOSVD) denoising algorithm (GL-HOSVD)-optimized diffusion-weighted imaging (DWI) image, which was compared with the deviation correction nonlocal mean (NL mean) and low-level edge algorithm (LR + edge). Regarding the peak signal-to-noise ratio (PSNR), root mean square error (RMSE), sensitivity, specificity, accuracy, and consistency, the application effect of the GL-HOSVD algorithm in DWI was investigated, and its adoption effect in the examination of ischemic penumbra (IP) of early acute cerebral infarction (ACI) patients was evaluated. A total of 210 patients with ACI were selected as the research subjects, who were randomly rolled into two groups. Those who were checked by conventional DWI were set as the control group, and those who used DWI based on the GL-HOSVD denoising algorithm were set as the observation group, with 105 people in each. Positron emission tomography (PET) test results were set as the gold standard to evaluate the application value of the two examination methods. It was found that under different noise levels, the peak signal-to-noise ratio (PSNR) of the GL-HOSVD algorithm and the root mean square error (RMSE) of the FA parameter were better than those of the nonlocal means (NL-means) of deviation correction and low-rank edge algorithm (LR + edge). The sensitivity, specificity, accuracy, and consistency (8.76%, 81.25%, 87.62%, and 0.52) of the observation group were higher than those of the control group (57.78%, 53.33%, 57.14%, and 0.35) (P < 0.05). Moreover, the apparent diffusion coefficient (ADC) of the DWI images of the observation group was basically consistent with that of the PET images, while the control group had a poor display effect and low definition. In summary, under different noise levels, the GL-HOSVD algorithm had a good denoising effect and greatly reduced fringe artifacts. DWI after denoising had high sensitivity, specificity, accuracy, and consistency in the detection of IP, which was worthy of clinical application and promotion.

[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.

Denoising of hyperpolarized 13 C MR images of the human brain using patch-based higher-order singular value decomposition

PURPOSE

To improve hyperpolarized ¹³ C (HP-¹³ C) MRI by image denoising with a new approach, patch-based higher-order singular value decomposition (HOSVD).

METHODS

The benefit of using a patch-based HOSVD method to denoise dynamic HP-¹³ C MR imaging data was investigated. Image quality and the accuracy of quantitative analyses following denoising were evaluated first using simulated data of [1-¹³ C]pyruvate and its metabolic product, [1-¹³ C]lactate, and compared the results to a global HOSVD method. The patch-based HOSVD method was then applied to healthy volunteer HP [1-¹³ C]pyruvate EPI studies. Voxel-wise kinetic modeling was performed on both non-denoised and denoised data to compare the number of voxels quantifiable based on SNR criteria and fitting error.

RESULTS

Simulation results demonstrated an 8-fold increase in the calculated SNR of [1-¹³ C]pyruvate and [1-¹³ C]lactate with the patch-based HOSVD denoising. The voxel-wise quantification of k_PL (pyruvate-to-lactate conversion rate) showed a 9-fold decrease in standard errors for the fitted k_PL after denoising. The patch-based denoising performed superior to the global denoising in recovering k_PL information. In volunteer data sets, [1-¹³ C]lactate and [¹³ C]bicarbonate signals became distinguishable from noise across captured time points with over a 5-fold apparent SNR gain. This resulted in >3-fold increase in the number of voxels quantifiable for mapping k_PB (pyruvate-to-bicarbonate conversion rate) and whole brain coverage for mapping k_PL .

CONCLUSIONS

Sensitivity enhancement provided by this denoising significantly improved quantification of metabolite dynamics and could benefit future studies by improving image quality, enabling higher spatial resolution, and facilitating the extraction of metabolic information for clinical research.

Quality of Prostate MRI: Is the PI-RADS Standard Sufficient?

RATIONALE AND OBJECTIVE

The Prostate Imaging Reporting and Data System version 2 (PI-RADSv2) published a set of minimum technical standards (MTS) to improve image quality and reduce variability in multiparametric prostate MRI. The effect of PIRADSv2 MTS on image quality has not been validated. We aimed to determine whether adherence to PI-RADSv2 MTS improves study adequacy and perceived quality.

MATERIALS AND METHODS

Sixty-two prostate MRI examinations including T2 weighted (T2W) and diffusion weighted image (DWI) consecutively referred to our center from 62 different institutions within a 12-month period (September 2017 to September 2018) were included. Six readers assessed images as adequate or inadequate for use in PCa detection and a numerical image quality ranking was given using a 1-5 scale. The PI-RADSv2 MTS were synthesized into sets of seven and 10 rules for T2W and DWI, respectively. Image adherence was assessed using Digital Imaging and Communications in Medicine (DICOM) metadata. Statistical analysis of survey results and image adherence was performed based on reader quality scoring (Kendall Rank tau-b) and reader adequate scoring (Wilcoxon test for association) for T2 and DWI quality assessment.

