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

A Fast Patch-Based Hankel Low-Rank Method for Magnetic Resonance Spectroscopy Reconstruction

Sparse sampling is an effective strategy for accelerating the acquisition of multi-dimensional magnetic resonance spectroscopy (MRS), crucial in disciplines such as chemistry and structural biology. The state-of-the-art low-rank reconstruction methods enable the high-fidelity recovery of sparsely-sampled MRS but are limited by lengthy reconstruction times, posing a significant challenge. In this work, we introduce a novel approach that significantly reduces the dimensionality of the constructed low-rank Hankel-like matrix. This reduction leads to lower computational complexity and, as a result, a substantial acceleration in reconstruction times compared to conventional low-rank methods. Experimental evaluations on both simulated and real MRS demonstrate that our method achieves a reduction in reconstruction times by over fourfold without sacrificing the quality of spectrum reconstructions.

Multi-Parametric Molecular Imaging of the Brain Using Optimized Multi-TE Subspace MRSI

OBJECTIVE

To develop a novel multi-TE MR spectroscopic imaging (MRSI) approach to enable label-free, simultaneous, high-resolution mapping of several molecules and their biophysical parameters in the brain.

METHODS

The proposed method uniquely integrated an augmented molecular-component-specific subspace model for multi-TE 1H-MRSI signals, an estimation-theoretic experiment optimization (nonuniform TE selection) for molecule separation and parameter estimation, a physics-driven subspace learning strategy for spatiospectral reconstruction and molecular quantification, and a new accelerated multi-TE MRSI acquisition for generating high-resolution data in clinically relevant times. Numerical studies, phantom and in vivo experiments were conducted to validate the optimized experiment design and demonstrate the imaging capability offered by the proposed method.

RESULTS

The proposed TE optimization improved estimation of metabolites, neurotransmitters and their T2's over conventional TE choices, e.g., reducing variances of neurotransmitter concentration by  ∼  40% and metabolite T2 by  ∼  60%. Simultaneous metabolite and neurotransmitter mapping of the brain can be achieved at a nominal resolution of 3.4 × 3.4 × 6.4 mm 3. High-resolution, 3D metabolite T2 mapping was made possible for the first time. The translational potential of the proposed method was demonstrated by mapping biochemical abnormality in a post-traumatic epilepsy (PTE) patient.

CONCLUSION

The feasibility for high-resolution mapping of metabolites/neurotransmitters and metabolite T2's within clinically relevant time was demonstrated. We expect our method to offer richer information for revealing and understanding metabolic alterations in neurological diseases.

SIGNIFICANCE

A novel multi-TE MRSI approach was presented that enhanced the technological capability of multi-parametric molecular imaging of the brain. The proposed method presents new technology development and application opportunities for providing richer molecular level information to uncover and comprehend metabolic changes relevant in various neurological applications.

A Sparse Model-Inspired Deep Thresholding Network for Exponential Signal Reconstruction-Application in Fast Biological Spectroscopy

The nonuniform sampling (NUS) is a powerful approach to enable fast acquisition but requires sophisticated reconstruction algorithms. Faithful reconstruction from partially sampled exponentials is highly expected in general signal processing and many applications. Deep learning (DL) has shown astonishing potential in this field, but many existing problems, such as lack of robustness and explainability, greatly limit its applications. In this work, by combining the merits of the sparse model-based optimization method and data-driven DL, we propose a DL architecture for spectra reconstruction from undersampled data, called MoDern. It follows the iterative reconstruction in solving a sparse model to build the neural network, and we elaborately design a learnable soft-thresholding to adaptively eliminate the spectrum artifacts introduced by undersampling. Extensive results on both synthetic and biological data show that MoDern enables more robust, high-fidelity, and ultrafast reconstruction than the state-of-the-art methods. Remarkably, MoDern has a small number of network parameters and is trained on solely synthetic data while generalizing well to biological data in various scenarios. Furthermore, we extend it to an open-access and easy-to-use cloud computing platform (XCloud-MoDern), contributing a promising strategy for further development of biological applications.

