Reconstruction of a high-resolution image by simultaneous registration, restoration, and interpolation of low-resolution images

In this paper a solution is provided to the problem of obtaining a high resolution image from several low resolution images that have been subsampled and displaced by different amounts of sub-pixel shifts. In its most general form, this problem can be broken up into three sub-problems: registration, restoration, and interpolation. Previous work has either solved all three sub-problems independently, or more recently, solved either the first two steps (registration and restoration) or the last two steps together. However, none of the existing methods solve all three sub-problems simultaneously. This paper poses the low resolution to high resolution problem as a Maximum Likelihood (ML) problem which is solved by the Expectation-Maximization (EM) algorithm. By exploiting the structure of the matrices involved, the problem can be solved in the discrete frequency domain. The ML problem is then the estimation of the sub-pixel shifts, the noise variances of each image, the power spectra of the high resolution image, and the high resolution image itself. Experimental results are shown which demonstrate the effectiveness of this approach.