BLOCK SUBSPACE PURSUIT FOR BLOCK-SPARSE SIGNAL RECONSTRUCTION

Abstract

Subspace Pursuit (SP) is an efficient algorithm for sparse signal reconstruction. Whenthe interested signal is block sparse, i.e., the nonzero elements occur in clusters, block sparserecovery algorithms are developed. In this paper, a blocked algorithm based on SP, namely BlockSP (BSP) is presented. Contrary to the previous algorithms such as Block Orthogonal MatchingPursuit (BOMP) and mixed 2 1 l /l -norm, our approach presents better recovery performance andrequires less time when non-zero elements appear in fixed blocks in a particular hardware in mostof the cases. It is demonstrated that our proposed algorithm can precisely reconstruct the blocksparsesignals, provided that the sampling matrix satisfies the block restricted isometry property -which is a generalization of the standard RIP widely used in the context of compressed sensingwitha constant parameter. Furthermore, it is experimentally illustrated that the BSP algorithmoutperforms other methods such as SP, mixed 2 1 l /l -norm and BOMP. This is more pronouncedwhen the block length is small.