A Variational Pan-Sharpening Method Based on Spatial Fractional-Order Geometry and Spectral-Spatial Low-Rank Priors

Pan-sharpening refers to the fusion of a low-resolution (LR) multispectral (MS) image and a high-resolution (HR) panchromatic (PAN) image to obtain an HR MS image (i.e., pan-sharpened MS image). From the point of view of variational complementary data fusion, it becomes an optimization problem with geometry and spectral preserving constraints. In this paper, a novel unified optimizing pan-sharpening model is proposed by integrating a data-generative fidelity term and a compound prior term, which incorporates both spatial fractional-order geometry and spectral-spatial low-rank priors. Specifically, the proposed model consists of three important ingredients: 1) data-generative fidelity term, which models the degradation relationship between the LR and HR MS images to enforce the geometry and spectral preserving constraints; 2) fractional-order total variation-based spatial fractional-order geometry prior term, which especially exploits the spatial fractional-order gradient feature consistence between the PAN and pan-sharpened MS images to transfer the spatial structure information of the PAN image into the pan-sharpened MS image; and 3) weighted nuclear norm-based spectral-spatial low-rank prior term, which exploits the nonlocal patches-based low-rank structural sparsity simultaneously in the pan-sharpened MS image and the LR MS image for further preserving image spatial structures and spectral information. Thus, the main novelty behind the proposed model is an optimizing mechanism by fully taking advantage of the spatial details and texture expressive power of the spatial fractional-order geometry prior as well as the spectral-spatial correlation preserving capacity of the low-rank prior. Finally, the proposed model can be implemented in an alternating direction method of multipliers framework, and thus, an efficient algorithm is presented. To verify the validity, the new proposed method is systematically compared with some state-of-the-art techniques using the Pleiades, GeoEye-1, QuickBird, and WorldView2 satellite data sets in the subjective, objective, and efficiency aspects. The results show that the proposed method performs better than the compared methods in terms of higher spatial and spectral qualities.