Title: Estimation of block sparsity in compressive sensing,
Abstract: In this paper, we consider a soft measure of block sparsity,
$k_\alpha(\mathbf{x})=\left(\lVert\mathbf{x}\rVert_{2,\alpha}/\lVert\mathbf{x}\rVert_{2,1}\right)^{\frac{\alpha}{1-\alpha}},\alpha\in[0,\infty]$
and propose a procedure to estimate it by using multivariate isotropic
symmetric $\alpha$-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.