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Rank Awareness in Group-Sparse Recovery of Multi-Echo MR Images
Indraprastha Institute of Information Technology, Delhi 110020, India
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; in revised form: 21 February 2013 / Accepted: 7 March 2013 / Published: 20 March 2013
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
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MDPI and ACS Style
Majumdar, A.; Ward, R. Rank Awareness in Group-Sparse Recovery of Multi-Echo MR Images. Sensors 2013, 13, 3902-3921.
Majumdar A, Ward R. Rank Awareness in Group-Sparse Recovery of Multi-Echo MR Images. Sensors. 2013; 13(3):3902-3921.
Majumdar, Angshul; Ward, Rabab. 2013. "Rank Awareness in Group-Sparse Recovery of Multi-Echo MR Images." Sensors 13, no. 3: 3902-3921.