Robust reconstruction of MRSI data using a sparse spectral model and high resolution MRI priors

Joint learning of nonlinear representation and projection for fast constrained MRSI reconstruction

PURPOSE

To develop and evaluate a novel method for computationally efficient reconstruction from noisy MR spectroscopic imaging (MRSI) data.

METHODS

The proposed method features (a) a novel strategy that jointly learns a nonlinear low-dimensional representation of high-dimensional spectroscopic signals and a neural-network-based projector to recover the low-dimensional embeddings from noisy/limited data; (b) a formulation that integrates the forward encoding model, a regularizer exploiting the learned representation, and a complementary spatial constraint; and (c) a highly efficient algorithm enabled by the learned projector within an alternating direction method of multipliers (ADMM) framework, circumventing the computationally expensive network inversion subproblem.

RESULTS

The proposed method has been evaluated using simulations as well as in vivo  1 $$ {}^1 $$ H and  31 $$ {}^{31} $$ P MRSI data, demonstrating improved performance over state-of-the-art methods, with about 6× $$ \times $$ fewer averages needed than standard Fourier reconstruction for similar metabolite estimation variances and up to 100× $$ \times $$ reduction in processing time compared to a prior neural network constrained reconstruction method. Computational and theoretical analyses were performed to offer further insights into the effectiveness of the proposed method.

CONCLUSION

A novel method was developed for fast, high-SNR spatiospectral reconstruction from noisy MRSI data. We expect our method to be useful for enhancing the quality of MRSI or other high-dimensional spatiospectral imaging data.

Arterial spin labeling MR image denoising and reconstruction using unsupervised deep learning

Arterial spin labeling (ASL) imaging is a powerful magnetic resonance imaging technique that allows to quantitatively measure blood perfusion non-invasively, which has great potential for assessing tissue viability in various clinical settings. However, the clinical applications of ASL are currently limited by its low signal-to-noise ratio (SNR), limited spatial resolution, and long imaging time. In this work, we propose an unsupervised deep learning-based image denoising and reconstruction framework to improve the SNR and accelerate the imaging speed of high resolution ASL imaging. The unique feature of the proposed framework is that it does not require any prior training pairs but only the subject's own anatomical prior, such as T1-weighted images, as network input. The neural network was trained from scratch in the denoising or reconstruction process, with noisy images or sparely sampled k-space data as training labels. Performance of the proposed method was evaluated using in vivo experiment data obtained from 3 healthy subjects on a 3T MR scanner, using ASL images acquired with 44-min acquisition time as the ground truth. Both qualitative and quantitative analyses demonstrate the superior performance of the proposed txtc framework over the reference methods. In summary, our proposed unsupervised deep learning-based denoising and reconstruction framework can improve the image quality and accelerate the imaging speed of ASL imaging.

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.

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.

Method for fast lipid reconstruction and removal processing in 1 H MRSI of the brain

PURPOSE

To develop a new rapid spatial filtering method for lipid removal, fast lipid reconstruction and removal processing (FLIP), which selectively isolates and removes interfering lipid signals from outside the brain in a full-FOV 2D MRSI and whole-brain 3D echo planar spectroscopic imaging (EPSI).

THEORY AND METHODS

FLIP uses regularized least-squares regression based on spatial prior information from MRI to selectively remove lipid signals originating from the scalp and measure the brain metabolite signals with minimum cross contamination. FLIP is a noniterative approach, thus allowing a rapid processing speed, and uses only spatial information without any spectral priors. The performance of FLIP was compared with the Papoulis-Gerchberg algorithm (PGA), Hankel singular value decomposition (HSVD), and fast image reconstruction with L2 regularization (L2).

RESULTS

FLIP in both 2D and 3D MRSI resulted in consistent metabolite quantification in a greater number of voxels with less concentration variation than other algorithms, demonstrating effective and robust lipid-removal performance. The percentage of voxels that met quality criteria with FLIP, PGA, HSVD, and L2 processing were 90%, 57%, 29%, and 42% in 2D MRSI, and 80%, 75%, 76%, and 74% in 3D EPSI, respectively. The quantification results of full-FOV MRSI using FLIP were comparable to those of volume-localized MRSI, while allowing significantly increased spatial coverage. FLIP performed the fastest in 2D MRSI.

CONCLUSION

FLIP is a new lipid-removal algorithm that promises fast and effective lipid removal with improved volume coverage in MRSI.

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.

