Denoising MR spectroscopic imaging data with low-rank approximations

Mapping intracellular NAD content in entire human brain using phosphorus-31 MR spectroscopic imaging at 7 Tesla

Introduction

Nicotinamide adenine dinucleotide (NAD) is a crucial molecule in cellular metabolism and signaling. Mapping intracellular NAD content of human brain has long been of interest. However, the sub-millimolar level of cerebral NAD concentration poses significant challenges for in vivo measurement and imaging.

Methods

In this study, we demonstrated the feasibility of non-invasively mapping NAD contents in entire human brain by employing a phosphorus-31 magnetic resonance spectroscopic imaging (31P-MRSI)-based NAD assay at ultrahigh field (7 Tesla), in combination with a probabilistic subspace-based processing method.

Results

The processing method achieved about a 10-fold reduction in noise over raw measurements, resulting in remarkably reduced estimation errors of NAD. Quantified NAD levels, observed at approximately 0.4 mM, exhibited good reproducibility within repeated scans on the same subject and good consistency across subjects in group data (2.3 cc nominal resolution). One set of higher-resolution data (1.0 cc nominal resolution) unveiled potential for assessing tissue metabolic heterogeneity, showing similar NAD distributions in white and gray matter. Preliminary analysis of age dependence suggested that the NAD level decreases with age.

Discussion

These results illustrate favorable outcomes of our first attempt to use ultrahigh field 31P-MRSI and advanced processing techniques to generate a whole-brain map of low-concentration intracellular NAD content in the human brain.

High-resolution 1H-MRSI at 9.4 T by integrating relaxation enhancement and subspace imaging

Achieving high-resolution and high signal-to-noise ratio (SNR) in vivo metabolic imaging via fast magnetic resonance spectroscopic imaging (MRSI) has been a longstanding challenge. This study combines the methods of relaxation enhancement (RE) and subspace imaging for the first time, enabling high-resolution and high-SNR in vivo MRSI of rodent brains at 9.4 T. Specifically, an RE-based chemical shift imaging sequence, which combines a frequency-selective pulse to excite only the metabolite frequencies with minimum perturbation of the water spins and a pair of adiabatic pulses to spatially localize the slice of interest, is designed and evaluated in vivo. This strategy effectively shortens the apparent T1 of metabolites, thereby increasing the SNR during relatively short repetition time ((TR) compared with acquisitions with only spatially selective wideband excitations, and does not require water suppression. The SNR was further enhanced via a state-of-the-art subspace reconstruction method. A novel subspace learning strategy tailored for 9.4 T and RE acquisitions is developed. In vivo, high-resolution (e.g., voxel size of 0.6 × 0.6 × 1.5 mm3) MRSI of both healthy mouse brains and a glioma-bearing mouse brain in 12.5 min has been demonstrated.

Whole-brain deuterium metabolic imaging via concentric ring trajectory readout enables assessment of regional variations in neuronal glucose metabolism

Deuterium metabolic imaging (DMI) is an emerging magnetic resonance technique, for non-invasive mapping of human brain glucose metabolism following oral or intravenous administration of deuterium-labeled glucose. Regional differences in glucose metabolism can be observed in various brain pathologies, such as Alzheimer's disease, cancer, epilepsy or schizophrenia, but the achievable spatial resolution of conventional phase-encoded DMI methods is limited due to prolonged acquisition times rendering submilliliter isotropic spatial resolution for dynamic whole brain DMI not feasible. The purpose of this study was to implement non-Cartesian spatial-spectral sampling schemes for whole-brain 2H FID-MR Spectroscopic Imaging to assess time-resolved metabolic maps with sufficient spatial resolution to reliably detect metabolic differences between healthy gray and white matter regions. Results were compared with lower-resolution DMI maps, conventionally acquired within the same session. Six healthy volunteers (4 m/2 f) were scanned for ~90 min after administration of 0.8 g/kg oral [6,6']-2H glucose. Time-resolved whole brain 2H FID-DMI maps of glucose (Glc) and glutamate + glutamine (Glx) were acquired with 0.75 and 2 mL isotropic spatial resolution using density-weighted concentric ring trajectory (CRT) and conventional phase encoding (PE) readout, respectively, at 7 T. To minimize the effect of decreased signal-to-noise ratios associated with smaller voxels, low-rank denoising of the spatiotemporal data was performed during reconstruction. Sixty-three minutes after oral tracer uptake three-dimensional (3D) CRT-DMI maps featured 19% higher (p = .006) deuterium-labeled Glc concentrations in GM (1.98 ± 0.43 mM) compared with WM (1.66 ± 0.36 mM) dominated regions, across all volunteers. Similarly, 48% higher (p = .01) 2H-Glx concentrations were observed in GM (2.21 ± 0.44 mM) compared with WM (1.49 ± 0.20 mM). Low-resolution PE-DMI maps acquired 70 min after tracer uptake featured smaller regional differences between GM- and WM-dominated areas for 2H-Glc concentrations with 2.00 ± 0.35 mM and 1.71 ± 0.31 mM, respectively (+16%; p = .045), while no regional differences were observed for 2H-Glx concentrations. In this study, we successfully implemented 3D FID-MRSI with fast CRT encoding for dynamic whole-brain DMI at 7 T with 2.5-fold increased spatial resolution compared with conventional whole-brain phase encoded (PE) DMI to visualize regional metabolic differences. The faster metabolic activity represented by 48% higher Glx concentrations was observed in GM- compared with WM-dominated regions, which could not be reproduced using whole-brain DMI with the low spatial resolution protocol. Improved assessment of regional pathologic alterations using a fully non-invasive imaging method is of high clinical relevance and could push DMI one step toward clinical applications.

