{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T12:42:09Z","timestamp":1774528929088,"version":"3.50.1"},"reference-count":28,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2013,6]]},"abstract":"<jats:p> The low-rank matrix recovery (LMR) arises in many fields such as signal and image processing, quantum state tomography, magnetic resonance imaging, system identification and control, and it is generally NP-hard. Recently, Majumdar and Ward [Majumdar, A and RK Ward (2011). An algorithm for sparse MRI reconstruction by Schatten p-norm minimization. Magnetic Resonance Imaging, 29, 408\u2013417]. had successfully applied nonconvex Schatten p-minimization relaxation of LMR in magnetic resonance imaging. In this paper, our main aim is to establish RIP theoretical result for exact LMR via nonconvex Schatten p-minimization. Carefully speaking, letting [Formula: see text] be a linear transformation from \u211d<jats:sup>m\u00d7n<\/jats:sup> into \u211d<jats:sup>s<\/jats:sup> and r be the rank of recovered matrix X \u2208 \u211d<jats:sup>m\u00d7n<\/jats:sup>, and if [Formula: see text] satisfies the RIP condition [Formula: see text] for a given positive integer k \u2208 {1, 2, \u2026, m \u2013 r}, then r-rank matrix can be exactly recovered. In particular, we obtain a uniform bound on restricted isometry constant [Formula: see text] for any p \u2208 (0, 1] for LMR via Schatten p-minimization. <\/jats:p>","DOI":"10.1142\/s0217595913400101","type":"journal-article","created":{"date-parts":[[2013,6,27]],"date-time":"2013-06-27T06:06:26Z","timestamp":1372313186000},"page":"1340010","source":"Crossref","is-referenced-by-count":21,"title":["EXACT LOW-RANK MATRIX RECOVERY VIA NONCONVEX SCHATTEN p-MINIMIZATION"],"prefix":"10.1142","volume":"30","author":[{"given":"LINGCHEN","family":"KONG","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Beijing Jiaotong University, Beijing, 100044, People's Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"NAIHUA","family":"XIU","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Beijing Jiaotong University, Beijing, 100044, People's Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,6,26]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2003.1177153"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1137\/060657704"},{"key":"rf5","first-page":"1300","volume":"58","author":"Cai T. 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