A Fast Algorithm for Convolutional Structured Low-Rank Matrix Recovery

Gregory Ongie; Mathews Jacob

doi:10.1109/TCI.2017.2721819

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Journal article

A Fast Algorithm for Convolutional Structured Low-Rank Matrix Recovery

Gregory Ongie and Mathews Jacob

IEEE transactions on computational imaging, Vol.3(4), pp.535-550

12/2017

DOI: 10.1109/TCI.2017.2721819

PMCID: PMC5999344

PMID: 29911129

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https://www.ncbi.nlm.nih.gov/pmc/articles/5999344View

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Abstract

Fourier-domain structured low-rank matrix priors are emerging as powerful alternatives to traditional image recovery methods such as total variation and wavelet regularization. These priors specify that a convolutional structured matrix, i.e., Toeplitz, Hankel, or their multilevel generalizations, built from Fourier data of the image should be low-rank. The main challenge in applying these schemes to large-scale problems is the computational complexity and memory demand resulting from lifting the image data to a large-scale matrix. We introduce a fast and memory-efficient approach called the generic iterative reweighted annihilation filter algorithm that exploits the convolutional structure of the lifted matrix to work in the original unlifted domain, thus considerably reducing the complexity. Our experiments on the recovery of images from undersampled Fourier measurements show that the resulting algorithm is considerably faster than previously proposed algorithms and can accommodate much larger problem sizes than previously studied.

Jacobian matrices

Transmission line matrix methods

Convolution

compressed sensing

Magnetic resonance imaging

finite rate of innovation

multi-level Toeplitz matrices

structured low-rank matrix recovery

Approximation algorithms

Annihilating filter

MRI reconstruction

Image reconstruction

Details

Title: Subtitle: A Fast Algorithm for Convolutional Structured Low-Rank Matrix Recovery
Creators: Gregory Ongie - Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA
Mathews Jacob - Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA, USA
Resource Type: Journal article
Publication Details: IEEE transactions on computational imaging, Vol.3(4), pp.535-550
DOI: 10.1109/TCI.2017.2721819
PMID: 29911129
PMCID: PMC5999344
NLM abbreviation: IEEE Trans Comput Imaging
ISSN: 2573-0436
eISSN: 2333-9403
Publisher: IEEE
Grant note: CCF-1116067 / NSF (10.13039/100003187) N00014-13-1-0202 / ONR (10.13039/100000006) 1R01EB019961-01A1 / NIH (10.13039/100000002) RSG-11-267-01-CCE / ACS (10.13039/100000048)
Language: English
Date published: 12/2017
Academic Unit: Roy J. Carver Department of Biomedical Engineering; Radiology; Electrical and Computer Engineering; Iowa Neuroscience Institute; Radiation Oncology
Record Identifier: 9984071603002771

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