3D ultra-short echo time 31P-MRSI with rosette k-space pattern: Feasibility and comparison with conventional weighted CSI

Phosphorus-31 magnetic resonance spectroscopic imaging (31P-MRSI) provides valuable non-invasive in vivo information on tissue metabolism but is burdened by poor sensitivity and prolonged scan duration. Ultra-short echo time (UTE) acquisitions minimize signal loss when probing signals with relatively short spin-spin relaxation time (T2), while also preventing first-order dephasing. Here, a three-dimensional (3D) UTE sequence with a rosette k-space trajectory is applied to 31P-MRSI at 3T. Conventional chemical shift imaging (CSI) employs highly regular Cartesian k-space sampling, susceptible to substantial artifacts when accelerated via undersampling. In contrast, this novel sequence's "petal-like" pattern offers incoherent sampling more suitable for compressed sensing (CS). These results showcase the competitive performance of UTE rosette 31P-MRSI against conventional weighted CSI with simulation, phantom, and in vivo leg muscle comparisons.

Strategically Acquired Gradient Echo (STAGE) Imaging, part IV: Constrained Reconstruction of White Noise (CROWN) Processing as a Means to Improve Signal-to-Noise in STAGE Imaging at 3 Tesla

Increasing the signal-to-noise ratio (SNR) has always been of critical importance for magnetic resonance imaging. Although increasing field strength provides a linear increase in SNR, it is more and more costly as field strength increases. Therefore, there is a major effort today to use signal processing methods to improve SNR since it is more efficient and economical. There are a variety of methods to improve SNR such as averaging the data at the expense of imaging time, or collecting the data with a lower resolution, all of these methods, including imaging processing methods, usually come at the expense of loss of image detail or image blurring. Therefore, we developed a new mathematical approach called CROWN (Constrained Reconstruction of White Noise) to enhance SNR without loss of structural detail and without affecting scanning time. In this study, we introduced and tested the concept behind CROWN specifically for STAGE (strategically acquired gradient echo) imaging. The concept itself is presented first, followed by simulations to demonstrate its theoretical effectiveness. Then the SNR improvement on proton spin density (PSD) and R2⁎ maps was investigated using brain STAGE data acquired from 10 healthy controls (HCs) and 10 patients with Parkinson's disease (PD). For the PSD and R2* maps, the SNR and CNR between white matter and gray matter were improved by a factor of 1.87 ± 0.50 and 1.72 ± 0.88, respectively. The white matter hyperintensity lesions in PD patients were more clearly defined after CROWN processing. Using these improved maps, simulated images for any repeat time, echo time or flip angle can be created with improved SNR. The potential applications of this technology are to trade off the increased SNR for higher resolution images and/or faster imaging.

Water removal in MR spectroscopic imaging with Casorati singular value decomposition

PURPOSE

Water removal is one of the computational bottlenecks in the processing of high-resolution MRSI data. The purpose of this work is to propose an approach to reduce the computing time required for water removal in large MRS data.

METHODS

In this work, we describe a singular value decomposition-based approach that uses the partial position-time separability and the time-domain linear predictability of MRSI data to reduce the computational time required for water removal. Our approach arranges MRS signals in a Casorati matrix form, applies low-rank approximations utilizing singular value decomposition, removes residual water from the most prominent left-singular vectors, and finally reconstructs the water-free matrix using the processed left-singular vectors.

RESULTS

We have demonstrated the effectiveness of our proposed algorithm for water removal using both simulated and in vivo data. The proposed algorithm encompasses a pip-installable tool ( https://pypi.org/project/CSVD/), available on GitHub ( https://github.com/amirshamaei/CSVD), empowering researchers to use it in future studies. Additionally, to further promote transparency and reproducibility, we provide comprehensive code for result replication.

CONCLUSIONS

The findings of this study suggest that the proposed method is a promising alternative to existing water removal methods due to its low processing time and good performance in removing water 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.

Exponential Signal Reconstruction With Deep Hankel Matrix Factorization

Exponential function is a basic form of temporal signals, and how to fast acquire this signal is one of the fundamental problems and frontiers in signal processing. To achieve this goal, partial data may be acquired but result in severe artifacts in its spectrum, which is the Fourier transform of exponentials. Thus, reliable spectrum reconstruction is highly expected in the fast data acquisition in many applications, such as chemistry, biology, and medical imaging. In this work, we propose a deep learning method whose neural network structure is designed by imitating the iterative process in the model-based state-of-the-art exponentials' reconstruction method with the low-rank Hankel matrix factorization. With the experiments on synthetic data and realistic biological magnetic resonance signals, we demonstrate that the new method yields much lower reconstruction errors and preserves the low-intensity signals much better than compared methods.

High-Dimensional MR Spatiospectral Imaging by Integrating Physics-Based Modeling and Data-Driven Machine Learning: Current progress and future directions

Magnetic resonance spectroscopic imaging (MRSI) offers a unique molecular window into the physiological and pathological processes in the human body. However, the applications of MRSI have been limited by a number of long-standing technical challenges due to high dimensionality and low signal-to-noise ratio (SNR). Recent technological developments integrating physics-based modeling and data-driven machine learning that exploit unique physical and mathematical properties of MRSI signals have demonstrated impressive performance in addressing these challenges for rapid, high-resolution, quantitative MRSI. This paper provides a systematic review of these progresses in the context of MRSI physics and offers perspectives on promising future directions.

Ultra-short T2 components imaging of the whole brain using 3D dual-echo UTE MRI with rosette k-space pattern

PURPOSE

This study aimed to develop a new 3D dual-echo rosette k-space trajectory, specifically designed for UTE MRI applications. The imaging of the ultra-short transverse relaxation time (uT₂ ) of brain was acquired to test the performance of the proposed UTE sequence.

THEORY AND METHODS

The rosette trajectory was developed based on rotations of a "petal-like" pattern in the k_x -k_y plane, with oscillated extensions in the k_z -direction for 3D coverage. Five healthy volunteers underwent 10 dual-echo 3D rosette UTE scans with various TEs. Dual-exponential complex model fitting was performed on the magnitude data to separate uT₂ signals, with the output of uT₂ fraction, uT₂ value, and long-T₂ value.

