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Erschienen in:
22.11.2016
Greedy Block Coordinate Descent under Restricted Isometry Property
Erschienen in: Mobile Networks and Applications | Ausgabe 3/2017
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Abstract
Exact support recovery of K-group sparse matrices X from the multiple measurement vectors (MMV) model Y = A
X arises from many applications and has been extensively studied. In this paper, we investigate the restricted isometry property (RIP) based condition that guarantees exact support recovery of K-group sparse matrices X from the MMV model with greedy block coordinate descent (GBCD) algorithm in K iterations. We show that if A satisfies the RIP with \(\delta _{K+1}<1/\sqrt {K+1}\), then GBCD recovers the support of any K-group sparse matrix X in K iterations. This RIP condition is sharp since GBCD may fail to recover the support of a K-group sparse matrix in K iterations if \(\delta _{K+1}\geq 1/\sqrt {K+1}\). As far as we know, this is the first sharp condition for GBCD.