BLOCK SUBSPACE PURSUIT FOR BLOCK-SPARSE SIGNAL RECONSTRUCTION

Subspace Pursuit (SP) is an efficient algorithm for sparse signal reconstruction. When
the interested signal is block sparse, i.e., the nonzero elements occur in clusters, block sparse
recovery algorithms are developed. In this paper, a blocked algorithm based on SP, namely Block
SP (BSP) is presented. Contrary to the previous algorithms such as Block Orthogonal Matching
Pursuit (BOMP) and mixed 2 1 l /l -norm, our approach presents better recovery performance and
requires less time when non-zero elements appear in fixed blocks in a particular hardware in most
of the cases. It is demonstrated that our proposed algorithm can precisely reconstruct the blocksparse
signals, 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 sensingwith
a constant parameter. Furthermore, it is experimentally illustrated that the BSP algorithm
outperforms other methods such as SP, mixed 2 1 l /l -norm and BOMP. This is more pronounced
when the block length is small.