RESULTS

The 3D rosette dual-echo UTE sequence showed better performance than a 3D radial UTE acquisition. More significant signal intensity decay in white matter than gray matter was observed along with the TEs. The white matter regions had higher uT₂ fraction values than gray matter (10.9% ± 1.9% vs. 5.7% ± 2.4%). The uT₂ value was approximately 0.10 ms in white matter .

CONCLUSION

The higher uT₂ fraction value in white matter compared to gray matter demonstrated the ability of the proposed sequence to capture rapidly decaying signals.

Three-dimensional, 2.5-minute, 7T phosphorus magnetic resonance spectroscopic imaging of the human heart using concentric rings

A three-dimensional (3D), density-weighted, concentric rings trajectory (CRT) magnetic resonance spectroscopic imaging (MRSI) sequence is implemented for cardiac phosphorus (³¹ P)-MRS at 7 T. The point-by-point k-space sampling of traditional phase-encoded chemical shift imaging (CSI) sequences severely restricts the minimum scan time at higher spatial resolutions. Our proposed CRT sequence implements a stack of concentric rings, with a variable number of rings and planes spaced to optimise the density of k-space weighting. This creates flexibility in acquisition time, allowing acquisitions substantially faster than traditional phase-encoded CSI sequences, while retaining high signal-to-noise ratio (SNR). We first characterise the SNR and point-spread function of the CRT sequence in phantoms. We then evaluate it at five different acquisition times and spatial resolutions in the hearts of five healthy participants at 7 T. These different sequence durations are compared with existing published 3D acquisition-weighted CSI sequences with matched acquisition times and spatial resolutions. To minimise the effect of noise on the short acquisitions, low-rank denoising of the spatiotemporal data was also performed after acquisition. The proposed sequence measures 3D localised phosphocreatine to adenosine triphosphate (PCr/ATP) ratios of the human myocardium in 2.5 min, 2.6 times faster than the minimum scan time for acquisition-weighted phase-encoded CSI. Alternatively, in the same scan time, a 1.7-times smaller nominal voxel volume can be achieved. Low-rank denoising reduced the variance of measured PCr/ATP ratios by 11% across all protocols. The faster acquisitions permitted by 7-T CRT ³¹ P-MRSI could make cardiac stress protocols or creatine kinase rate measurements (which involve repeated scans) more tolerable for patients without sacrificing spatial resolution.

Spatiotemporal encoding MRI using subspace-constrained sampling and locally-low-rank regularization: Applications to diffusion weighted and diffusion kurtosis imaging of human brain and prostate

The benefits of performing locally low-rank (LLR) reconstructions on subsampled diffusion weighted and diffusion kurtosis imaging data employing spatiotemporal encoding (SPEN) methods, is investigated. SPEN allows for self-referenced correction of motion-induced phase errors in case of interleaved diffusion-oriented acquisitions, and allows one to overcome distortions otherwise observed along EPI's phase-encoded dimension. In combination with LLR-based reconstructions of the pooled imaging data and with a joint subsampling of b-weighted and interleaved images, additional improvements in terms of sensitivity as well as shortened acquisition times are demonstrated, without noticeable penalties. Details on how the LLR-regularized, subspace-constrained image reconstructions were adapted to SPEN are given; the improvements introduced by adopting these reconstruction frameworks for the accelerated acquisition of diffusivity and of kurtosis imaging data in both relatively homogeneous regions like the human brain and in more challenging regions like the human prostate, are presented and discussed within the context of similar efforts in the field.

Mapping of magnetic resonance imaging's transverse relaxation time at low signal-to-noise ratio using Bloch simulations and principal component analysis image denoising

High-resolution mapping of magnetic resonance imaging (MRI)'s transverse relaxation time (T₂ ) can benefit many clinical applications by offering improved anatomic details, enhancing the ability to probe tissues' microarchitecture, and facilitating the identification of early pathology. Increasing spatial resolutions, however, decreases data's signal-to-noise ratio (SNR), particularly at clinical scan times. This impairs imaging quality, and the accuracy of subsequent radiological interpretation. Recently, principal component analysis (PCA) was employed for denoising diffusion-weighted MR images and was shown to be effective for improving parameter estimation in multiexponential relaxometry. This study combines the Marchenko-Pastur PCA (MP-PCA) signal model with the echo modulation curve (EMC) algorithm for denoising multiecho spin-echo (MESE) MRI data and improving the precision of EMC-generated single T₂ relaxation maps. The denoising technique was validated on simulations, phantom scans, and in vivo brain and knee data. MESE scans were performed on a 3-T Siemens scanner. The acquired images were denoised using the MP-PCA algorithm and were then provided as input for the EMC T₂ -fitting algorithm. Quantitative analysis of the denoising quality included comparing the standard deviation and coefficient of variation of T₂ values, along with gold standard SNR estimation of the phantom scans. The presented denoising technique shows an increase in T₂ maps' precision and SNR, while successfully preserving the morphological features of the tissue. Employing MP-PCA denoising as a preprocessing step decreases the noise-related variability of T₂ maps produced by the EMC algorithm and thus increases their precision. The proposed method can be useful for a wide range of clinical applications by facilitating earlier detection of pathologies and improving the accuracy of patients' follow-up.

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.

Developments in proton MR spectroscopic imaging of prostate cancer

In this paper, we review the developments of 1H-MR spectroscopic imaging (MRSI) methods designed to investigate prostate cancer, covering key aspects such as specific hardware, dedicated pulse sequences for data acquisition and data processing and quantification techniques. Emphasis is given to recent advancements in MRSI methodologies, as well as future developments, which can lead to overcome difficulties associated with commonly employed MRSI approaches applied in clinical routine. This includes the replacement of standard PRESS sequences for volume selection, which we identified as inadequate for clinical applications, by sLASER sequences and implementation of 1H MRSI without water signal suppression. These may enable a new evaluation of the complementary role and significance of MRSI in prostate cancer management.

