{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:35:38Z","timestamp":1772296538846,"version":"3.50.1"},"reference-count":21,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2013,3,20]],"date-time":"2013-03-20T00:00:00Z","timestamp":1363737600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>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\u2019s 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.<\/jats:p>","DOI":"10.3390\/s130303902","type":"journal-article","created":{"date-parts":[[2013,3,20]],"date-time":"2013-03-20T13:23:35Z","timestamp":1363785815000},"page":"3902-3921","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Rank Awareness in Group-Sparse Recovery of Multi-Echo  MR Images"],"prefix":"10.3390","volume":"13","author":[{"given":"Angshul","family":"Majumdar","sequence":"first","affiliation":[{"name":"Indraprastha Institute of Information Technology, Delhi 110020, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rabab","family":"Ward","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of British Columbia,  Vancouver, BC V6T 1Z4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2013,3,20]]},"reference":[{"key":"ref_1","unstructured":"Haacke, E.M., Brown, R.R., Thomson, M.R., and Venkatesh, R. (1999). Magnetic Resonance Imaging: Physical Principals and Sequence Design, John Wiley and Sons."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1182","DOI":"10.1002\/mrm.21391","article-title":"Sparse MRI: The application of compressed sensing for rapid MR imaging","volume":"58","author":"Lustig","year":"2007","journal-title":"Magn. Reson. Med."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1109\/TMI.2008.927346","article-title":"Highly undersampled magnetic resonance image reconstruction via homotopic l0-minimization","volume":"28","author":"Trzasko","year":"2009","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"899","DOI":"10.1016\/j.mri.2011.03.008","article-title":"Joint reconstruction of multi-echo MR images using correlated sparsity","volume":"29","author":"Majumdar","year":"2011","journal-title":"Magn. Reson. Imaging"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.jmr.2011.02.015","article-title":"Accelerating multi-echo T2 weighted MR imaging: Analysis prior group sparse optimization","volume":"201","author":"Majumdar","year":"2011","journal-title":"J. Magn. Reson."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1109\/TIT.2011.2173722","article-title":"Rank awareness in joint sparse recovery","volume":"58","author":"Davies","year":"2012","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_7","unstructured":"Golbabaee, M., and Vandergheynst, P. (June, January 27\u2013). Guaranteed Recovery of a Low-rank and Joint-sparse Matrix from Incomplete and Noisy Measurements. Edinburgh UK."},{"key":"ref_8","unstructured":"Van Den, B.E., Schmidt, M., Friedlander, M.P., and Murphy, K. (2009). Group Sparsity via Linear-Time Projection, Department of Computer Science, University of British Columbia. 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