Accelerated MR spectroscopic imaging-a review of current and emerging techniques

Over more than 30 years in vivo MR spectroscopic imaging (MRSI) has undergone an enormous evolution from theoretical concepts in the early 1980s to the robust imaging technique that it is today. The development of both fast and efficient sampling and reconstruction techniques has played a fundamental role in this process. State-of-the-art MRSI has grown from a slow purely phase-encoded acquisition technique to a method that today combines the benefits of different acceleration techniques. These include shortening of repetition times, spatial-spectral encoding, undersampling of k-space and time domain, and use of spatial-spectral prior knowledge in the reconstruction. In this way in vivo MRSI has considerably advanced in terms of spatial coverage, spatial resolution, acquisition speed, artifact suppression, number of detectable metabolites and quantification precision. Acceleration not only has been the enabling factor in high-resolution whole-brain 1 H-MRSI, but today is also common in non-proton MRSI (31 P, 2 H and 13 C) and applied in many different organs. In this process, MRSI techniques had to constantly adapt, but have also benefitted from the significant increase of magnetic field strength boosting the signal-to-noise ratio along with high gradient fidelity and high-density receive arrays. In combination with recent trends in image reconstruction and much improved computation power, these advances led to a number of novel developments with respect to MRSI acceleration. Today MRSI allows for non-invasive and non-ionizing mapping of the spatial distribution of various metabolites' tissue concentrations in animals or humans, is applied for clinical diagnostics and has been established as an important tool for neuro-scientific and metabolism research. This review highlights the developments of the last five years and puts them into the context of earlier MRSI acceleration techniques. In addition to 1 H-MRSI it also includes other relevant nuclei and is not limited to certain body regions or specific applications.

Separation of Metabolites and Macromolecules for Short-TE 1H-MRSI Using Learned Component-Specific Representations

Short-echo-time (TE) proton magnetic resonance spectroscopic imaging (MRSI) allows for simultaneously mapping a number of molecules in the brain, and has been recognized as an important tool for studying in vivo biochemistry in various neuroscience and disease applications. However, separation of the metabolite and macromolecule (MM) signals present in the short-TE data with significant spectral overlaps remains a major technical challenge. This work introduces a new approach to solve this problem by integrating imaging physics and representation learning. Specifically, a mixed unsupervised and supervised learning-based strategy was developed to learn the metabolite and MM-specific low-dimensional representations using deep autoencoders. A constrained reconstruction formulation is proposed to integrate the MRSI spatiospectral encoding model and the learned representations as effective constraints for signal separation. An efficient algorithm was developed to solve the resulting optimization problem with provable convergence. Simulation and experimental results have been obtained to demonstrate the component-specific representation power of the learned models and the capability of the proposed method in separating metabolite and MM signals for practical short-TE [Formula: see text]-MRSI data.

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.

Dynamic hyperpolarized 13 C MR spectroscopic imaging using SPICE in mouse kidney at 9.4 T

This study aims to investigate the feasibility of dynamic hyperpolarized ¹³ C MR spectroscopic imaging (MRSI) using the SPectroscopic Imaging by exploiting spatiospectral CorrElation (SPICE) technique and an estimation of the spatially resolved conversion constant rate (k_pl ). An acquisition scheme comprising a single training dataset and several imaging datasets was proposed considering hyperpolarized ¹³ C circumstances. The feasibility and advantage of the scheme were investigated in two parts: (a) consistency of spectral basis over time and (b) accuracy of the estimated k_pl . The simulations and in vivo experiments support accurate k_pl estimation with consistent spectral bases. The proposed method was implemented in an enzyme phantom and via in vivo experiments. In the enzyme phantom experiments, spatially resolved homogeneous k_pl maps were observed. In the in vivo experiments, normal diet (ND) mice and high-fat diet (HFD) mice had k_pl (s^-1 ) values of medullar (ND: 0.0119 ± 0.0022, HFD: 0.0195 ± 0.0005) and cortical (ND: 0.0148 ±0.0023, HFD: 0.0224 ±0.0054) regions which were higher than vascular (ND: 0.0087 ±0.0013, HFD: 0.0132 ±0.0050) regions. In particular, the k_pl value in the medullar region exhibited a significant difference between the two diet groups. In summary, the feasibility of using modified SPICE for dynamic hyperpolarized ¹³ C MRSI was demonstrated via simulations and in vivo experiments. The consistency of spectral bases over time and the accuracy of the estimated k_pl values validate the proposed acquisition scheme, which comprises only a single training dataset. The proposed method improved the spatial resolution of dynamic hyperpolarized ¹³ C MRSI, which could be used for k_pl estimation using high signal-to-noise ratio spectral bases.

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.

