Total variation reconstruction for Kronecker compressive sensing with a new regularization

Recovery algorithm based on total variation (TV) has shown its capability to recover high quality image in compressive sensing by preserving edges well but not fine details and textures. Recently, to improve this deficiency, characteristics of natural images are further utilized by adding some regularization terms into its recovery problem. In these efforts, this paper proposes a new regularization exploiting nonlocal properties of image using the nonlocal means filter in the gradient domain instead of the spatial domain. The Split Bregman method is applied to solve a combination of total variation and a new regularization term under the framework of Kronecker compressive sensing. Numerical experiments with the proposed and related regularizations verify significant improvement of the proposed method in term of both objective and subjective qualities.