PDE based deconvolution with forward-backward diffusivities and diffusion tensors

Abstract: Deblurring with a spatially invariant kernel of arbitrary shape is a frequent problem in image processing. We address this task by studying nonconvex variational functionals that lead to diffusion-reaction equations of Perona-Malik type. Further we consider novel deblurring PDEs with anisotropic diffusion tensors. In order to improve deblurring quality we propose a continuation strategy in which the diffusion weight is reduced during the process. To evaluate our methods, we compare them to two established techniques: Wiener filtering which is regarded as the best linear filter, and a total variation based deconvolution which is the most widespread deblurring PDE. The experiments confirm the favourable performance of our methods, both visually and in terms of signal-to-noise ratio.