DENOISING AND DEINTERLEAVING OF EPSI DATA USING STRUCTURED LOW-RANK MATRIX RECOVERY

Echo-planar spectroscopic imaging (EPSI) sequence with spectrally interleaving is often used to rapidly collect metabolic MRI data. The main problem in using it on high field scanners is the presence of spurious peaks resulting from phase distortions between interleaves as well as the low signal to noise ratio. We introduce a novel structured low-rank framework for the simultaneous denoising and deinterleaving of spectrally interleaved EPSI data. The proposed algorithm exploits annihilation relations resulting from the linear predicability of exponential signals as well as due to uncorrected phase relations between interleaves. The algorithm is formulated as a structured nuclear norm minimization of a block Hankel matrix, derived from the interleaves. Experiments using hyperpolarized 13 C mouse kidney EPSI data demonstrate the ability of the algorithm to remove ghost peaks from EPSI data collected using bipolar readout gradients.

Prior-knowledge Fitting of Accelerated Five-dimensional Echo Planar J-resolved Spectroscopic Imaging: Effect of Nonlinear Reconstruction on Quantitation

¹H Magnetic Resonance Spectroscopic imaging (SI) is a powerful tool capable of investigating metabolism in vivo from mul- tiple regions. However, SI techniques are time consuming, and are therefore difficult to implement clinically. By applying non-uniform sampling (NUS) and compressed sensing (CS) reconstruction, it is possible to accelerate these scans while re- taining key spectral information. One recently developed method that utilizes this type of acceleration is the five-dimensional echo planar J-resolved spectroscopic imaging (5D EP-JRESI) sequence, which is capable of obtaining two-dimensional (2D) spectra from three spatial dimensions. The prior-knowledge fitting (ProFit) algorithm is typically used to quantify 2D spectra in vivo, however the effects of NUS and CS reconstruction on the quantitation results are unknown. This study utilized a simulated brain phantom to investigate the errors introduced through the acceleration methods. Errors (normalized root mean square error >15%) were found between metabolite concentrations after twelve-fold acceleration for several low concentra- tion (<2 mM) metabolites. The Cramér Rao lower bound% (CRLB%) values, which are typically used for quality control, were not reflective of the increased quantitation error arising from acceleration. Finally, occipital white (OWM) and gray (OGM) human brain matter were quantified in vivo using the 5D EP-JRESI sequence with eight-fold acceleration.

High-resolution 1 H-MRSI of the brain using short-TE SPICE

PURPOSE

To improve signal-to-noise ratio (SNR) for high-resolution spectroscopic imaging using a subspace-based technique known as SPectroscopic Imaging by exploiting spatiospectral CorrElation (SPICE).

METHODS

The proposed method is based on a union-of-subspaces model of MRSI signals, which exploits the partial separability properties of water, lipid, baseline and metabolite signals. Enabled by this model, a special scheme is used for accelerated data acquisition, which includes a double-echo CSI component used to collect a "training" dataset (for determination of the basis functions) and a short-TE EPSI component used to collect a sparse "imaging" dataset (for determination of the overall spatiospectral distributions). A set of signal processing algorithms are developed to remove the water and lipid signals and jointly reconstruct the metabolite and baseline signals.

RESULTS

In vivo 1 H-MRSI results show that the proposed method can effectively remove the remaining water and lipid signals from sparse MRSI data acquired at 20 ms TE. Spatiospectral distributions of metabolite signals at 2 mm in-plane resolution with good SNR were obtained in a 15.5 min scan.

CONCLUSIONS

The proposed method can effectively remove nuisance signals and reconstruct high-resolution spatiospectral functions from sparse data to make short-TE SPICE possible. The method should prove useful for high-resolution 1 H-MRSI of the brain. Magn Reson Med 77:467-479, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Imaging based magnetic resonance spectroscopy (MRS) localization for quantitative neurochemical analysis and cerebral metabolism studies

Accurate quantitative metabolic imaging of the brain presents significant challenges due to the complexity and heterogeneity of its structures and compositions with distinct compartmentations of brain tissue types (e.g., gray and white matter). The brain is compartmentalized into various regions based on their unique functions and locations. In vivo magnetic resonance spectroscopy (MRS) techniques allow non-invasive measurements of neurochemicals in either single voxel or multiple voxels, yet the spatial resolution and detection sensitivity of MRS are significantly lower compared with MRI. A fundamentally different approach, namely spectral localization by imaging (SLIM) provides a new framework that overcomes major limitations of conventional MRS techniques. Conventional MRS allows only rectangular voxel shapes that do not conform to the shapes of brain structures or lesions, while SLIM allows compartments with arbitrary shapes. However, the restrictive assumption proposed in the original concept of SLIM, i.e., compartmental homogeneity, led to spectral localization errors, which have limited its broad applications. This review focuses on the recent technical frontiers of image-based MRS localization techniques that overcome the limitations of SLIM through the development and implementation of various new strategies, including incorporation of magnetic field inhomogeneity corrections, the use of multiple receiver coils, and prospective optimization of data acquisition.

