A convergent framework with learnable feasibility for Hadamard-based image recovery

In this paper, we propose a framework for recovering image degradations that can be formulated by the Hadamard product of clear images with degradation factors. By training the mapping from datasets, we show that implicit feasibilities can be learned in forms of latent domains. Then with the feasibilities and acknowledged data priors, the recovery problems are formulated as a general optimization model in which the domain knowledge of degradations are also nicely involved. Then we solve the model based on the classical coordinate update with plugged-in networks so that all the variables can be well estimated. Even better, our updating scheme is designed under the guidance of theoretical analyses, thus its stability can always be guaranteed in practice. We show that different recovery problems can be solved under our unified framework, and the extensive experimental results verify that the proposed framework is superior to state-of-the-art methods in both benchmark datasets and real-world images.