Adaptively-Regularized Compressive Sensing With Sparsity Bound Learning

In this letter, an adaptively-regularized iterative reweighted least squares algorithm with sparsity bound learning is designed to efficiently recover sparse signals from measurements. In particular, at each iteration the support of estimated signal is exploited to construct a sparsity-promoting matrix and, then, formulate an adaptive regularization. Since this algorithm could learn sparsity information at each iteration, it ensures a sparser and sparser solution, and the mean squared error analysis corroborates its convergence. Experimental results demonstrate that the proposed algorithm outperforms other typical ones in terms of sparsity level, compressive ratio, and detection probability.