Simultaneous Fidelity and Regularization Learning for Image Restoration.

Most existing non-blind restoration methods are based on the assumption that a precise degradation model is known. As the degradation process can only partially known or inaccurately modeled, images may not be well restored. For rain streak removal, although an input image can be decomposed into a scene layer and a rain streak layer, there exists no explicit formulation for modeling rain streaks and the composition with scene layer. For blind deconvolution, as estimation error of blur kernel is usually introduced, the subsequent non-blind deconvolution process does not restore the latent image well. We propose a principled algorithm within the maximum a posterior framework to tackle image restoration with a partially known or inaccurate degradation model. The residual caused by a partially known or inaccurate degradation model is spatially dependent and complexly distributed. With a training set of degraded and ground-truth image pairs, we parameterize and learn the fidelity term for a degradation model in a task-driven manner. The regularization term can also be learned along with the fidelity term, thereby forming a simultaneous fidelity and regularization learning model. Extensive experimental results demonstrate the effectiveness of the proposed model for image deconvolution with inaccurate blur kernels and rain streak removal.