A regularized pan-sharpening approach based on self-similarity and Gabor prior

In this article, we propose a new regularization-based approach for pan-sharpening based on the concepts of self-similarity and Gabor prior. The given low spatial resolution (LR) and high spectral resolution multi-spectral (MS) image is modelled as degraded and noisy version of the unknown high spatial resolution (HR) version. Since this problem is ill-posed, we use regularization to obtain the final solution. In the proposed method, we first obtain an initial HR approximation of the unknown pan-sharpened image using self-similarity and sparse representation (SR) theory. Using self-similarity, we obtain the HR patches from the given LR observation by searching for matching patches in its coarser resolution, thereby obtaining LR–HR pairs. An SR framework is used to obtain the patch pairs for which no matches are available for the patches in LR observation. The entire set of matched HR patches constitutes initial HR approximation (initial estimate) to the final pan-sharpened image which is used to estimate the degradation matrix as used in our model. A regularization framework is then used to obtain the final solution in which we propose to use a new prior which we refer as Gabor prior that extracts the bandpass details from the registered panchromatic (Pan) image. In addition, we also include Markov random field (MRF) smoothness prior that preserves the smoothness in the final pan-sharpened image. MRF parameter is derived using the initial estimate image. The final cost function consists of data fitting term and two prior terms corresponding to Gabor and MRF. Since the derived cost function is convex, simple gradient-based method is used to obtain the final solution. The efficacy of the proposed method is evaluated by conducting the experiments on degraded as well as on un-degraded datasets of three different satellites, i.e., Ikonos-2, Quickbird, and Worldview-2. The results are compared on the basis of traditional measures as well as recently proposed quality with no reference (QNR) measure, which does not require the reference image.