Compartmentalized low-rank recovery for high-resolution lipid unsuppressed MRSI

PURPOSE

To introduce a novel algorithm for the recovery of high-resolution magnetic resonance spectroscopic imaging (MRSI) data with minimal lipid leakage artifacts, from dual-density spiral acquisition.

METHODS

The reconstruction of MRSI data from dual-density spiral data is formulated as a compartmental low-rank recovery problem. The MRSI dataset is modeled as the sum of metabolite and lipid signals, each of which is support limited to the brain and extracranial regions, respectively, in addition to being orthogonal to each other. The reconstruction problem is formulated as an optimization problem, which is solved using iterative reweighted nuclear norm minimization.

RESULTS

The comparisons of the scheme against dual-resolution reconstruction algorithm on numerical phantom and in vivo datasets demonstrate the ability of the scheme to provide higher spatial resolution and lower lipid leakage artifacts. The experiments demonstrate the ability of the scheme to recover the metabolite maps, from lipid unsuppressed datasets with echo time (TE) = 55 ms.

CONCLUSION

The proposed reconstruction method and data acquisition strategy provide an efficient way to achieve high-resolution metabolite maps without lipid suppression. This algorithm would be beneficial for fast metabolic mapping and extension to multislice acquisitions. Magn Reson Med 78:1267-1280, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Pilot Assessment of Brain Metabolism in Perinatally HIV-Infected Youths Using Accelerated 5D Echo Planar J-Resolved Spectroscopic Imaging

Purpose

To measure cerebral metabolite levels in perinatally HIV-infected youths and healthy controls using the accelerated five dimensional (5D) echo planar J-resolved spectroscopic imaging (EP-JRESI) sequence, which is capable of obtaining two dimensional (2D) J-resolved spectra from three spatial dimensions (3D).

Materials and Methods

After acquisition and reconstruction of the 5D EP-JRESI data, T₁-weighted MRIs were used to classify brain regions of interest for HIV patients and healthy controls: right frontal white (FW), medial frontal gray (FG), right basal ganglia (BG), right occipital white (OW), and medial occipital gray (OG). From these locations, respective J-resolved and TE-averaged spectra were extracted and fit using two different quantitation methods. The J-resolved spectra were fit using prior knowledge fitting (ProFit) while the TE-averaged spectra were fit using the advanced method for accurate robust and efficient spectral fitting (AMARES).

Results

Quantitation of the 5D EP-JRESI data using the ProFit algorithm yielded significant metabolic differences in two spatial locations of the perinatally HIV-infected youths compared to controls: elevated NAA/(Cr+Ch) in the FW and elevated Asp/(Cr+Ch) in the BG. Using the TE-averaged data quantified by AMARES, an increase of Glu/(Cr+Ch) was shown in the FW region. A strong negative correlation (r < -0.6) was shown between tCh/(Cr+Ch) quantified using ProFit in the FW and CD4 counts. Also, strong positive correlations (r > 0.6) were shown between Asp/(Cr+Ch) and CD4 counts in the FG and BG.

Conclusion

The complimentary results using ProFit fitting of J-resolved spectra and AMARES fitting of TE-averaged spectra, which are a subset of the 5D EP-JRESI acquisition, demonstrate an abnormal energy metabolism in the brains of perinatally HIV-infected youths. This may be a result of the HIV pathology and long-term combinational anti-retroviral therapy (cART). Further studies of larger perinatally HIV-infected cohorts are necessary to confirm these findings.

COMPARTMENTALIZED LOW-RANK REGULARIZATION WITH ORTHOGONALITY CONSTRAINTS FOR HIGH-RESOLUTION MRSI

We introduce a novel compartmental low rank algorithm for high resolution MR spectroscopic imaging. We model the field inhomogeneity compensated MRSI dataset as the sum of a lipid dataset and a metabolite dataset using the spatial compartmental information obtained from water reference data. Both these datasets are modeled as low-rank subspaces, and are assumed to be orthogonal to each other. We formulate the recovery of the dataset from spiral measurements as a low-rank recovery problem. Experiments using numerical phantom and in-vivo data demonstrates the ability of the algorithm to provide improved spatial resolution and nuisance signal free spectra.

Mechanisms of SNR and line shape improvement by B0 correction in overdiscrete MRSI reconstruction

PURPOSE

Inhomogeneities of the main magnetic field cause line broadening and location-dependent frequency shifts in brain MRSI. These are often visible despite advanced B₀ shimming. The purpose of this work is to propose an advanced B₀ correction method that can easily be applied during postprocessing.

METHODS

A target-driven overdiscrete reconstruction method previously introduced for MRSI is modified by dividing it into two steps. In a first step, an intermediate spectroscopic image with arbitrarily high resolution is generated, on which B₀ correction is performed as an additional processing step based on an additionally acquired B₀ map. This frequency-aligns metabolite peaks and destroys noise correlations between neighboring subvoxels. Second, the voxel is shaped by application of the spatial response target. The method was tested with simulated spectroscopic imaging data as well as in a series of MRSI data sets obtained from four healthy volunteers at 7T.

