Compressed sensing is applied to multiview image sets and inter-image disparity compensation is incorporated into image reconstruction in order to take advantage of the high degree of inter-image correlation common to multiview scenarios. Instead of recovering images in the set independently from one another, two neighboring images are used to calculate a prediction of a target image, and the difference between the original measurements and the compressed-sensing projection of the prediction is then reconstructed as a residual and added back to the prediction in an iterated fashion. The proposed method shows large gains in performance over straightforward, independent compressed-sensing recovery. Additionally, projection and recovery are block-based to significantly reduce computation time.