Logo image
Back
Structured Low-Rank Algorithms: Theory, Magnetic Resonance Applications, and Links to Machine Learning
Journal article   Peer reviewed

Structured Low-Rank Algorithms: Theory, Magnetic Resonance Applications, and Links to Machine Learning

Mathews Jacob, Merry P Mani and Jong Chul Ye
IEEE Signal Processing Magazine, Vol.37(1), pp.54-68
01/2020
DOI: 10.1109/MSP.2019.2950432
PMCID: PMC8754413
PMID: 35027816
url
https://arxiv.org/pdf/1910.12162View
Open Access

Abstract

In this survey, we provide a detailed review of recent advances in the recovery of continuous domain multidimensional signals from their few non-uniform (multichannel) measurements using structured low-rank matrix completion formulation. This framework is centered on the fundamental duality between the compactness (e.g., sparsity) of the continuous signal and the rank of a structured matrix, whose entries are functions of the signal. This property enables the reformulation of the signal recovery as a low-rank structured matrix completion, which comes with performance guarantees. We will also review fast algorithms that are comparable in complexity to current compressed sensing methods, which enables the application of the framework to large-scale magnetic resonance (MR) recovery problems. The remarkable flexibility of the formulation can be used to exploit signal properties that are difficult to capture by current sparse and low-rank optimization strategies. We demonstrate the utility of the framework in a wide range of MR imaging (MRI) applications, including highly accelerated imaging, calibration-free acquisition, MR artifact correction, and ungated dynamic MRI. Comment: Accepted for IEEE Signal Processing Magazine
 Computer Science - Machine Learning Statistics - Machine Learning Computer Science - Information Theory Computer Science - Computer Vision and Pattern Recognition

Details

Metrics

27 Record Views
51 Times Cited - Web of Science
Logo image