A Generalized Structured Low-Rank Matrix Completion Algorithm for MR Image Recovery

Yue Hu; Xiaohan Liu; Mathews Jacob

doi:10.1109/TMI.2018.2886290

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A Generalized Structured Low-Rank Matrix Completion Algorithm for MR Image Recovery

Journal article

Open access

Peer reviewed

A Generalized Structured Low-Rank Matrix Completion Algorithm for MR Image Recovery

Yue Hu, Xiaohan Liu and Mathews Jacob

IEEE transactions on medical imaging, Vol.38(8), pp.1841-1851

08/2019

DOI: 10.1109/TMI.2018.2886290

PMCID: PMC6559879

PMID: 30561342

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https://www.ncbi.nlm.nih.gov/pmc/articles/6559879View

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Abstract

Recent theory of mapping an image into a structured low-rank Toeplitz or Hankel matrix has become an effective method to restore images. In this paper, we introduce a generalized structured low-rank algorithm to recover images from their undersampled Fourier coefficients using infimal convolution regularizations. The image is modeled as the superposition of a piecewise constant component and a piecewise linear component. The Fourier coefficients of each component satisfy an annihilation relation, which results in a structured Toeplitz matrix. We exploit the low-rank property of the matrices to formulate a combined regularized optimization problem. In order to solve the problem efficiently and to avoid the high-memory demand resulting from the large-scale Toeplitz matrices, we introduce a fast and a memory-efficient algorithm based on the half-circulant approximation of the Toeplitz matrix. We demonstrate our algorithm in the context of single and multi-channel MR images recovery. Numerical experiments indicate that the proposed algorithm provides improved recovery performance over the state-of-the-art approaches.

Magnetic Resonance Imaging

Optimization

Jacobian matrices

image recovery

Convolution

compressed sensing

Structured low-rank matrix

Approximation algorithms

Image reconstruction

infimal convolution

Details

Title: Subtitle: A Generalized Structured Low-Rank Matrix Completion Algorithm for MR Image Recovery
Creators: Yue Hu - School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin, China
Xiaohan Liu - School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin, China
Mathews Jacob - Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA, USA
Resource Type: Journal article
Publication Details: IEEE transactions on medical imaging, Vol.38(8), pp.1841-1851
DOI: 10.1109/TMI.2018.2886290
PMID: 30561342
PMCID: PMC6559879
NLM abbreviation: IEEE Trans Med Imaging
ISSN: 0278-0062
eISSN: 1558-254X
Publisher: Institute of Electrical and Electronics Engineers
Grant note: 1R01EB019961-01A1 / National Natural Science Foundation of China (10.13039/501100001809)\nF2016018 / NIH Blueprint for Neuroscience Research (10.13039/100000135)\n61501146; 61871159 / National Natural Science Foundation of China (10.13039/501100001809)
Language: English
Date published: 08/2019
Academic Unit: Roy J. Carver Department of Biomedical Engineering; Radiology; Electrical and Computer Engineering; Iowa Neuroscience Institute; Radiation Oncology
Record Identifier: 9984070949302771

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