Spectral Gradient Fidelity and Spatial Hessian Hyper-Laplacian Sparsity Constraints for Variational Pansharpening

In this article, an effectively variational pansharpening method with spectral gradient fidelity and spatial Hessian hyper-Laplacian sparsity constraints (PSGFSHHS) was proposed to fuse the low resolution multispectral (LRMS) and panchromatic (Pan) images to the high resolution multispectral (HRMS) image. First, the spectral feature correlation prior between LRMS and HRMS was modeled by the spectral gradient fidelity constraint. Second, the spatial correlation prior between Pan and HRMS was particularly modeled by the spatial Hessian hyper-Laplacian sparsity constraint from the statistical perspective, which clearly held strong novelty for pansharpening recently by the spatial Hessian hyper-Laplacian sparsity modeling. Third, by combining the spectral gradient fidelity constraint and the spatial Hessian hyper-Laplacian sparsity constraint, the PSGFSHHS model was formed and the alternating direction method of multipliers method was utilized for optimization. Finally, the experimental fusion examples clearly illustrated the effectiveness and capability of PSGFSHHS.