Exact image super-resolution for pure translational motion and shift-invariant blur

In this work, a special case of image super-resolution problem where the only type of motion is global translational motion and the blurs are shift-invariant is investigated. The necessary conditions for exact reconstruction of the original image by using finite impulse-response reconstruction filters are developed. If the number of low-resolution images is larger than a threshold and the blur functions meet a certain property, then a reconstruction filter set for exact super-resolution can be generated. If the conditions are not fully satisfied, then the high-resolution image is reconstructed with some error.