Estimation of block sparsity in compressive sensing

Abstract

Explicitly using the block structure of the unknown signal can achieve better reconstruction performance in compressive sensing. An unknown signal with block structure can be accurately recovered from under-determined linear measurements provided that it is sufficiently block sparse. However, in practice, the block sparsity level is typically unknown. In this paper, we propose a soft measure of block sparsity [Formula: see text] with [Formula: see text], and present a procedure to estimate it by using multivariate centered isotropic symmetric [Formula: see text]-stable random projections. The limiting distribution of the estimator is given. Simulations are conducted to illustrate our theoretical results.