Hybrid sparsity learning for image restoration: An iterative and trainable approach

State-of-the-art approaches toward image restoration can be classified into model-based and learning-based. The former class strives to exploit internal prior knowledge about the unknown target images by constructing advanced mathematical models; while the latter class leverages external image prior from a training dataset through powerful neural networks. It is natural to explore their middle ground and pursue a principled approach to learning the hybrid image prior in order to combine the strengths from both worlds. In this paper, we present a systematic approach to achieving this goal called Structured Analysis Sparsity Learning (SASL). Inspired by the strategy of iterative regularization, we propose to learn a hybrid sparse prior from both a collection of reference images (external prior) and the given degraded image (internal prior). Unlike previous hybrid approaches that simply take the average of restored images by different priors, we advocate our approach of combining complementary structured sparse priors in an iterative and trainable manner. By incorporating the knowledge from both domains (internal vs. external), we demonstrate that our iterative and trainable image restoration with a hybrid prior can boost the performance of common tasks including denoising and deblurring. Experimental results show that the proposed SASL image restoration techniques perform comparably with and often better than current state-of-the-art techniques.