High-fidelity intravoxel incoherent motion parameter mapping using locally low-rank and subspace modeling.

PURPOSE: Intravoxel incoherent motion (IVIM) is a quantitative magnetic resonance imaging (MRI) method used to quantify perfusion properties of tissue non-invasively without contrast. However, clinical applications are limited by unreliable parameter estimates, particularly for the perfusion fraction (f) and pseudodiffusion coefficient (D*). This study aims to develop a high-fidelity reconstruction for reliable estimation of IVIM parameters. The proposed method is versatile and amenable to various acquisition schemes and fitting methods. METHODS: To address current challenges with IVIM, we adapted several advanced reconstruction techniques. We used a low-rank approximation of IVIM images and temporal subspace modeling to constrain the magnetization dynamics of the bi-exponential diffusion signal decay. In addition, motion-induced phase variations were corrected between diffusion directions and b-values, facilitating the use of high SNR real-valued diffusion data. The proposed method was evaluated in simulations and in vivo brain acquisitions in six healthy subjects and six individuals with a history of SARS-CoV-2 infection and compared with the conventionally reconstructed magnitude data. Following reconstruction, IVIM parameters were estimated voxel-wise. RESULTS: Our proposed method reduced noise contamination in simulations, resulting in a 60%, 58.9%, and 83.9% reduction in the NRMSE for D, f, and D*, respectively, compared to the conventional reconstruction. In vivo, anisotropic properties of D, f, and D* were preserved with the proposed method, highlighting microvascular differences in gray matter between individuals with a history of COVID-19 and those without (p = 0.0210), which wasn't observed with the conventional reconstruction. CONCLUSION: The proposed method yielded a more reliable estimation of IVIM parameters with less noise than the conventional reconstruction. Further, the proposed method preserved anisotropic properties of IVIM parameter estimates and demonstrated differences in microvascular perfusion in COVID-affected subjects, which weren't observed with conventional reconstruction methods.

Accelerating T2 mapping of the brain by integrating deep learning priors with low-rank and sparse modeling.

PURPOSE: To accelerate T2 mapping with highly sparse sampling by integrating deep learning image priors with low-rank and sparse modeling. METHODS: The proposed method achieves high-speed T2 mapping by highly sparsely sampling (k, TE)-space. Image reconstruction from the undersampled data was done by exploiting the low-rank structure and sparsity in the T2 -weighted image sequence and image priors learned from training data. The image priors for a single TE were generated from the public Human Connectome Project data using a tissue-based deep learning method; the image priors were then transferred to other TEs using a generalized series-based method. With these image priors, the proposed reconstruction method used a low-rank model and a sparse model to capture subject-dependent novel features. RESULTS: The proposed method was evaluated using experimental data obtained from both healthy subjects and tumor patients using a turbo spin-echo sequence. High-quality T2 maps at the resolution of 0.9 × 0.9 × 3.0 mm3 were obtained successfully from highly undersampled data with an acceleration factor of 8. Compared with the existing compressed sensing-based methods, the proposed method produced significantly reduced reconstruction errors. Compared with the deep learning-based methods, the proposed method recovered novel features better. CONCLUSION: This paper demonstrates the feasibility of learning T2 -weighted image priors for multiple TEs using tissue-based deep learning and generalized series-based learning. A new method was proposed to effectively integrate these image priors with low-rank and sparse modeling to reconstruct high-quality images from highly undersampled data. The proposed method will supplement other acquisition-based methods to achieve high-speed T2 mapping.

[High quality reconstruction algorithm for cardiac magnetic resonance images based on multiscale low rank modeling].

