Self-Convolution: A Highly-Efficient Operator for Non-Local Image Restoration

Constructing effective image priors is critical to solving ill-posed inverse problems, such as image restoration. Recent works proposed to exploit image non-local similarity for inverse problems by grouping similar patches, and demonstrated state-of-the-art results in many applications. However, comparing to classic local methods based on filtering or sparsity, most of the non-local algorithms are time-consuming, mainly due to the highly inefficient and redundant block matching step, where the distance between each pair of overlapping patches needs to be computed. In this work, we propose a novel Self-Convolution operator to exploit image non-local similarity in a self-supervised way. The proposed Self-Convolution can generalize the commonly-used block matching step, and produce the equivalent results with much cheaper computation. Based on Self-Convolution, we propose an effective multi-modality image restoration scheme, which is much more efficient than conventional block matching for non-local modeling. Experimental results also demonstrate that Self-Convolution can significantly speed up most of the popular non-local image restoration algorithms, with two-fold to nine-fold faster block matching. The codes will be released on GitHub.