High-Quality MR Fingerprinting Reconstruction Using Structured Low-Rank Matrix Completion and Subspace Projection

Due to the capability of fast multiparametric quantitative imaging, magnetic resonance fingerprinting (MRF) is becoming a promising quantitative magnetic resonance imaging approach. However, the artifacts caused by the highly undersampled data acquisition lead to inaccurate estimation of the tissue parameter maps. Based on the assumption that the 3-D MRF data can be modeled as a piecewise smooth signal, with the discontinuities localized to the zero sets of a bandlimited function, we exploit the low-rank property of the structured Toeplitz matrix constructed from the Fourier measurements. In addition, we adopt the subspace projection scheme to improve the accuracy of parameter estimation. In order to efficiently solve the regularized problem, we propose an iterative two-stage algorithm, which alternately updates the k -space data and projects the space-time matrix into the dictionary space. Numerical experiments demonstrate that the proposed algorithm shows significant improvement in MRF time-series images reconstruction and can provide more accurate parameter maps over the state-of-the-art algorithms.

SNR Enhancement for Multi-TE MRSI Using Joint Low-Dimensional Model and Spatial Constraints

We present a novel method to enhance the SNR for multi-TE MR spectroscopic imaging (MRSI) data by integrating learned nonlinear low-dimensional model and spatial constraints. A deep complex convolutional autoen-coder (DCCAE) was developed to learn a nonlinear low-dimensional representation of the high-dimensional multi-TE 1 H spectroscopy signals. The learned model significantly reduces the data dimension thus serving as an effective constraint for noise reduction. A reconstruction formulation was proposed to integrate the spatiospectral encoding model, the learned model, and a spatial constraint for an SNR-enhancing reconstruction from multi-TE data. The proposed method has been evaluated using both numerical simulations and in vivo brain MRSI experiments. The superior denoising performance of the proposed over alternative methods was demonstrated, both qualitatively and quantitatively. In vivo multi-TE data was used to assess the improved metabolite quantification reproducibility and accuracy achieved by the proposed method. We expect the proposed SNR-enhancing reconstruction to enable faster and/or higher-resolution multi-TE 1 H-MRSI of the brain, potentially useful for various clinical applications.

Epigenetic MRI: Noninvasive imaging of DNA methylation in the brain

Dynamic epigenetic activity is a fundamental mechanism underpinning how the brain changes its function during development and aging and in response to environmental and disease stimuli. We developed a technology called epigenetic MRI (eMRI) that enables noninvasive imaging of DNA methylation in the brain, a major epigenetic mechanism. eMRI reveals strong regional differences in global DNA methylation in pig brains, a model with stronger resemblance to human brains than are rodents. Given the noninvasive nature of eMRI, our results pave the way for a DNA-methylation imaging paradigm for living human brains. We expect eMRI to enable many studies to unravel the molecular control of brain function and disease.

Both neuronal and genetic mechanisms regulate brain function. While there are excellent methods to study neuronal activity in vivo, there are no nondestructive methods to measure global gene expression in living brains. Here, we present a method, epigenetic MRI (eMRI), that overcomes this limitation via direct imaging of DNA methylation, a major gene-expression regulator. eMRI exploits the methionine metabolic pathways for DNA methylation to label genomic DNA through ¹³C-enriched diets. A ¹³C magnetic resonance spectroscopic imaging method then maps the spatial distribution of labeled DNA. We validated eMRI using pigs, whose brains have stronger similarity to humans in volume and anatomy than rodents, and confirmed efficient ¹³C-labeling of brain DNA. We also discovered strong regional differences in global DNA methylation. Just as functional MRI measurements of regional neuronal activity have had a transformational effect on neuroscience, we expect that the eMRI signal, both as a measure of regional epigenetic activity and as a possible surrogate for regional gene expression, will enable many new investigations of human brain function, behavior, and disease.

Whole-brain high-resolution metabolite mapping with 3D compressed-sensing SENSE low-rank 1 H FID-MRSI

There is a growing interest in the neuroscience community to map the distribution of brain metabolites in vivo. Magnetic resonance spectroscopic imaging (MRSI) is often limited by either a poor spatial resolution and/or a long acquisition time, which severely restricts its applications for clinical and research purposes. Building on a recently developed technique of acquisition-reconstruction for 2D MRSI, we combined a fast Cartesian ¹ H-FID-MRSI acquisition sequence, compressed-sensing acceleration, and low-rank total-generalized-variation constrained reconstruction to produce 3D high-resolution whole-brain MRSI with a significant acquisition time reduction. We first evaluated the acceleration performance using retrospective undersampling of a fully sampled dataset. Second, a 20 min accelerated MRSI acquisition was performed on three healthy volunteers, resulting in metabolite maps with 5 mm isotropic resolution. The metabolite maps exhibited the detailed neurochemical composition of all brain regions and revealed parts of the underlying brain anatomy. The latter assessment used previous reported knowledge and a atlas-based analysis to show consistency of the concentration contrasts and ratio across all brain regions. These results acquired on a clinical 3 T MRI scanner successfully combined 3D ¹ H-FID-MRSI with a constrained reconstruction to produce detailed mapping of metabolite concentrations at high resolution over the whole brain, with an acquisition time suitable for clinical or research settings.

Machine Learning-Enabled High-Resolution Dynamic Deuterium MR Spectroscopic Imaging

Deuterium magnetic resonance spectroscopic imaging (DMRSI) has recently been recognized as a potentially powerful tool for noninvasive imaging of brain energy metabolism and tumor. However, the low sensitivity of DMRSI has significantly limited its utility for both research and clinical applications. This work presents a novel machine learning-based method to address this limitation. The proposed method synergistically integrates physics-based subspace modeling and data-driven deep learning for effective denoising, making high-resolution dynamic DMRSI possible. Specifically, a novel subspace model was used to represent the dynamic DMRSI signals; deep neural networks were trained to capture the low-dimensional manifolds of the spectral and temporal distributions of practical dynamic DMRSI data. The learned subspace and manifold structures were integrated via a regularization formulation to remove measurement noise. Theoretical analysis, computer simulations, and in vivo experiments have been conducted to demonstrate the denoising efficacy of the proposed method which enabled high-resolution imaging capability. The translational potential was demonstrated in tumor-bearing rats, where the Warburg effect associated with cancer metabolism and tumor heterogeneity were successfully captured. The new method may not only provide an effective tool to enhance the sensitivity of DMRSI for basic research and clinical applications but also provide a framework for denoising other spatiospectral data.