RESULTS

A systematic gain in spectral signal-to-noise ratio is achieved, due to spatial averaging now occurring over peak aligned and noise decorrelated subvoxel spectra. At the same time, metabolite peak line widths are reduced.

CONCLUSION

In the presence of B₀ inhomogeneities across the field of view, the proposed method offers the potential to improve spectral quality with only a minimal additional effort during acquisition. Magn Reson Med 77:44-56, 2017. © 2015 Wiley Periodicals, Inc.

Magnetic resonance spectroscopic imaging at superresolution: Overview and perspectives

The notion of non-invasive, high-resolution spatial mapping of metabolite concentrations has long enticed the medical community. While magnetic resonance spectroscopic imaging (MRSI) is capable of achieving the requisite spatio-spectral localization, it has traditionally been encumbered by significant resolution constraints that have thus far undermined its clinical utility. To surpass these obstacles, research efforts have primarily focused on hardware enhancements or the development of accelerated acquisition strategies to improve the experimental sensitivity per unit time. Concomitantly, a number of innovative reconstruction techniques have emerged as alternatives to the standard inverse discrete Fourier transform (DFT). While perhaps lesser known, these latter methods strive to effect commensurate resolution gains by exploiting known properties of the underlying MRSI signal in concert with advanced image and signal processing techniques. This review article aims to aggregate and provide an overview of the past few decades of so-called "superresolution" MRSI reconstruction methodologies, and to introduce readers to current state-of-the-art approaches. A number of perspectives are then offered as to the future of high-resolution MRSI, with a particular focus on translation into clinical settings.

Sparse spectral deconvolution algorithm for noncartesian MR spectroscopic imaging

PURPOSE

To minimize line shape distortions and spectral leakage artifacts in MR spectroscopic imaging (MRSI).

METHODS

A spatially and spectrally regularized non-Cartesian MRSI algorithm that uses the line shape distortion priors, estimated from water reference data, to deconvolve the spectra is introduced. Sparse spectral regularization is used to minimize noise amplification associated with deconvolution. A spiral MRSI sequence that heavily oversamples the central k-space regions is used to acquire the MRSI data. The spatial regularization term uses the spatial supports of brain and extracranial fat regions to recover the metabolite spectra and nuisance signals at two different resolutions. Specifically, the nuisance signals are recovered at the maximum resolution to minimize spectral leakage, while the point spread functions of metabolites are controlled to obtain acceptable signal-to-noise ratio.

RESULTS

The comparisons of the algorithm against Tikhonov regularized reconstructions demonstrates considerably reduced line-shape distortions and improved metabolite maps.

CONCLUSION

The proposed sparsity constrained spectral deconvolution scheme is effective in minimizing the line-shape distortions. The dual resolution reconstruction scheme is capable of minimizing spectral leakage artifacts.

Off-the-Grid Recovery of Piecewise Constant Images from Few Fourier Samples

We introduce a method to recover a continuous domain representation of a piecewise constant two-dimensional image from few low-pass Fourier samples. Assuming the edge set of the image is localized to the zero set of a trigonometric polynomial, we show the Fourier coefficients of the partial derivatives of the image satisfy a linear annihilation relation. We present necessary and sufficient conditions for unique recovery of the image from finite low-pass Fourier samples using the annihilation relation. We also propose a practical two-stage recovery algorithm which is robust to model-mismatch and noise. In the first stage we estimate a continuous domain representation of the edge set of the image. In the second stage we perform an extrapolation in Fourier domain by a least squares two-dimensional linear prediction, which recovers the exact Fourier coefficients of the underlying image. We demonstrate our algorithm on the super-resolution recovery of MRI phantoms and real MRI data from low-pass Fourier samples, which shows benefits over standard approaches for single-image super-resolution MRI.

High-resolution (1) H-MRSI of the brain using SPICE: Data acquisition and image reconstruction

PURPOSE

To develop data acquisition and image reconstruction methods to enable high-resolution (1) H MR spectroscopic imaging (MRSI) of the brain, using the recently proposed subspace-based spectroscopic imaging framework called SPICE (SPectroscopic Imaging by exploiting spatiospectral CorrElation).

