A Fast Low-Rank Matrix Factorization Method for Dynamic Magnetic Resonance Imaging Restoration

2019 ◽  
Author(s):  
Fei Xu ◽  
Jingjing Zhang ◽  
Yanmei Shi ◽  
Kaixin Kang ◽  
Shuguo Yang
Keyword(s):  
Magnetic Resonance Imaging ◽  
Magnetic Resonance ◽  
Matrix Factorization ◽  
Factorization Method ◽  
Dynamic Magnetic Resonance Imaging ◽  
Low Rank ◽  
Resonance Imaging ◽  
Dynamic Magnetic Resonance ◽  
Rank Matrix ◽  
Low Rank Matrix

scholarly journals Dynamic Magnetic Resonance Imaging Reconstruction Based on Nonconvex Low-Rank Model

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Lixia Chen ◽  
Bin Yang ◽  
Xuewen Wang
Keyword(s):  
Magnetic Resonance Imaging ◽  
Magnetic Resonance ◽  
Magnetic Resonance Images ◽  
Dynamic Magnetic Resonance Imaging ◽  
Low Rank ◽  
Data Sets ◽  
Resonance Imaging ◽  
Dynamic Magnetic Resonance ◽  
Imaging Reconstruction

The quality of dynamic magnetic resonance imaging reconstruction has heavy impact on clinical diagnosis. In this paper, we propose a new reconstructive algorithm based on the L+S model. In the algorithm, the l1 norm is substituted by the lp norm to approximate the l0 norm; thus the accuracy of the solution is improved. We apply an alternate iteration method to solve the resulting problem of the proposed method. Experiments on nine data sets show that the proposed algorithm can effectively reconstruct dynamic magnetic resonance images.

EXACT LOW-RANK MATRIX RECOVERY VIA NONCONVEX SCHATTEN p-MINIMIZATION

2013 ◽  
Vol 30 (03) ◽  
pp. 1340010 ◽  
Author(s):  
LINGCHEN KONG ◽  
NAIHUA XIU
Keyword(s):  
Magnetic Resonance Imaging ◽  
Magnetic Resonance ◽  
Low Rank ◽  
Magnetic Resonance Imaging System ◽  
Resonance Imaging ◽  
Matrix Recovery ◽  
Rank Matrix ◽  
Restricted Isometry Constant ◽  
Low Rank Matrix Recovery ◽  
Low Rank Matrix

The low-rank matrix recovery (LMR) arises in many fields such as signal and image processing, quantum state tomography, magnetic resonance imaging, system identification and control, and it is generally NP-hard. Recently, Majumdar and Ward [Majumdar, A and RK Ward (2011). An algorithm for sparse MRI reconstruction by Schatten p-norm minimization. Magnetic Resonance Imaging, 29, 408–417]. had successfully applied nonconvex Schatten p-minimization relaxation of LMR in magnetic resonance imaging. In this paper, our main aim is to establish RIP theoretical result for exact LMR via nonconvex Schatten p-minimization. Carefully speaking, letting [Formula: see text] be a linear transformation from ℝm×n into ℝs and r be the rank of recovered matrix X ∈ ℝm×n, and if [Formula: see text] satisfies the RIP condition [Formula: see text] for a given positive integer k ∈ {1, 2, …, m – r}, then r-rank matrix can be exactly recovered. In particular, we obtain a uniform bound on restricted isometry constant [Formula: see text] for any p ∈ (0, 1] for LMR via Schatten p-minimization.

scholarly journals Low-Rank Matrix Denoising Algorithm-Based Magnetic Resonance Imaging Combined with Computed Tomography Images in the Diagnosis of Cerebral Aneurysm

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Daigui Zhang ◽  
Lihua Zhou ◽  
Tingdi Zhang ◽  
Shuai Wang ◽  
Yue Li
Keyword(s):  
Magnetic Resonance Imaging ◽  
Computed Tomography ◽  
Magnetic Resonance ◽  
Low Rank ◽  
Resonance Imaging ◽  
Ct Diagnosis ◽  
Rank Matrix ◽  
Mri Diagnosis ◽  
Low Rank Matrix ◽  
Better Than

This study was to analyze the diagnostic effects of computed tomography (CT) and magnetic resonance imaging (MRI) in patients with cerebrovascular diseases (CVDs) based on low-rank matrix denoising (LRMD) algorithm. The LRMD algorithm was adopted for MRI diagnosis and CT diagnosis for comparative analysis. 129 CVD patients were selected as the research objects, 43 cases were diagnosed by CT, 43 cases were diagnosed by MRI under LRMD, and the other 43 cases were diagnosed by CT + MRI. The results showed that the diagnostic compliance rates (DCRs) of CT group in the cerebral hemorrhage (CH), cerebral infarction (CI), and cerebral aneurysm (CA) were 95.1%, 94.7%, and 70%, respectively, while those in the MRI group were 99.01%, 97.71%, and 100%, respectively. Thus, it was obtained that MRI diagnosis was much better than CT diagnosis, and CT + MRI showed the best diagnosis efficacy, showing statistical differences ( P < 0.05 ). The accuracy, sensitivity, and specificity of MRI diagnosis under the LRMD algorithm were 96.28%, 88.76%, and 90.62%, respectively, which were superior to those of CT diagnosis (92.71%, 84.94%, and 80.71%, respectively). The diagnosis cost per case (DC/C) (799.73 ± 100.02 yuan) and the total diagnosis cost (TDC) (58,521.67 ± 301.62 yuan) in the MRI group were higher than those in the CT group (601.42 ± 83.61 yuan and 39,819.2 ± 198.72, respectively) ( P < 0.05 ). In conclusion, CT + MRI under the LRMD algorithm showed good potential in diagnosis of CVD; MRI based on the LRMD algorithm showed a higher positive rate in the diagnosis of CA and was better than CT diagnosis, and CT + MRI showed the best diagnosis effect and could improve the clinical diagnosis rate.

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