A Robust Variational Model for Positive Image Deconvolution

Abstract: In this paper, an iterative method for robust deconvolution with positivity constraints is discussed. It is based on the known variational interpretation of the Richardson-Lucy iterative deconvolution as fixed-point iteration for the minimisation of an information divergence functional under a multiplicative perturbation model. The asymmetric penaliser function involved in this functional is then modified into a robust penaliser, and complemented with a regulariser. The resulting functional gives rise to a fixed point iteration that we call robust and regularised Richardson-Lucy deconvolution. It achieves an image restoration quality comparable to state-of-the-art robust variational deconvolution with a computational efficiency similar to that of the original Richardson-Lucy method. Experiments on synthetic and real-world image data demonstrate the performance of the proposed method.