Image Inpainting with Primal-Dual Soft Threshold Algorithm for Total Variation and Curvelet Prior

Primal-Dual scheme is particularly suitable for solving the non-smooth Total Variation (TV) model in imaging, and the soft thresholding algorithm is simple and effective for the Curvelet prior. We propose a hybrid prior of TV and Curvelet Prior (TVCP) model for the image restoration problems. In order to obtain high restoration quality, we propose Primal-Dual and Soft Threshold (PDST) algorithm to solve this convex optimization model (TVCP). Our inpainting experimental results have shown that PDST algorithm significantly outperforms Primal-Dual for TV (PDTV) and Primal-Dual for Curvelet (PDC), in both subjective and objective image quality. Furthermore, TVCP model and PDST algorithm can be easily applied to solving other challenging problems in image, such as denosing, deconvolution, compressed sensing etc.