Estimation of block sparsity in compressive sensing

Explicitly using the block structure of the unknown signal can achieve better recovery performance in compressive censing. An unknown signal with block structure can be accurately recovered from underdetermined linear measurements provided that it is sufficiently block sparse. However, in practice, the block sparsity level is typically unknown. In this paper, we consider a soft measure of block sparsity, kα(x) = (‖x‖2,α/‖x‖2,1) α 1−α , α ∈ [0,∞] and propose a procedure to estimate it by using multivariate isotropic symmetric α-stable random projections without sparsity or block sparsity assumptions. The limiting distribution of the estimator is given. Some simulations are conducted to illustrate our theoretical results. Index Terms Block sparsity; Multivariate isotropic symmetric α-stable distribution; Compressive sensing; Characteristic function.