Constrained Mix Sparse Optimization via Hard Thresholding Pursuit

Mix sparse structure, namely the sparse structure appearing in the inter-group and intra-group manners simultaneously, is inherited in a wide class of practical applications. Hard thresholding pursuit (HTP) is a practical and efficient algorithm for solving a least square problem with cardinality constraint. In this paper, we propose an algorithm based on HTP to solve a constrained mix sparse optimization problem, named MixHTP, and establish its linear convergence property under the restricted isometry property. Moreover, we apply the MixHTP to compressive sensing with simulated data and enhanced indexation with real data. Numerical results exhibit an excellent performance of MixHTP on approaching a solution with mix sparse structure and MixHTP outperforms several state-of-the-art algorithms in the literature.