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

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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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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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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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