Panchromatic sharpening of multispectral satellite imagery via an explicitly defined convex self-similarity regularization

In satellite imaging remote sensing, injecting spatial details extracted from a panchromatic image into a multispectral image is referred to as pansharpening, which is ill-posed and requires regularization. Self-similarity, a critical prior knowledge yielding great success in regularizing various imaging inverse problems, has been widely observed in natural images; its formalization is not, however, straightforward. Very recently, we mathematically described the self-similarity pattern as a weighted graph, which can then be transformed into an explicit convex regularizer, that is adopted in our pansharpening criterion design. Most importantly, such convexity allows the adoption of convex optimization theory in solving self-similarity regularized inverse problems with convergence guarantee. One step of our pansharpening algorithm is exactly the proximal operator induced by our new self-similarity regularizer, which is solved by another customized algorithm that is interesting in its own right as could be used as a denoiser. Experiments show promising performance of the proposed method.