Achieving high-resolution 1H-MRSI of the human brain with compressed-sensing and low-rank reconstruction at 7 Tesla

Low sensitivity MR techniques such as magnetic resonance spectroscopic imaging (MRSI) greatly benefit from the gain in signal-to-noise provided by ultra-high field MR. High-resolution and whole-slab brain MRSI remains however very challenging due to lengthy acquisition, low signal, lipid contamination and field inhomogeneity. In this study, we propose an acquisition-reconstruction scheme that combines 1H free-induction-decay (FID)-MRSI sequence, short TR acquisition, compressed sensing acceleration and low-rank modeling with total-generalized-variation constraint to achieve metabolite imaging in two and three dimensions at 7 Tesla. The resulting images and volumes reveal highly detailed distributions that are specific to each metabolite and follow the underlying brain anatomy. The MRSI method was validated in a high-resolution phantom containing fine metabolite structures, and in five healthy volunteers. This new application of compressed sensing acceleration paves the way for high-resolution MRSI in clinical setting with acquisition times of 5 min for 2D MRSI at 2.5 mm and of 20 min for 3D MRSI at 3.3 mm isotropic.

Uncertainty in denoising of MRSI using low-rank methods

PURPOSE

Low-rank denoising of MRSI data results in an apparent increase in spectral SNR. However, it is not clear if this translates to a lower uncertainty in metabolite concentrations after spectroscopic fitting. Estimation of the true uncertainty after denoising is desirable for downstream analysis in spectroscopy. In this work, the uncertainty reduction from low-rank denoising methods based on spatiotemporal separability and linear predictability in MRSI are assessed. A new method for estimating metabolite concentration uncertainty after denoising is proposed. Automatic rank threshold selection methods are also assessed in simulated low SNR regimes.

METHODS

Assessment of denoising methods is conducted using Monte Carlo simulation of proton MRSI data and by reproducibility of repeated in vivo acquisitions in 5 subjects.

RESULTS

In simulated and in vivo data, spatiotemporal based denoising is shown to reduce the concentration uncertainty, but linear prediction denoising increases uncertainty. Uncertainty estimates provided by fitting algorithms after denoising consistently underestimate actual metabolite uncertainty. However, the proposed uncertainty estimation, based on an analytical expression for entry-wise variance after denoising, is more accurate. It is also shown automated rank threshold selection using Marchenko-Pastur distribution can bias the data in low SNR conditions. An alternative soft-thresholding function is proposed.

CONCLUSION

Low-rank denoising methods based on spatiotemporal separability do reduce uncertainty in MRS(I) data. However, thorough assessment is needed as assessment by SNR measured from residual baseline noise is insufficient given the presence of non-uniform variance. It is also important to select the right rank thresholding method in low SNR cases.

Motion compensation combining with local low rank regularization for low dose dynamic CT myocardial perfusion reconstruction

Dynamic CT myocardial perfusion imaging (DCT-MPI) is a reliable examination tool for the assessment of myocardium and vascular, while its special scan protocol may result in excessive radiation exposure to patients and inevitable inter-frame motion. Lowering the tube current is a simple way to reduce radiation exposure. However, low mAs will certainly cause severe image noise, thus may further impact the accuracy of functional hemodynamic parameters, which are used for the assessment of blood supply. In this work, we present a novel scheme applying motion compensation and local low rank regularization (MC-LLR) for obtaining high quality motion compensated DCT-MPI images. Specifically, motion compensation by using robust data decomposition registration (RDDR) was introduced. Robust principal component analysis coupled with optical flow-based registration algorithm were used in RDDR. Then, the local low rank constraint on the motion compensated time series images was applied for the DCT-MPI reconstruction. One healthy mini pig and two patient datasets were used to evaluate the proposed MC-LLR algorithm. Results show that the present method achieved satisfactory image quality with higher CNRs, smaller rRMSEs, and more accurate hemodynamic parameter maps.

3D 31 P MRSI of the human brain at 9.4 Tesla: Optimization and quantitative analysis of metabolic images

PURPOSE

To present ³¹ P whole brain MRSI with a high spatial resolution to probe quantitative tissue analysis of ³¹ P MRSI at an ultrahigh field strength of 9.4 Tesla.

METHODS

The study protocol included a ³¹ P MRSI measurement with an effective resolution of 2.47 mL. For SNR optimization, the nuclear Overhauser enhancement at 9.4 Tesla was investigated. A sensitivity correction was achieved by applying a low rank approximation of the γ-adenosine triphosphate signal. Group analysis and regression on individual volunteers were performed to investigate quantitative concentration differences between different tissue types.

RESULTS

Differences in gray and white matter tissue ³¹ P concentrations could be investigated for 12 different ³¹ P resonances. In addition, the first highly resolved quantitative MRSI images measured at B₀ = 9.4 Tesla of ³¹ P detectable metabolites with high SNR could be presented.

CONCLUSION

With an ultrahigh field strength B₀ = 9.4 Tesla, ³¹ P MRSI moves further toward quantitative metabolic imaging, and subtle differences in concentrations between different tissue types can be detected.

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.

