Efficient general sparse denoising with non-convex sparse constraint and total variation regularization

In this paper, we proposed an effective and computationally efficient algorithm without iterations, named general sparse denoising with total variation regularization (GSDN-TV), for solving the convex optimization problem of combining the sparse regularization and total variation (TV) regularization. In the GSDN-TV, the original convex optimization problem is divided into two convex optimization subproblems. Each of the subproblems only contains one regularization and can be efficiently solved or has the closed-form solution. The final solution of the original problem can be obtained by solving the two subproblems one by one without iterations. By using the non-convex firm penalty function in the sparse regularization, the GSDN-TV is applied to the wavelet-TV denoising problem and achieves outstanding performances.