An Iterative Sure-Let Deconvolution Algorithm Based on BM3D Denoiser

Recently, the plug-and-play priors (PPP) have been a popular technique for image reconstruction. Based on the basic iterative thresholding scheme, we in this paper propose a new iterative SURE-LET deconvolution algorithm with a plug-in BM3D denoiser. To optimize the deconvolution process, we linearly parametrize the thresholding function by using multiple BM3D denoisers as elementary functions. The key contributions of our approach are: (1) the linear combination of several BM3D denoisers with different (but fixed) parameters, which avoids the manual adjustment of a single non-linear parameter; (2) linear parametrization makes the minimization of Stein's unbiased risk estimate (SURE) finally boil down to solving a linear system of equations, leading to a very fast and exact optimization during each iteration. In particular, the SURE of BM3D denoiser is approximately evaluated by finite-difference Monte-Carlo technique. Experiments show that the proposed algorithm, in average, achieves better deconvolution performance than other state-of-the-art methods, both numerically and visually.