A Fast Majorize―Minimize Algorithm for the Recovery of Sparse and Low-Rank Matrices

Yue Hu; Sajan Goud Lingala; Mathews JACOB

doi:10.1109/TIP.2011.2165552

Back

A Fast Majorize―Minimize Algorithm for the Recovery of Sparse and Low-Rank Matrices

Journal article

Peer reviewed

A Fast Majorize―Minimize Algorithm for the Recovery of Sparse and Low-Rank Matrices

Yue Hu, Sajan Goud Lingala and Mathews JACOB

IEEE transactions on image processing, Vol.21(2), pp.742-753

2012

DOI: 10.1109/TIP.2011.2165552

PMID: 21859601

View Online

Abstract

We introduce a novel algorithm to recover sparse and low-rank matrices from noisy and undersampled measurements. We pose the reconstruction as an optimization problem, where we minimize a linear combination of data consistency error, nonconvex spectral penalty, and nonconvex sparsity penalty. We majorize the nondifferentiable spectral and sparsity penalties in the criterion by quadratic expressions to realize an iterative three-step alternating minimization scheme. Since each of these steps can be evaluated either analytically or using fast schemes, we obtain a computationally efficient algorithm. We demonstrate the utility of the algorithm in the context of dynamic magnetic resonance imaging (MRI) reconstruction from sub-Nyquist sampled measurements. The results show a significant improvement in signal-to-noise ratio and image quality compared with classical dynamic imaging algorithms. We expect the proposed scheme to be useful in a range of applications including video restoration and multidimensional MRI.

Applied Sciences

Signal Processing

Signal and communications theory

Image processing

Telecommunications and information theory

Exact sciences and technology

Signal, noise

Information, signal and communications theory

Detection, estimation, filtering, equalization, prediction

Details

Title: Subtitle: A Fast Majorize―Minimize Algorithm for the Recovery of Sparse and Low-Rank Matrices
Creators: Yue Hu - Department of Electrical and Computer Engineering, University of Rochester, Rochester, NY 014627, United States
Sajan Goud Lingala - Department of Biomedical Engileering and the Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA 52242, United States
Mathews JACOB - Department of Biomedical Engileering and the Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA 52242, United States
Resource Type: Journal article
Publication Details: IEEE transactions on image processing, Vol.21(2), pp.742-753
Publisher: Institute of Electrical and Electronics Engineers; New York, NY
DOI: 10.1109/TIP.2011.2165552
PMID: 21859601
ISSN: 1057-7149
eISSN: 1941-0042
Language: English
Date published: 2012
Academic Unit: Roy J. Carver Department of Biomedical Engineering; Radiology; Electrical and Computer Engineering; Iowa Neuroscience Institute; Radiation Oncology
Record Identifier: 9984070849902771

Metrics

33 Record Views

42 Times Cited - Web of Science