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Sensors 2013, 13(3), 3902-3921; doi:10.3390/s130303902
Communication

Rank Awareness in Group-Sparse Recovery of Multi-Echo MR Images

1,*  and 2
1 Indraprastha Institute of Information Technology, Delhi 110020, India 2 Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
* Author to whom correspondence should be addressed.
Received: 1 February 2013 / Revised: 21 February 2013 / Accepted: 7 March 2013 / Published: 20 March 2013
(This article belongs to the Special Issue Medical & Biological Imaging)
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Abstract

This work addresses the problem of recovering multi-echo T1 or T2 weighted images from their partial K-space scans. Recent studies have shown that the best results are obtained when all the multi-echo images are reconstructed by simultaneously exploiting their intra-image spatial redundancy and inter-echo correlation. The aforesaid studies either stack the vectorised images (formed by row or columns concatenation) as columns of a Multiple Measurement Vector (MMV) matrix or concatenate them as a long vector. Owing to the inter-image correlation, the thus formed MMV matrix or the long concatenated vector is row-sparse or group-sparse respectively in a transform domain (wavelets). Consequently the reconstruction problem was formulated as a row-sparse MMV recovery or a group-sparse vector recovery. In this work we show that when the multi-echo images are arranged in the MMV form, the thus formed matrix is low-rank. We show that better reconstruction accuracy can be obtained when the information about rank-deficiency is incorporated into the row/group sparse recovery problem. Mathematically, this leads to a constrained optimization problem where the objective function promotes the signal’s groups-sparsity as well as its rank-deficiency; the objective function is minimized subject to data fidelity constraints. The experiments were carried out on ex vivo and in vivo T2 weighted images of a rat's spinal cord. Results show that this method yields considerably superior results than state-of-the-art reconstruction techniques.
Keywords: MRI reconstruction; compressed sensing; low-rank matrix recovery MRI reconstruction; compressed sensing; low-rank matrix recovery
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Majumdar, A.; Ward, R. Rank Awareness in Group-Sparse Recovery of Multi-Echo MR Images. Sensors 2013, 13, 3902-3921.

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