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In this paper, we propose a new approach for multiresolution fusion, i.e., obtaining a high spatial and spectral resolution multispectral (MS) image using the available low spatial resolution MS and the high spatial resolution Panchromatic (Pan) image. Our approach is based on the idea of compressive sensing (CS) and graph cuts. Assuming that both the MS and Pan images have the same sparseness, a close approximation to the MS image is obtained from the Pan image using the theory of compressive sensing and l1 minimization. We then use regularization framework to obtain fused image. The low resolution (LR) MS image is modeled as degraded and noisy version of fused image in which degradation matrix entires estimated using the close approximation are used. The regularization is carried out by using truncated quadratic smoothness prior which takes care of preservation of the discontinuities in the fused image. A suitable energy function is then formed consisting of data fitting term and prior term. Minimization of the energy function is carried out using a computationally efficient graph cuts optimization to obtain final fused image. Advantage of our approach is that the Pan and MS images need not be registered. This is because, we are not directly using the Pan digital numbers to derive the fused image. The effectiveness of the proposed method is illustrated by conducting experiments on real satellite images. Subjective and quantitative comparison of the proposed method with the state-of-the-art approaches indicates efficacy of our approach.