Pan-sharpening of multi-spectral images using a new variational model

In remote-sensing image processing, pan-sharpening is used to obtain a high-resolution multi-spectral image by combining a low-resolution multi-spectral image with a corresponding high-resolution panchromatic image. In this article, to preserve the geometry, spectrum, and correlation information of the original images, three hypotheses are presented, i.e. (1) the geometry information contained in the pan-sharpened image should also be contained in the panchromatic bands; (2) the upsampled multi-spectral image can be seen as a blurred form of the fused image with an unknown kernel; and (3) the fused bands should keep the correlation between each band of the upsampled multi-spectral image. A variational energy functional is then built based on the assumptions, of which the minimizer is the target fused image. The existence of a minimizer of the proposed energy is further analysed, and the numerical scheme based on the split Bregman framework is presented. To verify the validity, the new proposed method is compared with several state-of-the-art techniques using QuickBird data in subjective, objective, and efficiency aspects. The results show that the proposed approach performs better than some compared methods according to the performance metrics.