Multiresolution fusion using compressive sensing and graph cuts

Abstract

Multiresolution fusion refers to the enhancement of low spatial resolution (LR) of Multispectral (MS) images to that of Panchromatic (Pan ) image without compro- mising on the spectral details. Many of the present day methods for multiresolution fusion require that the Pan and MS images are registered. In this thesis we propose a new approach for multiresolution fusion which is based on the theory of compressive sensing and graph cuts. We rst estimate a close approximation to the fused image by using the sparseness in the given Pan and MS images. Assuming that the Pan and LR MS image have the same sparseness, the initial estimate of the fused image is obtained as the linear combination of the Pan blocks. The weights in the linear combination are estimated using the l1 minimization by making use of MS and the down sampled Pan image. The nal solution is obtained by using a model based approach. The low resolution MS image is modeled as the degraded and noisy version of the fused image in which the degradation matrix entries are estimated by using the initial estimate and the MS image. Since the MS fusion is an ill-posed inverse problem, we use a regularization based approach to obtain the nal solution. We use the truncated quadratic prior for the preservation of the discontinuities in the fused image. A suitable energy function is then formed which consists of data tting term and the prior term and is minimized using a graph cuts based approach in order to obtain the fused image. The advantage of the proposed method is that it does not require the registration of Pan and MS data. Also the spectral characteristics are well preserved in the fused image since we are not directly operating on the Pan digital numbers. Effectiveness of the proposed method is illustrated by conducting experiments on synthetic as well as on real satellite images. Quantitative comparison of the proposed method in terms of Erreur Relative Globale Adimensionnelle de Synthse (ERGAS), Correlation Coecient(CC) , Relative Average Spectral Error(RASE) and Spectral Aangle Mapper(SAM) with the state of the art approaches indicate superiority of our approach