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.

Resolution enhancement of NMR by decoupling with the low-rank Hankel model

Nuclear magnetic resonance (NMR) spectroscopy has become a formidable tool for biochemistry and medicine. Although J-coupling carries essential structural information it may also limit the spectral resolution. Homonuclear decoupling remains a challenging problem. In this work, we introduce a new approach that uses a specific coupling value as prior knowledge, and the Hankel property of the exponential NMR signal to achieve broadband heteronuclear decoupling using the low-rank method. Our results on synthetic and realistic HMQC spectra demonstrate that the proposed method not only effectively enhances resolution by decoupling, but also maintains sensitivity and suppresses spectral artefacts. The approach can be combined with non-uniform sampling, which means that the resolution can be further improved without any extra acquisition time.

High-resolution, 3D multi-TE 1 H MRSI using fast spatiospectral encoding and subspace imaging

PURPOSE

To develop a novel method to achieve fast, high-resolution, 3D multi-TE ¹ H-MRSI of the brain.

METHODS

A new multi-TE MRSI acquisition strategy was developed that integrates slab selective excitation with adiabatic refocusing for better volume coverage, rapid spatiospectral encoding, sparse multi-TE sampling, and interleaved water navigators for field mapping and calibration. Special data processing strategies were developed to interpolate the sparsely sampled data, remove nuisance signals, and reconstruct multi-TE spatiospectral distributions with high SNR. Phantom and in vivo experiments have been carried out to demonstrate the capability of the proposed method.

RESULTS

The proposed acquisition can produce multi-TE ¹ H-MRSI data with three TEs at a nominal spatial resolution of 3.4 × 3.4 × 5.3 mm³ in around 20 min. High-SNR brain metabolite spatiospectral reconstructions can be obtained from both a metabolite phantom and in vivo experiments by the proposed method.

CONCLUSION

High-resolution, 3D multi-TE ¹ H-MRSI of the brain can be achieved within clinically feasible time. This capability, with further optimizations, could be translated to clinical applications and neuroscience studies where simultaneously mapping metabolites and neurotransmitters and TE-dependent molecular spectral changes are of interest.

Coil Combination of Multichannel Single Voxel Magnetic Resonance Spectroscopy with Repeatedly Sampled In Vivo Data

Magnetic resonance spectroscopy (MRS), as a noninvasive method for molecular structure determination and metabolite detection, has grown into a significant tool in clinical applications. However, the relatively low signal-to-noise ratio (SNR) limits its further development. Although the multichannel coil and repeated sampling are commonly used to alleviate this problem, there is still potential room for promotion. One possible improvement way is combining these two acquisition methods so that the complementary of them can be well utilized. In this paper, a novel coil-combination method, average smoothing singular value decomposition, is proposed to further improve the SNR by introducing repeatedly sampled signals into multichannel coil combination. Specifically, the sensitivity matrix of each sampling was pretreated by whitened singular value decomposition (WSVD), then the smoothing was performed along the repeated samplings’ dimension. By comparing with three existing popular methods, Brown, WSVD, and generalized least squares, the proposed method showed better performance in one phantom and 20 in vivo spectra.

Deep learning can accelerate and quantify simulated localized correlated spectroscopy