Super Resolution of Magnetic Resonance Images

In this work, novel denoising and super resolution (SR) approaches for magnetic resonance (MR) images are addressed, and are integrated in a unified framework, which do not require example low resolution (LR)/high resolution (HR)/cross-modality/noise-free images and prior information of noise–noise variance. The proposed method categorizes the patches as either smooth or textured and then denoises them by deploying different denoising strategies for efficient denoising. The denoising algorithm is integrated into the SR approach, which uses a gradient profile-based constraint in a sparse representation-based framework to improve the resolution of MR images with reduced smearing of image details. This constraint regularizes the estimation of HR images such that the estimated HR image has gradient profiles similar to the gradient profiles of the original HR image. For this, the gradient profile sharpness (GPS) values of an unknown HR image are estimated using an approximated piece-wise linear relation among GPS values of LR and upsampled LR images. The experiments are performed on three different publicly available datasets. The proposed SR approach outperforms the existing unsupervised SR approach addressed for real MR images that exploits low rank and total variation (LRTV) regularization, by an average peak signal to noise ratio (PSNR) of 0.73 dB and 0.38 dB for upsampling factors 2 and 3, respectively. For the super resolution of noisy real MR images (degraded with 2% noise), the proposed approach outperforms the LRTV approach by an average PSNR of 0.54 dB and 0.46 dB for upsampling factors 2 and 3, respectively. The qualitative analysis is shown for real MR images from healthy subjects and subjects with Alzheimer’s disease and structural deformity, i.e., cavernoma.

Review and prospect: NMR spectroscopy denoising and reconstruction with low-rank Hankel matrices and tensors

Nuclear magnetic resonance (NMR) spectroscopy is an important analytical tool in chemistry, biology, and life science, but it suffers from relatively low sensitivity and long acquisition time. Thus, improving the apparent signal-to-noise ratio and accelerating data acquisition became indispensable. In this review, we summarize the recent progress on low-rank Hankel matrix and tensor methods, which exploit the exponential property of free-induction decay signals, to enable effective denoising and spectra reconstruction. We also outline future developments that are likely to make NMR spectroscopy a far more powerful technique.

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.

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.

Fast in vivo 23 Na imaging and T 2 ∗ mapping using accelerated 2D-FID UTE magnetic resonance spectroscopic imaging at 3 T: Proof of concept and reliability study

PURPOSE

To implement an accelerated MR-acquisition method allowing to map T 2 ∗ relaxation and absolute concentration of sodium within skeletal muscles at 3T.

METHODS

A fast-UTE-2D density-weighted concentric-ring-trajectory ²³ Na-MRSI technique was used to acquire 64 time points of FID with a spectral bandwidth of 312.5 Hz with an in-plane resolution of 2.5 × 2.5 mm² in ~15 min. The fast-relaxing ²³ Na signal was localized with a single-shot, inversion-recovery-based, non-echo (SIRENE) outer volume suppression (OVS) method. The sequence was verified using simulation and phantom studies before implementing it in human calf muscles. To evaluate the 2D-SIRENE-MRSI (UTE = 0.55 ms) imaging performance, it was compared to a 3D-MRI (UTE = 0.3 ms) sequence. Both data sets were acquired within 2 same-day sessions to assess repeatability. The T 2 ∗ values were fitted voxel-by-voxel using a biexponential model for the 2D-MRSI data. Finally, intra-subject coefficients of variation (CV) were estimated.

RESULTS

The MRSI-FID data allowed us to map the fast and slow components of T 2 ∗ in the calf muscles. The spatial distributions of ²³ Na concentration for both MRSI and 3D-MRI acquisitions were significantly correlated (P < .001). The test-retest analysis rendered high repeatability for MRSI with a CV of 5%. The mean T 2 Fast ∗ in muscles was 0.7 ± 0.1 ms (contribution fraction = 37%), whereas T 2 Slow ∗ was 13.2 ± 0.2 ms (63%). The mean absolute muscle ²³ Na concentration calculated from the T 2 ∗ -corrected data was 28.6 ± 3.3 mM.

CONCLUSION

The proposed MRSI technique is a reliable technique to map sodium's absolute concentration and T 2 ∗ within a clinically acceptable scan time at 3T.

Effects of apodization smoothing and denoising on spectral fitting

PURPOSE

Visual review of individual spectra in magnetic resonance spectroscopic imaging (MRSI) data benefits from the application of spectral smoothing; however, if this processing step is applied prior to spectral analysis this can impact the accuracy of the quantitation. This study aims to analyze the effect of spectral denoising and apodization smoothing on the quantitation of whole-brain MRSI data obtained at short TE.

METHODS

Short-TE MRSI data obtained at 3 T were analyzed with no spectral smoothing, following (i) Gaussian apodization with values of 1, 2, 4, 6, and 8 Hz, and (ii) denoising using principal component analysis (dnPCA) with 3 different values for the number of retained principal components. The mean lobar white matter estimates for four metabolites, signal-to-noise ratio (SNR), spectral linewidth, and confidence intervals were compared to data reconstructed using no smoothing. Additionally, a voxel-wise comparison for N-acetylaspartate quantitation with different smoothing schemes was performed.

RESULTS

Significant pairwise differences were seen for all Gaussian smoothing methods as compared to no smoothing (p<0.001) in linewidth and metabolite estimates, whereas dnPCA methods showing no statistically significant differences in these measures. Confidence intervals decreased, and SNR increased with increasing levels of apodization smoothing or dnPCA denoising.

CONCLUSION

Mild Gaussian apodization (≤2 Hz at 3 T) can be applied with minimal (1%) errors in quantitation; however, smoothing values greater than that can significantly affect metabolite quantification. In contrast, mild to moderate dnPCA based denoising provides quantitative results that are consistent with the analysis of unsmoothed data and this method is recommended for spectral denoising.

Constrained Magnetic Resonance Spectroscopic Imaging by Learning Nonlinear Low-Dimensional Models

Magnetic resonance spectroscopic imaging (MRSI) is a powerful molecular imaging modality but has very limited speed, resolution, and SNR tradeoffs. Construction of a low-dimensional model to effectively reduce the dimensionality of the imaging problem has recently shown great promise in improving these tradeoffs. This paper presents a new approach to model and reconstruct the spectroscopic signals by learning a nonlinear low-dimensional representation of the general MR spectra. Specifically, we trained a deep neural network to capture the low-dimensional manifold, where the high-dimensional spectroscopic signals reside. A regularization formulation is proposed to effectively integrate the learned model and physics-based data acquisition model for MRSI reconstruction with the capability to incorporate additional spatiospectral constraints. An efficient numerical algorithm was developed to solve the associated optimization problem involving back-propagating the trained network. Simulation and experimental results were obtained to demonstrate the representation power of the learned model and the ability of the proposed formulation in producing SNR-enhancing reconstruction from the practical MRSI data.

