Stable Cosparse Recovery via \ell_q-analysis Optimization

In this paper we study the lq-analysis optimization (0 < q ≤ 1) problem for cosparse signal recovery. Our results show that the nonconvex lq-analysis optimization with q < 1 has better properties in terms of stability and robustness than the convex l1-analysis optimization. In addition, we develop an iteratively reweighted method to solve this problem under the variational framework. Theoretical analysis demonstrates that our method is capable of pursuing a local minima close to the global minima. The empirical results show that the nonconvex approach performs better than its convex counterpart. It is also illustrated that our method outperforms the other state-of-the-art methods for cosparse signal recovery.