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Iterative positive thresholding algorithm for non-negative sparse optimization

Abstract The non-negative regularization problem has been widely studied for finding non-negative sparse solutions of linear inverse problems and gained successful applications in various application areas. In the present paper, we propose an iterative positive thresholding algorithm (IPTA) to solve the non-negative regularization problem and investigate its convergence properties in finite- or infinite-dimensional Hilbert spaces. The significant advantage of the IPTA is that it is very simple and of low computation cost, and thus, it is practically attractive, especially for large-scale problems. The global convergence of the IPTA is achieved under some mild assumptions on algorithmic parameters. Furthermore, we introduce a notion of positive orthogonal sparsity pattern, and use it to establish the linear convergence rate of the IPTA to a global minimum. Finally, the numerical study on compressive sensing shows that the proposed IPTA is efficient in approaching the non-negative sparse solutions of linear inverse problems and outperforms several existing algorithms in sparse optimization.