Taking advantages of the sparsity or compressibility inherent in real world signals, compressed sensing (CS) can collect compressed data at the sampling rate much lower than that needed in Shannon's theorem. The combination of CS and low rank modeling is used to medical imaging techniques to increase the scanning speed of cardiac magnetic resonance (CMR), alleviate the patients' suffering and improve the images quality. The alternating direction method of multipliers (ADMM) algorithm is proposed for multiscale low rank matrix decomposition of CMR images. The algorithm performance is evaluated quantitatively by the peak signal to noise ratio (PSNR) and relative l 2 norm error (RLNE), with the human visual system and the local region magnification as the qualitative comparison. Compared to L + S, kt FOCUSS, k-t SPARSE SENSE algorithms, experimental results demonstrate that the proposed algorithm can achieve the best performance indices, and maintain the most detail features and edge contours. The proposed algorithm can encourage the development of fast imaging techniques, and improve the diagnoses values of CMR in clinical applications.

Improved magnetic resonance fingerprinting reconstruction with low-rank and subspace modeling.

PURPOSE: This article introduces a constrained imaging method based on low-rank and subspace modeling to improve the accuracy and speed of MR fingerprinting (MRF). THEORY AND METHODS: A new model-based imaging method is developed for MRF to reconstruct high-quality time-series images and accurate tissue parameter maps (e.g., T1 , T2 , and spin density maps). Specifically, the proposed method exploits low-rank approximations of MRF time-series images, and further enforces temporal subspace constraints to capture magnetization dynamics. This allows the time-series image reconstruction problem to be formulated as a simple linear least-squares problem, which enables efficient computation. After image reconstruction, tissue parameter maps are estimated via dictionary-based pattern matching, as in the conventional approach. RESULTS: The effectiveness of the proposed method was evaluated with in vivo experiments. Compared with the conventional MRF reconstruction, the proposed method reconstructs time-series images with significantly reduced aliasing artifacts and noise contamination. Although the conventional approach exhibits some robustness to these corruptions, the improved time-series image reconstruction in turn provides more accurate tissue parameter maps. The improvement is pronounced especially when the acquisition time becomes short. CONCLUSIONS: The proposed method significantly improves the accuracy of MRF, and also reduces data acquisition time. Magn Reson Med 79:933-942, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Real-time phase-contrast flow cardiovascular magnetic resonance with low-rank modeling and parallel imaging.

BACKGROUND: Conventional phase-contrast cardiovascular magnetic resonance (PC-CMR) employs cine-based acquisitions to assess blood flow condition, in which electro-cardiogram (ECG) gating and respiration control are generally required. This often results in lower acquisition efficiency, and limited utility in the presence of cardiovascular pathology (e.g., cardiac arrhythmia). Real-time PC-CMR, without ECG gating and respiration control, is a promising alternative that could overcome limitations of the conventional approach. But real-time PC-CMR involves image reconstruction from highly undersampled (k, t)-space data, which is very challenging. In this study, we present a novel model-based imaging method to enable high-resolution real-time PC-CMR with sparse sampling. METHODS: The proposed method captures spatiotemporal correlation among flow-compensated and flow-encoded image sequences with a novel low-rank model. The image reconstruction problem is then formulated as a low-rank matrix recovery problem. With proper temporal subspace modeling, it results in a convex optimization formulation. We further integrate this formulation with the SENSE-based parallel imaging model to handle multichannel acquisitions. The performance of the proposed method was systematically evaluated in 2D real-time PC-CMR with flow phantom experiments and in vivo experiments (with healthy subjects). Additionally, we performed a feasibility study of the proposed method on patients with cardiac arrhythmia. RESULTS: The proposed method achieves a spatial resolution of 1.8 mm and a temporal resolution of 18 ms for 2D real-time PC-CMR with one directional flow encoding. For the flow phantom experiments, both regular and irregular flow patterns were accurately captured. For the in vivo experiments with healthy subjects, flow dynamics obtained from the proposed method correlated well with those from the cine-based acquisitions. For the experiments with the arrhythmic patients, the proposed method demonstrated excellent capability of resolving the beat-by-beat flow variations, which cannot be obtained from the conventional cine-based method. CONCLUSION: The proposed method enables high-resolution real-time PC-CMR at 2D without ECG gating and respiration control. It accurately resolves beat-by-beat flow variations, which holds great promise for studying patients with irregular heartbeats.

Accelerated phase contrast flow imaging with direct complex difference reconstruction.

