Framelet based pan-sharpening via a variational method

Abstract

Pan-sharpening is a process of combining a low resolution multi-spectral (MS) image and a high resolution panchromatic (PAN) image to obtain a single high resolution MS image. In this paper, we propose two pan-sharpening methods based on the framelet framework. The first method, as a basic work, is called a framelet-based pan-sharpening (FP) method. In the FP method, we first decompose the MS and PAN images into framelet coefficients, then obtain a new set of coefficients by choosing the approximation coefficients in MS and detail coefficients in PAN, and finally construct the pan-sharpened image from the new set of coefficients. To overcome the inflexibility of FP, in the second method, by combining FP and other three fusion requirements, i.e., geometry keeping, spectral preserving and the sparsity of the image in the framelet domain, four assumptions are established. Based on these assumptions, a framelet based variational energy functional, whose minimizer is related to the final pan-sharpened result, is then formulated. To improve the numerical efficiency, the split Bregman iteration is further introduced, and the result of FP method is set as an initial value. We refer this method as the variational framelet pan-sharpening (VFP) method. To verify the effectiveness of our methods, we present the results of the two methods on the QuickBird and IKONOS images, compare them with five existing methods qualitatively and quantitatively, analyze the influence of parameters of VFP, and extend the VFP to hyperspectral data as well as comparison study. The experimental results demonstrate the superiority of our methods.