Ultrafast magnetic resonance spectroscopic imaging using SPICE with learned subspaces

PURPOSE

To develop a subspace learning method for the recently proposed subspace-based MRSI approach known as SPICE, and achieve ultrafast 1 H-MRSI of the brain.

THEORY AND METHODS

A novel strategy is formulated to learn a low-dimensional subspace representation of MR spectra from specially acquired training data and use the learned subspace for general MRSI experiments. Specifically, the subspace learning problem is formulated as learning "empirical" distributions of molecule-specific spectral parameters (e.g., concentrations, lineshapes, and frequency shifts) by integrating physics-based model and the training data. The learned spectral parameters and quantum mechanical simulation basis can then be combined to construct acquisition-specific subspace for spatiospectral encoding and processing. High-resolution MRSI acquisitions combining ultrashort-TE/short-TR excitation, sparse sampling, and the elimination of water suppression have been performed to evaluate the feasibility of the proposed method.

RESULTS

The accuracy of the learned subspace and the capability of the proposed method in producing high-resolution 3D 1 H metabolite maps and high-quality spatially resolved spectra (with a nominal resolution of ∼2.4 × 2.4 × 3 mm3 in 5 minutes) were demonstrated using phantom and in vivo studies. By eliminating water suppression, we are also able to extract valuable information from the water signals for data processing ( B 0 map, frequency drift, and coil sensitivity) as well as for mapping tissue susceptibility and relaxation parameters.

CONCLUSIONS

The proposed method enables ultrafast 1 H-MRSI of the brain using a learned subspace, eliminating the need of acquiring subject-dependent navigator data (known as D 1 ) in the original SPICE technique. It represents a new way to perform MRSI experiments and an important step toward practical applications of high-resolution MRSI.

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.

Bio-SCOPE: fast biexponential T1ρ mapping of the brain using signal-compensated low-rank plus sparse matrix decomposition

PURPOSE

To develop and evaluate a fast imaging method based on signal-compensated low-rank plus sparse matrix decomposition to accelerate data acquisition for biexponential brain T_1ρ mapping (Bio-SCOPE).

METHODS

Two novel strategies were proposed to improve reconstruction performance. A variable-rate undersampling scheme was used with a varied acceleration factor for each k-space along the spin-lock time direction, and a modified nonlinear thresholding scheme combined with a feature descriptor was used for Bio-SCOPE reconstruction. In vivo brain T_1ρ mappings were acquired from 4 volunteers. The fully sampled k-space data acquired from 3 volunteers were retrospectively undersampled by net acceleration rates (R) of 4.6 and 6.1. Reference values were obtained from the fully sampled data. The agreement between the accelerated T_1ρ measurements and reference values was assessed with Bland-Altman analyses. Prospectively undersampled data with R = 4.6 and R = 6.1 were acquired from 1 volunteer.

RESULTS

T_1ρ -weighted images were successfully reconstructed using Bio-SCOPE for R = 4.6 and 6.1 with signal-to-noise ratio variations <1 dB and normalized root mean square errors <4%. Accelerated and reference T_1ρ measurements were in good agreement for R = 4.6 (T_{1ρ s} : 18.6651 ± 1.7786 ms; T_{1ρ l} : 88.9603 ± 1.7331 ms) and R = 6.1 (T_{1ρ s} : 17.8403 ± 3.3302 ms; T_{1ρ l} : 88.0275 ± 4.9606 ms) in the Bland-Altman analyses. T_1ρ parameter maps from prospectively undersampled data also show reasonable image quality using the Bio-SCOPE method.

CONCLUSION

Bio-SCOPE achieves a high net acceleration rate for biexponential T_1ρ mapping and improves reconstruction quality by using a variable-rate undersampling data acquisition scheme and a modified soft-thresholding algorithm in image reconstruction.

Manifold recovery using kernel low-rank regularization: application to dynamic imaging

We introduce a novel kernel low-rank algorithm to recover free-breathing and ungated dynamic MRI data from highly undersampled measurements. The image frames in the free breathing and ungated dataset are assumed to be points on a bandlimited manifold. We show that the non-linear features of these images satisfy annihilation conditions, which implies that the kernel matrix derived from the dataset is low-rank. We penalize the nuclear norm of the feature matrix to recover the images from highly undersampled measurements. The regularized optimization problem is solved using an iterative reweighted least squares (IRLS) algorithm, which alternates between the update of the Laplacian matrix of the manifold and the recovery of the signals from the noisy measurements. To improve computational efficiency, we use a two step algorithm using navigator measurements. Specifically, the Laplacian matrix is estimated from the navigators using the IRLS scheme, followed by the recovery of the images using a quadratic optimization. We show the relation of this two step algorithm with our recent SToRM approach, thus reconciling SToRM and manifold regularization methods with algorithms that rely on explicit lifting of data to a high dimensional space. The IRLS based estimation of the Laplacian matrix is a systematic and noise-robust alternative to current heuristic strategies based on exponential maps. We also approximate the Laplacian matrix using a few eigen vectors, which results in a fast and memory efficient algorithm. The proposed scheme is demonstrated on several patients with different breathing patterns and cardiac rates.

Evaluation of principal component analysis image denoising on multi-exponential MRI relaxometry

PURPOSE

Multi-exponential relaxometry is a powerful tool for characterizing tissue, but generally requires high image signal-to-noise ratio (SNR). This work evaluates the use of principal-component-analysis (PCA) denoising to mitigate these SNR demands and improve the precision of relaxometry measures.

METHODS

PCA denoising was evaluated using both simulated and experimental MRI data. Bi-exponential transverse relaxation signals were simulated for a wide range of acquisition and sample parameters, and experimental data were acquired from three excised and fixed mouse brains. In both cases, standard relaxometry analysis was performed on both original and denoised image data, and resulting estimated signal parameters were compared.

