Multi-Wiener SURE-LET Deconvolution

In this paper, we propose a novel deconvolution algorithm based on the minimization of a regularized Stein´s unbiased risk estimate (SURE), which is a good estimate of the mean squared error. We linearly parametrize the deconvolution process by using multiple Wiener filters as elementary functions, followed by undecimated Haar-wavelet thresholding. Due to the quadratic nature of SURE and the linear parametrization, the deconvolution problem finally boils down to solving a linear system of equations, which is very fast and exact. The linear coefficients, i.e., the solution of the linear system of equations, constitute the best approximation of the optimal processing on the Wiener-Haar-threshold basis that we consider. In addition, the proposed multi-Wiener SURE-LET approach is applicable for both periodic and symmetric boundary conditions, and can thus be used in various practical scenarios. The very competitive (both in computation time and quality) results show that the proposed algorithm, which can be interpreted as a kind of nonlinear Wiener processing, can be used as a basic tool for building more sophisticated deconvolution algorithms.