THEORY AND METHODS

SPICE is characterized by the use of a subspace model for both data acquisition and image reconstruction. For data acquisition, we propose a novel spatiospectral encoding scheme that provides hybrid data sets for determining the subspace structure and for image reconstruction using the subspace model. More specifically, we use a hybrid chemical shift imaging /echo-planar spectroscopic imaging sequence for two-dimensional (2D) MRSI and a dual-density, dual-speed echo-planar spectroscopic imaging sequence for three-dimensional (3D) MRSI. For image reconstruction, we propose a method that can determine the subspace structure and the high-resolution spatiospectral reconstruction from the hybrid data sets generated by the proposed sequences, incorporating field inhomogeneity correction and edge-preserving regularization.

RESULTS

Phantom and in vivo brain experiments were performed to evaluate the performance of the proposed method. For 2D MRSI experiments, SPICE is able to produce high-SNR spatiospectral distributions with an approximately 3 mm nominal in-plane resolution from a 10-min acquisition. For 3D MRSI experiments, SPICE is able to achieve an approximately 3 mm in-plane and 4 mm through-plane resolution in about 25 min.

CONCLUSION

Special data acquisition and reconstruction methods have been developed for high-resolution (1) H-MRSI of the brain using SPICE. Using these methods, SPICE is able to produce spatiospectral distributions of (1) H metabolites in the brain with high spatial resolution, while maintaining a good SNR. These capabilities should prove useful for practical applications of SPICE. Magn Reson Med 76:1059-1070, 2016. © 2015 Wiley Periodicals, Inc.

Improved image reconstruction for subspace-based spectroscopic imaging using non-quadratic regularization

A new MR spectroscopic imaging method, called SPICE (SPectroscopic Imaging by exploiting spatiospectral CorrElation), has been recently proposed to enable high-resolution metabolic imaging with good SNR. A key problem within the SPICE framework is image reconstruction from a very noisy and sparsely sampled dataset. This paper addresses this problem by integrating the low-rank model used in SPICE reconstruction with a non-quadratic regularization. An efficient primal-dual based algorithm is described to solve the associated optimization problem. The proposed method has been validated using both simulation and phantom studies and is expected to enhance the unprecedented capability of SPICE for high-resolution metabolic imaging.

Improved Low-Rank Filtering of Magnetic Resonance Spectroscopic Imaging Data Corrupted by Noise and B₀ Field Inhomogeneity

GOAL

To improve the signal-to-noise ratio (SNR) of magnetic resonance spectroscopic imaging (MRSI) data.

METHODS

A low-rank filtering method recently proposed for denoising MRSI data is extended by: 1) incorporating tissue boundary constraints to enable local low-rank filtering, and 2) integrating B0 field inhomogeneity correction by rank-minimization to make the low-rank model more effective.

RESULTS

The proposed method was validated using both simulated and in vivo MRSI data. Its denoising performance is also compared with an upper bound based on the constrained Cramér-Rao lower bound for low-rank filtering.

CONCLUSION

Low-rank filtering can effectively improve the SNR of MRSI data corrupted by both noise and B0 field inhomogeneity.

SIGNIFICANCE

The proposed low-rank filtering method will enhance the practical utility of high-resolution MRSI, where SNR has been a limiting factor.

Accelerated five-dimensional echo planar J-resolved spectroscopic imaging: Implementation and pilot validation in human brain

PURPOSE

To implement an accelerated five-dimensional (5D) echo-planar J-resolved spectroscopic imaging sequence combining 3 spatial and 2 spectral encoding dimensions and to apply the sequence in human brain.

METHODS

An echo planar readout was used to acquire a single spatial and a single spectral dimension during one readout. Nonuniform sampling was applied to the two phase-encoded spatial directions and the indirect spectral dimension. Nonlinear reconstruction was used to minimize the ℓ1-norm or the total variation and included a spectral mask to enhance sparsity. Retrospective reconstructions at multiple undersamplings were performed in phantom. Ten healthy volunteers were scanned with 8× undersampling and compared to a fully sampled single slice scan.

RESULTS

Retrospective reconstruction of fully sampled phantom data showed excellent quality at 4×, 8×, 12×, and 16× undersampling using either reconstruction method. Reconstruction of prospectively acquired in vivo scans with 8× undersampling showed excellent quality in the occipito-parietal lobes and good quality in the frontal lobe, consistent with the fully sampled single slice scan.

CONCLUSION

By utilizing nonuniform sampling with nonlinear reconstruction, 2D J-resolved spectra can be acquired over a 3D spatial volume with a total scan time of 20 min, which is reasonable for in vivo studies.