PURPOSE: To propose and evaluate a new model-based reconstruction method for highly accelerated phase-contrast magnetic resonance imaging (PC-MRI) with sparse sampling. THEORY AND METHODS: This work presents a new constrained reconstruction method based on low-rank and sparsity constraints to accelerate PC-MRI. More specifically, we formulate the image reconstruction problem into separate reconstructions of flow-reference image sequence and complex differences. We then utilize the joint partial separability and sparsity constraints to enable high quality reconstruction from highly undersampled (k,t)-space data. We further integrate the proposed method with ESPIRiT based parallel imaging model to effectively handle multichannel acquisition. RESULTS: The proposed method was evaluated with in vivo data acquired from both 2D and 3D PC flow imaging experiments, and compared with several state-of-the-art methods. Experimental results demonstrate that the proposed method leads to more accurate velocity reconstruction from highly undersampled (k,t)-space data, and particularly superior capability of capturing the peak velocity of blood flow. In terms of flow visualization, blood flow patterns obtained from the proposed reconstruction also exhibit better agreement with those obtained from the fully sampled reference. CONCLUSION: The proposed method achieves improved accuracy over several state-of-the-art methods for velocity reconstruction with highly accelerated (k,t)-space data. Magn Reson Med 77:1036-1048, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Dynamic positron emission tomography restoration with low-rank representation incorporating edge preservation.

BACKGROUND: Dynamic positron emission tomography (PET) is a powerful tool that provides useful quantitative information on physiological and biochemical processes. However, the low signal-to-noise ratio (SNR) in short dynamic frames is a challenge. OBJECTIVE: To get high SNR in the dynamic PET and to achieve high-quality PET parametric image are the objective of this study. METHODS: Low-rank (LR) modeling and edge-preserving prior are incorporated in this study with a unified mathematical framework to improve the SNR of a dynamic PET image series. The proposed algorithm is designed to reduce noise in homogeneous areas while preserving the edges of regions of interest. RESULTS: The performance of the proposed method (LRH) is compared both visually and quantitatively by using the classic Gaussian filter and an LR expression filter on a digital brain phantom and in vivo rat study. Experimental results demonstrate that the proposed filter can achieve superior visual and quantitative performance without sacrificing spatial resolution. CONCLUSIONS: The proposed LRH is considerably effective and exhibits great potential in processing dynamic PET data with high noise levels.

Beyond Low Rank + Sparse: Multi-scale Low Rank Matrix Decomposition.

We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often exhibit local correlations in multiple scales. Concretely, we propose a multi-scale low rank modeling that represents a data matrix as a sum of block-wise low rank matrices with increasing scales of block sizes. We then consider the inverse problem of decomposing the data matrix into its multi-scale low rank components and approach the problem via a convex formulation. Theoretically, we show that under various incoherence conditions, the convex program recovers the multi-scale low rank components either exactly or approximately. Practically, we provide guidance on selecting the regularization parameters and incorporate cycle spinning to reduce blocking artifacts. Experimentally, we show that the multi-scale low rank decomposition provides a more intuitive decomposition than conventional low rank methods and demonstrate its effectiveness in four applications, including illumination normalization for face images, motion separation for surveillance videos, multi-scale modeling of the dynamic contrast enhanced magnetic resonance imaging and collaborative filtering exploiting age information.

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.

ACCELERATING CARDIOVASCULAR IMAGING BY EXPLOITING REGIONAL LOW-RANK STRUCTURE VIA GROUP SPARSITY.

Sparse sampling of (k, t)-space has proved useful for cardiac MRI. This paper builds on previous work on using partial separability (PS) and spatial-spectral sparsity for high-quality image reconstruction from highly undersampled (k, t)-space data. This new method uses a more flexible control over the PS-induced low-rank constraint via group-sparse regularization. A novel algorithm is also described to solve the corresponding (1,2)-norm regularized inverse problem. Reconstruction results from simulated cardiovascular imaging data are presented to demonstrate the performance of the proposed method.