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A typical consumer digital camera uses a Color Filter Array (CFA) to sense only one color component per image pixel. The original three-color image is reconstructed by interpolating the missing color components. This interpolation process (known as demosaicing) corresponds to solving an under-determined system of linear equations. In this paper, we show that by replacing the traditional CFA with a random panchromatic CFA, recent results in the emerging field of Compressed Sensing (CS) can be used to solve the demosaicing problem in a novel way. Specifically, during the image reconstruction process, we exploit the fact that the multi-dimensional color of each pixel has a compressible representation in a (possibly overcomplete) color system. While adhering to the “single color per pixel sensing” constraint at the sensing stage, during the reconstruction process we utilize the inter-pixel correlation by exploiting the compressible representation of the overall image in some sparsifying bases. Depending on the CFA, sparsifying bases and the color system, we form an underdetermined system of linear equations and find the sparsest solution for the color image by utilizing a CS solver. We illustrate that, for natural images, the proposed Compressive Demosaicing (CD) framework visually outperforms leading demosaicing methods in a consistent manner; in many cases it achieves clear visible improvements in a significant way.