RESULTS

Denoising reduced the root-mean-square-error of parameters estimated from multi-exponential relaxometry by factors of ≈3×, for typical acquisition and sample parameters. Denoised images and subsequent parameter maps showed little or no signs of spatial artifact or loss of resolution.

CONCLUSION

Experimental studies and simulations demonstrate that PCA denoising of MRI relaxometry data is an effective method of improving parameter precision without sacrificing image resolution. This simple yet important processing step thus paves the way for broader applicability of multi-exponential MRI relaxometry.

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.

Fast high-resolution brain metabolite mapping on a clinical 3T MRI by accelerated 1 H-FID-MRSI and low-rank constrained reconstruction

PURPOSE

Epitomizing the advantages of ultra short echo time and no chemical shift displacement error, high-resolution-free induction decay magnetic resonance spectroscopic imaging (FID-MRSI) sequences have proven to be highly effective in providing unbiased characterizations of metabolite distributions. However, its merits are often overshadowed in high-resolution settings by reduced signal-to-noise ratios resulting from the smaller voxel volumes procured by extensive phase encoding and the related acquisition times.

METHODS

To address these limitations, we here propose an acquisition and reconstruction scheme that offers both implicit dataset denoising and acquisition acceleration. Specifically, a slice selective high-resolution FID-MRSI sequence was implemented. Spectroscopic datasets were processed to remove fat contamination, and then reconstructed using a total generalized variation (TGV) regularized low-rank model. We further measured reconstruction performance for random undersampled data to assess feasibility of a compressed-sensing SENSE acceleration scheme. Performance of the lipid suppression was assessed using an ad hoc phantom, while that of the low-rank TGV reconstruction model was benchmarked using simulated MRSI data. To assess real-world performance, 2D FID-MRSI acquisitions of the brain in healthy volunteers were reconstructed using the proposed framework.

RESULTS

Results from the phantom and simulated data demonstrate that skull lipid contamination is effectively removed and that data reconstruction quality is improved with the low-rank TGV model. Also, we demonstrated that the presented acquisition and reconstruction methods are compatible with a compressed-sensing SENSE acceleration scheme.

CONCLUSIONS

An original reconstruction pipeline for 2D 1 H-FID-MRSI datasets was presented that places high-resolution metabolite mapping on 3T MR scanners within clinically feasible limits.

A Boosting SAR Image Despeckling Method Based on Non-Local Weighted Group Low-Rank Representation

In this paper, we propose a boosting synthetic aperture radar (SAR) image despeckling method based on non-local weighted group low-rank representation (WGLRR). The spatial structure information of SAR images leads to the similarity of the patches. Furthermore, the data matrix grouped by the similar patches within the noise-free SAR image is often low-rank. Based on this, we use low-rank representation (LRR) to recover the noise-free group data matrix. To maintain the fidelity of the recovered image, we integrate the corrupted probability of each pixel into the group LRR model as a weight to constrain the fidelity of recovered noise-free patches. Each single patch might belong to several groups, so different estimations of each patch are aggregated with a weighted averaging procedure. The residual image contains signal leftovers due to the imperfect denoising, so we strengthen the signal by leveraging on the availability of the denoised image to suppress noise further. Experimental results on simulated and actual SAR images show the superior performance of the proposed method in terms of objective indicators and of perceived image quality.

High-fidelity spectroscopy reconstruction in accelerated NMR

High-fidelity spectra, particularly low intensity peaks, are reconstructed for fast NMR with better rank approximation in the EnhanCed Low Rank (ECLR) method.

Estimation of Basis Line-Integrals in a Spectral Distortion-Modeled Photon Counting Detector Using Low-Rank Approximation-Based X-Ray Transmittance Modeling: K-Edge Imaging Application

Photon counting detectors (PCDs) provide multiple energy-dependent measurements for estimating basis line-integrals. However, the measured spectrum is distorted from the spectral response effect (SRE) via charge sharing, K-fluorescence emission, and so on. Thus, in order to avoid bias and artifacts in images, the SRE needs to be compensated. For this purpose, we recently developed a computationally efficient three-step algorithm for PCD-CT without contrast agents by approximating smooth X-ray transmittance using low-order polynomial bases. It compensated the SRE by incorporating the SRE model in a linearized estimation process and achieved nearly the minimum variance and unbiased (MVU) estimator. In this paper, we extend the three-step algorithm to K-edge imaging applications by designing optimal bases using a low-rank approximation to model X-ray transmittances with arbitrary shapes (i.e., smooth without the K-edge or discontinuous with the K-edge). The bases can be used to approximate the X-ray transmittance and to linearize the PCD measurement modeling and then the three-step estimator can be derived as in the previous approach: estimating the x-ray transmittance in the first step, estimating basis line-integrals including that of the contrast agent in the second step, and correcting for a bias in the third step. We demonstrate that the proposed method is more accurate and stable than the low-order polynomial-based approaches with extensive simulation studies using gadolinium for the K-edge imaging application. We also demonstrate that the proposed method achieves nearly MVU estimator, and is more stable than the conventional maximum likelihood estimator in high attenuation cases with fewer photon counts.

Recovery of Damped Exponentials Using Structured Low Rank Matrix Completion

We introduce a structured low rank matrix completion algorithm to recover a series of images from their under-sampled measurements, where the signal along the parameter dimension at every pixel is described by a linear combination of exponentials. We exploit the exponential behavior of the signal at every pixel, along with the spatial smoothness of the exponential parameters to derive an annihilation relation in the Fourier domain. This relation translates to a low-rank property on a structured matrix constructed from the Fourier samples. We enforce the low-rank property of the structured matrix as a regularization prior to recover the images. Since the direct use of current low rank matrix recovery schemes to this problem is associated with high computational complexity and memory demand, we adopt an iterative re-weighted least squares algorithm, which facilitates the exploitation of the convolutional structure of the matrix. Novel approximations involving 2-D fast Fourier transforms are introduced to drastically reduce the memory demand and computational complexity, which facilitates the extension of structured low-rank methods to large scale 3-D problems. We demonstrate our algorithm in the MR parameter mapping setting and show improvement over the state-of-the-art methods.