A new variational method for pan-sharpening

In this paper, we present a new variational method for pan-sharpening, which aims to obtain a high resolution multi-spectral (MS) image from a low resolution MS image and a high resolution panchromatic (PAN) image. Firstly, we assume that the desired high resolution MS image after down-sampling should be close to the low resolution MS image. More specifically, the intensity maps of PAN image and high resolution MS image bands are treated as three-dimensional (3D) differential surfaces. Then, we constrain that the surfaces of PAN image and high resolution MS image band should have the same bending directions at each point in 3D space. Based on these assumptions, a variational model is proposed and an efficient algorithm is designed to solve this variational model. Experimental results demonstrate that the proposed method outperforms various pan-sharpening methods in terms of both excellent spatial and spectral qualities.