Efficient shift-variant image restoration using deformable filtering (Part I)

In this study, we propose using the least squares optimal deformable filtering approximation as an efficient tool for linear shift variant (SV) filtering, in the context of restoring SV-degraded images. Based on this technique we propose a new formalism for linear SV operators, from which an efficient way to implement the transposed SV-filtering is derived. We also provide a method for implementing an approximation of the regularized inversion of a SV-matrix, under the assumption of having smoothly spatially varying kernels, and enough regularization. Finally, we applied these techniques to implement a SV-version of a recent successful sparsity-based image deconvolution method. A high performance (high speed, high visual quality and low mean squared error, MSE) is demonstrated through several simulation experiments (one of them based on the Hubble telescope PSFs), by comparison to two state-of-the-art methods.