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.
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