Edge-preserving image deconvolution with nonlocal domain transform

In this paper, we propose a new approach for performing efficient edge-preserving image deconvolution algorithm based on a nonlocal domain transform (NLDT). We present the geodesic distance-preserving transforming procedure of a 1D signal embedded in 2D space into a new 1D domain via a transformation for simplicity. The nonlocal domain transform derives from the (1D) nonlocal means filter kernel and iteratively and separably applies 1D edge-aware operations. In order to solve the main issue with noisy images that is finding robust estimates for their derivatives, we develop an efficient joint nonlocal domain transform filter in the deblurring process. Furthermore, we derive the discrepancy principle to automatically adjust the regularization parameter at each iteration. We compare our deconvolution algorithm with many competitive deconvolution techniques in terms of ISNR and visual quality.