RESULTS

Out of 62 images, 52 (83%) T2W and 38 (61%) DWIs were rated to be adequate by a majority of readers. Reader adequacy scores showed no significant association with adherence to PI-RADSv2. There was a weak (tau-b = 0.22) but significant (p value = 0.01) correlation between adherence to PIRADSv2 MTS and image quality for T2W. Studies following all PI-RADSv2 T2W rules achieved a higher median average quality score (3.58 for 7/7 vs. 3.0 for <7/7, p = 0.012). No statistical relationship with PI-RADSv2 MTS adherence and DWI quality was found.

CONCLUSION

Among 62 sites performing prostate MRI, few were considered of high quality, but the majority were considered adequate. DWI showed considerably lower rates of adequate studies in the sample. Adherence to PI-RADSv2 MTS did not increase the likelihood of having a qualitatively adequate T2W or DWI.

Tensor image enhancement and optimal multichannel receiver combination analyses for human hyperpolarized 13 C MRSI

PURPOSE

With the initiation of human hyperpolarized ¹³ C (HP-¹³ C) trials at multiple sites and the development of improved acquisition methods, there is an imminent need to maximally extract diagnostic information to facilitate clinical interpretation. This study aims to improve human HP-¹³ C MR spectroscopic imaging through means of Tensor Rank truncation-Image enhancement (TRI) and optimal receiver combination (ORC).

METHODS

A data-driven processing framework for dynamic HP ¹³ C MR spectroscopic imaging (MRSI) was developed. Using patient data sets acquired with both multichannel arrays and single-element receivers from the brain, abdomen, and pelvis, we examined the theory and application of TRI, as well as 2 ORC techniques: whitened singular value decomposition (WSVD) and first-point phasing. Optimal conditions for TRI were derived based on bias-variance trade-off.

RESULTS

TRI and ORC techniques together provided a 63-fold mean apparent signal-to-noise ratio (aSNR) gain for receiver arrays and a 31-fold gain for single-element configurations, which particularly improved quantification of the lower-SNR-[¹³ C]bicarbonate and [1-¹³ C]alanine signals that were otherwise not detectable in many cases. Substantial SNR enhancements were observed for data sets that were acquired even with suboptimal experimental conditions, including delayed (114 s) injection (8× aSNR gain solely by TRI), or from challenging anatomy or geometry, as in the case of a pediatric patient with brainstem tumor (597× using combined TRI and WSVD). Improved correlation between elevated pyruvate-to-lactate conversion, biopsy-confirmed cancer, and mp-MRI lesions demonstrated that TRI recovered quantitative diagnostic information.

CONCLUSION

Overall, this combined approach was effective across imaging targets and receiver configurations and could greatly benefit ongoing and future HP ¹³ C MRI research through major aSNR improvements.

Calibrationless parallel imaging reconstruction for multislice MR data using low-rank tensor completion

PURPOSE

To provide joint calibrationless parallel imaging reconstruction of highly accelerated multislice 2D MR k-space data.

METHODS

Adjacent image slices in multislice MR data have similar coil sensitivity maps, spatial support, and image content. Such similarities can be utilized to improve image quality by reconstructing multiple slices jointly with low-rank tensor completion. Specifically, the multichannel k-space data from multiple slices are constructed into a block-wise Hankel tensor and iteratively updated by promoting tensor low-rankness through higher-order SVD. This multislice block-wise Hankel tensor completion was implemented for 2D spiral and Cartesian k-space undersampling where sampling patterns vary between adjacent slices. The approach was evaluated with human brain MR data and compared to the traditional single-slice simultaneous autocalibrating and k-space estimation reconstruction.

RESULTS

The proposed multislice block-wise Hankel tensor completion approach robustly reconstructed highly undersampled multislice 2D spiral and Cartesian data. It produced substantially lower level of artifacts compared to the traditional single-slice simultaneous autocalibrating and k-space estimation reconstruction. Quantitative evaluation using error maps and root mean square error demonstrated its significantly improved performance in terms of residual artifacts and root mean square error.

CONCLUSION

Our proposed multislice block-wise Hankel tensor completion method exploits the similar coil sensitivity and image content within multislice MR data through a tensor completion framework. It offers a new and effective approach to acquire and reconstruct highly undersampled multislice MR data in a calibrationless manner.

