Deep Unfolding Real-Time Super-Resolution Using Subpixel-Shift Twin Image and Convex Self-Similarity Prior

Multi-image super-resolution (MISR) is a critical technique for satellite remote sensing. In the perspective of information, twin-image super-resolution (TISR) is regarded as the most challenging MISR scenario, having crucial applications like the SPOT-5 supermode imaging. In TISR, an image is super-resolved by its subpixel-shift counterpart (i.e., twin image), where the two images are typically offset by half a pixel both horizontally and vertically. We formulate the less investigated TISR using a convex criterion, which is implemented using a novel deep unfolding network. In the unfolding, an embedded simple shift operator trickily addresses the coupled TISR data-fitting terms, and a transformer trained with a convex self-similarity loss function elegantly implements the proximal mapping induced by the TISR regularizer. The proposed convex self-similarity unfolding supermode super-resolution (COSUP) algorithm is interpretable and achieves state-of-the-art performance with very fast millisecond-level computational time. COSUP is also tested on real-world data, for which the subpixel shifts would not be spatially uniform, with results showing great superiority over the official CNES supermode imaging product in terms of credible metrics (e.g., natural image quality evaluator, NIQE).