A primal-dual method for total-variation-based pansharpening

This paper presents a variational framework to enhance the spatial details of the low-resolution (LR) multispectral (MS) image by the rich spatial information obtained from the panchromatic (Pan) image. The target high-resolution (HR) MS image is estimated through an inverse super-resolution problem, where the LR MS and Pan images are the observations. The LR MS image is modelled by the decimation of the target HR MS image which takes into account the modulation transfer function (MTF) of the MS sensor. In addition, the Pan image is described as a linear combination of the bands of the target HR MS image. A variational pansharpening model is defined according to the image observation models and the total variation (TV) regularization. The target HR MS image is obtained by optimizing the variational model using an efficient primal-dual algorithm in the Euclidean setting. Compared to the other variational pansharpening algorithms adopting the vector representation, the proposed algorithm solves the pansharpening problem by a primal-dual algorithm in the Euclidean setting, resulting in a highly efficient and less complex algorithm. The result of comparing the proposed algorithm with a number of state-of-the-art pansharpening methods demonstrates that the proposed algorithm is visually and quantitatively able to produce much better results. Moreover, the proposed algorithm has several advantages such as higher accuracy in preserving small objects and sharp features, faster convergence, and lower memory requirements over the existing variational pansharpening methods.