Anatomically weighted second-order total variation reconstruction of 23Na MRI using prior information from 1H MRI

Sodium ((23)Na) MRI is a noninvasive tool to assess cell viability, which is linked to the total tissue sodium concentration (TSC). However, due to low in vivo concentrations, (23)Na MRI suffers from low signal-to-noise ratio (SNR) and limited spatial resolution. As a result, image quality is compromised by Gibbs ringing artifacts and partial volume effects. An iterative reconstruction algorithm that incorporates prior information from (1)H MRI is developed to reduce partial volume effects and to increase the SNR in non-proton MRI. Anatomically weighted second-order total variation (AnaWeTV) is proposed as a constraint for compressed sensing reconstruction of 3D projection reconstruction (3DPR) data. The method is evaluated in simulations and a MR measurement of a multiple sclerosis (MS) patient by comparing it to gridding and other reconstruction techniques. AnaWeTV increases resolution of known structures and reduces partial volume effects. In simulated MR brain data (nominal resolution Δx(3) = 3 × 3 × 3 mm(3)), the intensity error of four small MS lesions was reduced from (6.9 ± 3.8)% (gridding) to (2.8 ± 1.4)% (AnaWeTV with T2-weighted reference images). Compared to gridding, a substantial SNR increase of 130% was found in the white matter of the MS patient. The algorithm is robust against misalignment of the prior information on the order of the (23)Na image resolution. Features without prior information are still reconstructed with high contrast. AnaWeTV allows a more precise quantification of TSC in structures with prior knowledge. Thus, the AnaWeTV algorithm is in particular beneficial for the assessment of tissue structures that are visible in both (23)Na and (1)H MRI.

Accelerated 1 H MRSI using randomly undersampled spiral-based k-space trajectories

PURPOSE

To develop and evaluate the performance of an acquisition and reconstruction method for accelerated MR spectroscopic imaging (MRSI) through undersampling of spiral trajectories.

THEORY AND METHODS

A randomly undersampled spiral acquisition and sensitivity encoding (SENSE) with total variation (TV) regularization, random SENSE+TV, is developed and evaluated on single-slice numerical phantom, in vivo single-slice MRSI, and in vivo three-dimensional (3D)-MRSI at 3 Tesla. Random SENSE+TV was compared with five alternative methods for accelerated MRSI.

RESULTS

For the in vivo single-slice MRSI, random SENSE+TV yields up to 2.7 and 2 times reduction in root-mean-square error (RMSE) of reconstructed N-acetyl aspartate (NAA), creatine, and choline maps, compared with the denoised fully sampled and uniformly undersampled SENSE+TV methods with the same acquisition time, respectively. For the in vivo 3D-MRSI, random SENSE+TV yields up to 1.6 times reduction in RMSE, compared with uniform SENSE+TV. Furthermore, by using random SENSE+TV, we have demonstrated on the in vivo single-slice and 3D-MRSI that acceleration factors of 4.5 and 4 are achievable with the same quality as the fully sampled data, as measured by RMSE of reconstructed NAA map, respectively.

CONCLUSION

With the same scan time, random SENSE+TV yields lower RMSEs of metabolite maps than other methods evaluated. Random SENSE+TV achieves up to 4.5-fold acceleration with comparable data quality as the fully sampled acquisition. Magn Reson Med 74:13-24, 2015. © 2014 Wiley Periodicals, Inc.

Mean square optimal NUFFT approximation for efficient non-Cartesian MRI reconstruction

The fast evaluation of the discrete Fourier transform of an image at non-uniform sampling locations is key to efficient iterative non-Cartesian MRI reconstruction algorithms. Current non-uniform fast Fourier transform (NUFFT) approximations rely on the interpolation of oversampled uniform Fourier samples. The main challenge is high memory demand due to oversampling, especially when multidimensional datasets are involved. The main focus of this work is to design an NUFFT algorithm with minimal memory demands. Specifically, we introduce an analytical expression for the expected mean square error in the NUFFT approximation based on our earlier work. We then introduce an iterative algorithm to design the interpolator and scale factors. Experimental comparisons show that the proposed optimized NUFFT scheme provides considerably lower approximation errors than the previous designs [1] that rely on worst case error metrics. The improved approximations are also seen to considerably reduce the errors and artifacts in non-Cartesian MRI reconstruction.

A subspace approach to high-resolution spectroscopic imaging

PURPOSE

To accelerate spectroscopic imaging using sparse sampling of (k,t)-space and subspace (or low-rank) modeling to enable high-resolution metabolic imaging with good signal-to-noise ratio.

METHODS

The proposed method, called SPectroscopic Imaging by exploiting spatiospectral CorrElation, exploits a unique property known as partial separability of spectroscopic signals. This property indicates that high-dimensional spectroscopic signals reside in a very low-dimensional subspace and enables special data acquisition and image reconstruction strategies to be used to obtain high-resolution spatiospectral distributions with good signal-to-noise ratio. More specifically, a hybrid chemical shift imaging/echo-planar spectroscopic imaging pulse sequence is proposed for sparse sampling of (k,t)-space, and a low-rank model-based algorithm is proposed for subspace estimation and image reconstruction from sparse data with the capability to incorporate prior information and field inhomogeneity correction.