The impact of position-orientation adaptive smoothing in diffusion weighted imaging-From diffusion metrics to fiber tractography

In contrast to commonly used approaches to improve data quality in diffusion weighted imaging, position-orientation adaptive smoothing (POAS) provides an edge-preserving post-processing approach. This study aims to investigate its potential and effects on image quality, diffusion metrics, and fiber tractography of the corticospinal tract in relation to non-post-processed and averaged data. 22 healthy volunteers were included in this study. For each volunteer five clinically applicable diffusion weighted imaging data sets were acquired and post-processed by standard averaging and POAS. POAS post-processing led to significantly higher signal-to-noise-ratios (p < 0.001), lower fractional anisotropy across the whole brain (p < 0.05) and reduced intra-subject variability of diffusion weighted imaging signal intensity and fractional anisotropy (p < 0.001, p = 0.006). Fiber tractography of the corticospinal tract resulted in significantly (p = 0.027, p = 0.014) larger tract volumes while fiber density was the lowest. Similarity across tractography results was highest for POAS post-processed data (p < 0.001). POAS post-processing enhances image quality, decreases the intra-subject variability of signal intensity and fractional anisotropy, increases fiber tract volume of the corticospinal tract, and leads to higher reproducibility of tractography results. Thus, POAS post-processing supports a reliable and more accurate fiber tractography of the corticospinal tract, being mandatory for the clinical use.

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

Although shown to have a great utility for a wide range of neuroscientific and clinical applications, diffusion-weighted magnetic resonance imaging (dMRI) faces a major challenge of low signal-to-noise ratio (SNR), especially when pushing the spatial resolution for improved delineation of brain's fine structure or increasing the diffusion weighting for increased angular contrast or both. Here, we introduce a comprehensive denoising framework for denoising magnitude dMRI. The framework synergistically combines the variance stabilizing transform (VST) with optimal singular value manipulation. The purpose of VST is to transform the Rician data to Gaussian-like data so that an asymptotically optimal singular value manipulation strategy tailored for Gaussian data can be used. The output of the framework is the estimated underlying diffusion signal for each voxel in the image domain. The usefulness of the proposed framework for denoising magnitude dMRI is demonstrated using both simulation and real-data experiments. Our results show that the proposed denoising framework can significantly improve SNR across the entire brain, leading to substantially enhanced performances for estimating diffusion tensor related indices and for resolving crossing fibers when compared to another competing method. More encouragingly, the proposed method when used to denoise a single average of 7 ​Tesla Human Connectome Project-style diffusion acquisition provided comparable performances relative to those achievable with ten averages for resolving multiple fiber populations across the brain. As such, the proposed denoising method is expected to have a great utility for high-quality, high-resolution whole-brain dMRI, desirable for many neuroscientific and clinical applications.

Non-Local SVD Denoising of MRI Based on Sparse Representations

Magnetic Resonance (MR) Imaging is a diagnostic technique that produces noisy images, which must be filtered before processing to prevent diagnostic errors. However, filtering the noise while keeping fine details is a difficult task. This paper presents a method, based on sparse representations and singular value decomposition (SVD), for non-locally denoising MR images. The proposed method prevents blurring, artifacts, and residual noise. Our method is composed of three stages. The first stage divides the image into sub-volumes, to obtain its sparse representation, by using the KSVD algorithm. Then, the global influence of the dictionary atoms is computed to upgrade the dictionary and obtain a better reconstruction of the sub-volumes. In the second stage, based on the sparse representation, the noise-free sub-volume is estimated using a non-local approach and SVD. The noise-free voxel is reconstructed by aggregating the overlapped voxels according to the rarity of the sub-volumes it belongs, which is computed from the global influence of the atoms. The third stage repeats the process using a different sub-volume size for producing a new filtered image, which is averaged with the previously filtered images. The results provided show that our method outperforms several state-of-the-art methods in both simulated and real data.

An Improved Denoising Method for Partial Discharge Signals Contaminated by White Noise Based on Adaptive Short-Time Singular Value Decomposition

To extract partial discharge (PD) signals from white noise efficiently, this paper proposes a denoising method for PD signals, named adaptive short-time singular value decomposition (ASTSVD). First, a sliding window was moved along the time axis of a PD signal to cut a whole signal into segments with overlaps. The singular value decomposition (SVD) method was then applied to each segment to obtain its singular value sequence. The minimum description length (MDL) criterion was used to determine the number of effective singular values automatically. Then, the selected singular values of each signal segment were used to reconstruct the noise-free signal segment, from which the denoised PD signal was obtained. To evaluate ASTSVD, we applied ASTSVD and two other methods on simulated, laboratory-measured, and field-detected noisy PD signals, respectively. Compared to the other two methods, the denoised PD signals of ASTSVD contain less residual noise and exhibit smaller waveform distortion.