Nuclear magnetic resonance spectroscopy (MRS) allows for the determination of atomic structures and concentrations of different chemicals in a biochemical sample of interest. MRS is used in vivo clinically to aid in the diagnosis of several pathologies that affect metabolic pathways in the body. Typically, this experiment produces a one dimensional (1D) 1H spectrum containing several peaks that are well associated with biochemicals, or metabolites. However, since many of these peaks overlap, distinguishing chemicals with similar atomic structures becomes much more challenging. One technique capable of overcoming this issue is the localized correlated spectroscopy (L-COSY) experiment, which acquires a second spectral dimension and spreads overlapping signal across this second dimension. Unfortunately, the acquisition of a two dimensional (2D) spectroscopy experiment is extremely time consuming. Furthermore, quantitation of a 2D spectrum is more complex. Recently, artificial intelligence has emerged in the field of medicine as a powerful force capable of diagnosing disease, aiding in treatment, and even predicting treatment outcome. In this study, we utilize deep learning to: (1) accelerate the L-COSY experiment and (2) quantify L-COSY spectra. All training and testing samples were produced using simulated metabolite spectra for chemicals found in the human body. We demonstrate that our deep learning model greatly outperforms compressed sensing based reconstruction of L-COSY spectra at higher acceleration factors. Specifically, at four-fold acceleration, our method has less than 5% normalized mean squared error, whereas compressed sensing yields 20% normalized mean squared error. We also show that at low SNR (25% noise compared to maximum signal), our deep learning model has less than 8% normalized mean squared error for quantitation of L-COSY spectra. These pilot simulation results appear promising and may help improve the efficiency and accuracy of L-COSY experiments in the future.

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.

Review and Prospect: Deep Learning in Nuclear Magnetic Resonance Spectroscopy

Since the concept of deep learning (DL) was formally proposed in 2006, it has had a major impact on academic research and industry. Nowadays, DL provides an unprecedented way to analyze and process data with demonstrated great results in computer vision, medical imaging, natural language processing, and so forth. Herein, applications of DL in NMR spectroscopy are summarized, and a perspective for DL as an entirely new approach that is likely to transform NMR spectroscopy into a much more efficient and powerful technique in chemistry and life sciences is outlined.

Accelerated Nuclear Magnetic Resonance Spectroscopy with Deep Learning

Nuclear magnetic resonance (NMR) spectroscopy serves as an indispensable tool in chemistry and biology but often suffers from long experimental times. We present a proof-of-concept of the application of deep learning and neural networks for high-quality, reliable, and very fast NMR spectra reconstruction from limited experimental data. We show that the neural network training can be achieved using solely synthetic NMR signals, which lifts the prohibiting demand for a large volume of realistic training data usually required for a deep learning approach.

Phase-constrained reconstruction of high-resolution multi-shot diffusion weighted image

Diffusion weighted imaging (DWI) is a unique examining method in tumor diagnosis, acute stroke evaluation. Single-shot echo planar imaging is currently conventional method for DWI. However, single-shot DWI suffers from image distortion, blurring and low spatial resolution. Although multi-shot DWI improves image resolution, it brings phase variations among different shots at the same time. In this paper, we introduce a smooth phase constraint of each shot image into multi-shot navigator-free DWI reconstruction by imposing the low-rankness of Hankel matrix constructed from the k-space data. Furthermore, we exploit the partial sum minimization of singular values to constrain the low-rankness of Hankel matrix. Results on brain imaging data show that the proposed method outperforms the state-of-the-art methods in terms of artifacts removal and our method potentially has the ability to reconstruct high number of shot of DWI.

Compressed Ultrasound Signal Reconstruction Using a Low-Rank and Joint-Sparse Representation Model

With the introduction of very dense sensor arrays in ultrasound (US) imaging, data transfer rate and data storage can become a bottleneck in US system design. To reduce the amount of sampled channel data, we propose a new approach based on the low-rank and joint-sparse model that allows us to exploit the correlations between different US channels and transmissions. With this method, the minimum number of measurements at each channel can be lower than the sparsity in compressive sensing theory. The accuracy of the reconstruction is less dependent on the sparse basis. An optimization algorithm based on the simultaneous direction method of multipliers is proposed to efficiently solve the resulting optimization problem. Results on different data sets with different experimental settings show that the proposed method is better adapted to the US signals and can recover the image with fewer samples (e.g., 10% of the samples) than the existing compressive sensing-based methods, while maintaining reasonable 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.