In this paper, we consider the estimation of the unknown parameters for the problem of reconstructing a high-resolution image from multiple undersampled, shifted, degraded frames with subpixel displacement errors. We derive mathematical expressions for the iterative calculation of the maximum likelihood estimate of the unknown parameters given the low resolution observed images. These iterative procedures require the manipulation of block-semi circulant (BSC) matrices, that is, block matrices with circulant blocks. We show how these BSC matrices can be easily manipulated in order to calculate the unknown parameters. Finally the proposed method is tested on real and synthetic images.

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In this paper the subband decomposition of a single channel image restoration problem is examined. The decomposition is carried out in the image model (prior model) in order to take into account the frequency activity of each band of the original image. The hyperparameters associated with each band together with the original image are rigorously estimated within the Bayesian framework. Finally, the proposed method is tested and compared with other methods on real images.

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