A Compressed-Sensing-Based Pan-Sharpening Method for Spectral Distortion Reduction

Recently, the compressed sensing (CS) theory has become an interesting topic for pan-sharpening of multispectral images. The CS theory ensures that, under the sparsity regularization, an unknown sparse signal can be exactly recovered from a drastically smaller number of linear measurements. In this paper, we propose a CS-based approach for fusion of the multispectral and panchromatic satellite images. The contribution of this paper is twofold. First, with the spatial and spectral characteristics of the satellite images, we assume that each patch of the unknown high spatial resolution intensity (HRI) component can be represented as a linear combination of atoms in a dictionary trained only from the panchromatic image; thus, the problem of generating an optimal dictionary is solved. Second, we propose an iterative algorithm to obtain the sparsest coefficients. The sparsest coefficients ensure that the estimated HRI component can be correctly recovered from the panchromatic image. The IKONOS, QuickBird, and WorldView-2 data are used to evaluate the performance of the proposed method. The experimental results demonstrate that the proposed method generates high-quality pan-sharpened multispectral bands quantitatively and perceptually.