title: Rank awareness in group-sparse recovery of multi-echo MR images.
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.
authors.affiliation: Indraprastha Institute of Information Technology, Delhi 110020, India. angshul@iiitd.ac.in
authors.forename: Angshul
authors.initials: A
authors.lastname: Majumdar
authors.forename: Rabab
authors.initials: R
authors.lastname: Ward
mesh_terms: D000465:Algorithms; D000818:Animals; D001921:Brain / Q000000981:diagnostic imaging; D003952:Diagnostic Imaging; D006801:Humans; D007089:Image Enhancement; D007091:Image Processing, Computer-Assisted; D008279:Magnetic Resonance Imaging; D008962:Models, Theoretical; D011859:Radiography; D051381:Rats; D017207:Rats, Sprague-Dawley