Pansharpening via sparsity optimization using overcomplete transforms

In this paper we consider pansharpening of multispectral satellite imagery based on solving an under-determined inverse problem regularized by the ℓ₁-norm of the coefficients of overcomplete multi-scale transforms which all are tight-frame systems. There are two main approaches in sparsity promoting ℓ₁-norm regularization, the analysis and the synthesis approach. We perform a number of experiments using two real and well known datasets where the focus is the comparison of the two approaches. One dataset includes a high resolution reference image while the other needs to be degraded prior to pansharpening in order to use the original multispectral image as the reference. Experiments are performed for a range of values for the regularization parameter, where each resulting pansharpened image is evaluated using three quality metrics. The behavior of those metrics as a function of the regularization parameter is compared for the analysis and synthesis formulations and it is shown that analysis gives better results.