An improved IRLS algorithm for sparse recovery with intra-block correlation

Non-convex l2/lq(0 < q < 1) minimization method can efficiently recover the block-sparse signals whose non-zero coefficients occur in a few blocks. However, in many applications such as face recognition and fetal ECG monitoring, real-world signals also exhibit intra-block correlations aside from standard block-sparsity. In order to recover such signals exactly and robustly, the block sparse Bayesian learning framework is studied in this paper. In contrast to l2/lq norm minimization the proposed method involves a quadratic Mahalanobis distance measure on the block and a covariance matrix on the intra-block correlation. The improved iteratively reweighted least-squares algorithm for the induced framework is proposed than the recent known for mixed l2/lq optimization. The proposed algorithm is tested and compared with the mixed l2/lq algorithm on a series of signals modeled by autoregressive processes. Numerical results demonstrate the outperformance of the proposed algorithm and meanfulness of the novel strategy, especially in low sample ratio and large unknown noise level.