Dynamic Imaging of Glucose and Lactate Metabolism by 13C-MRS without Hyperpolarization

Metabolic reprogramming is one of the defining features of cancer and abnormal metabolism is associated with many other pathologies. Molecular imaging techniques capable of detecting such changes have become essential for cancer diagnosis, treatment planning, and surveillance. In particular, ¹⁸F-FDG (fluorodeoxyglucose) PET has emerged as an essential imaging modality for cancer because of its unique ability to detect a disturbed molecular pathway through measurements of glucose uptake. However, FDG-PET has limitations that restrict its usefulness in certain situations and the information gained is limited to glucose uptake only.¹³C magnetic resonance spectroscopy theoretically has certain advantages over FDG-PET, but its inherent low sensitivity has restricted its use mostly to single voxel measurements unless dissolution dynamic nuclear polarization (dDNP) is used to increase the signal, which brings additional complications for clinical use. We show here a new method of imaging glucose metabolism in vivo by MRI chemical shift imaging (CSI) experiments that relies on a simple, but robust and efficient, post-processing procedure by the higher dimensional analog of singular value decomposition, tensor decomposition. Using this procedure, we achieve an order of magnitude increase in signal to noise in both dDNP and non-hyperpolarized non-localized experiments without sacrificing accuracy. In CSI experiments an approximately 30-fold increase was observed, enough that the glucose to lactate conversion indicative of the Warburg effect can be imaged without hyper-polarization with a time resolution of 12s and an overall spatial resolution that compares favorably to ¹⁸F-FDG PET.

Technical Note: Clustering-based motion compensation scheme for multishot diffusion tensor imaging

PURPOSE

To extend image reconstruction using image-space sampling function (IRIS) to address large-scale motion in multishot diffusion-weighted imaging (DWI).

METHODS

A clustered IRIS (CIRIS) algorithm that would extend IRIS was proposed to correct for large-scale motion. For DWI, CIRIS initially groups the shots into clusters without intracluster large-scale motion and reconstructs each cluster by using IRIS. Then, CIRIS registers these cluster images and combines the registered images by using a weighted average to correct for voxel mismatch caused by intercluster large-scale motion. For diffusion tensor imaging (DTI), CIRIS further reduces the effect of motion on diffusion directions by treating motion-induced direction changes as additional diffusion directions. CIRIS also introduces the detection and rejection of motion-corrupted data to avoid corresponding image degradation. The proposed method was evaluated by simulation and in vivo diffusion datasets.

RESULTS

Experiments demonstrated that CIRIS can reduce motion-induced blurring and artifacts in DWI and provide more accurate DTI estimations in the presence of large-scale motion, compared with IRIS.

CONCLUSION

The proposed method presents a novel approach to correct for large-scale in-plane motion for multishot DWI and is expected to benefit the practical application of high-resolution diffusion imaging.

A diffusion-matched principal component analysis (DM-PCA) based two-channel denoising procedure for high-resolution diffusion-weighted MRI

Over the past several years, significant efforts have been made to improve the spatial resolution of diffusion-weighted imaging (DWI), aiming at better detecting subtle lesions and more reliably resolving white-matter fiber tracts. A major concern with high-resolution DWI is the limited signal-to-noise ratio (SNR), which may significantly offset the advantages of high spatial resolution. Although the SNR of DWI data can be improved by denoising in post-processing, existing denoising procedures may potentially reduce the anatomic resolvability of high-resolution imaging data. Additionally, non-Gaussian noise induced signal bias in low-SNR DWI data may not always be corrected with existing denoising approaches. Here we report an improved denoising procedure, termed diffusion-matched principal component analysis (DM-PCA), which comprises 1) identifying a group of (not necessarily neighboring) voxels that demonstrate very similar magnitude signal variation patterns along the diffusion dimension, 2) correcting low-frequency phase variations in complex-valued DWI data, 3) performing PCA along the diffusion dimension for real- and imaginary-components (in two separate channels) of phase-corrected DWI voxels with matched diffusion properties, 4) suppressing the noisy PCA components in real- and imaginary-components, separately, of phase-corrected DWI data, and 5) combining real- and imaginary-components of denoised DWI data. Our data show that the new two-channel (i.e., for real- and imaginary-components) DM-PCA denoising procedure performs reliably without noticeably compromising anatomic resolvability. Non-Gaussian noise induced signal bias could also be reduced with the new denoising method. The DM-PCA based denoising procedure should prove highly valuable for high-resolution DWI studies in research and clinical uses.