RESULTS

The performance of the proposed method has been evaluated using both computer simulations and phantom studies, which produced very encouraging results. For two-dimensional spectroscopic imaging experiments on a metabolite phantom, a factor of 10 acceleration was achieved with a minimal loss in signal-to-noise ratio compared to the long chemical shift imaging experiments and with a significant gain in signal-to-noise ratio compared to the accelerated echo-planar spectroscopic imaging experiments.

CONCLUSION

The proposed method, SPectroscopic Imaging by exploiting spatiospectral CorrElation, is able to significantly accelerate spectroscopic imaging experiments, making high-resolution metabolic imaging possible.

Data-driven MRSI spectral localization via low-rank component analysis

Magnetic resonance spectroscopic imaging (MRSI) is a powerful tool capable of providing spatially localized maps of metabolite concentrations. Its utility, however, is often depreciated by spectral leakage artifacts resulting from low spatial resolution measurements through an effort to reduce acquisition times. Though model-based techniques can help circumvent these drawbacks, they require strong prior knowledge, and can introduce additional artifacts when the underlying models are inaccurate. We introduce a novel scheme in which a generative model is estimated from the raw MRSI data via a regularized variational framework that minimizes the model approximation error within a measurement-prescribed subspace. As additional a priori information, our approach relies only upon a measured field inhomogeneity map at high spatial resolution. We demonstrate the feasibility of our approach on both synthetic and experimental data.

Interpolated compressed sensing for 2D multiple slice fast MR imaging

Sparse MRI has been introduced to reduce the acquisition time and raw data size by undersampling the k-space data. However, the image quality, particularly the contrast to noise ratio (CNR), decreases with the undersampling rate. In this work, we proposed an interpolated Compressed Sensing (iCS) method to further enhance the imaging speed or reduce data size without significant sacrifice of image quality and CNR for multi-slice two-dimensional sparse MR imaging in humans. This method utilizes the k-space data of the neighboring slice in the multi-slice acquisition. The missing k-space data of a highly undersampled slice are estimated by using the raw data of its neighboring slice multiplied by a weighting function generated from low resolution full k-space reference images. In-vivo MR imaging in human feet has been used to investigate the feasibility and the performance of the proposed iCS method. The results show that by using the proposed iCS reconstruction method, the average image error can be reduced and the average CNR can be improved, compared with the conventional sparse MRI reconstruction at the same undersampling rate.

Lipid suppression in CSI with spatial priors and highly undersampled peripheral k-space

Mapping 1H brain metabolites using chemical shift imaging is hampered by the presence of subcutaneous lipid signals, which contaminate the metabolites by ringing due to limited spatial resolution. Even though chemical shift imaging at spatial resolution high enough to mitigate the lipid artifacts is infeasible due to signal-to-noise constraints on the metabolites, the lipid signals have orders of magnitude of higher concentration, which enables the collection of high-resolution lipid maps with adequate signal-to-noise. The previously proposed dual-density approach exploits this high signal-to-noise property of the lipid layer to suppress truncation artifacts using high-resolution lipid maps. Another recent approach for lipid suppression makes use of the fact that metabolite and lipid spectra are approximately orthogonal, and seeks sparse metabolite spectra when projected onto lipid-basis functions. This work combines and extends the dual-density approach and the lipid-basis penalty, while estimating the high-resolution lipid image from 2-average k-space data to incur minimal increase on the scan time. Further, we exploit the spectral-spatial sparsity of the lipid ring and propose to estimate it from substantially undersampled (acceleration R=10 in the peripheral k-space) 2-average in vivo data using compressed sensing and still obtain improved lipid suppression relative to using dual-density or lipid-basis penalty alone.

Quantitative proton magnetic resonance spectroscopy and spectroscopic imaging of the brain: a didactic review

This article presents background information related to methodology for estimating brain metabolite concentration from magnetic resonance spectroscopy (MRS) and magnetic resonance spectroscopic imaging measurements of living human brain tissue. It reviews progress related to this methodology, with emphasis placed on progress reported during the past 10 years. It is written for a target audience composed of radiologists and magnetic resonance imaging technologists. It describes in general terms the relationship between MRS signal amplitude and concentration. It then presents an overview of the many practical problems associated with deriving concentration solely from absolute measured signal amplitudes and demonstrates how a various signal calibration approaches can be successfully used. The concept of integrated signal amplitude is presented with examples that are helpful for qualitative reading of MRS data as well as for understanding the methodology used for quantitative measurements. The problems associated with the accurate measurement of individual signal amplitudes in brain spectra having overlapping signals from other metabolites and overlapping nuisance signals from water and lipid are presented. Current approaches to obtaining accurate amplitude estimates with least-squares fitting software are summarized.