Problem Setting

High-resolution image reconstruction refers to the problem of constructing a high resolution image from low resolution images. One of the methods to obtain the low resolution images is to use a sensor array with many low resolution sensors. In the array, each sensor is perturbed by subpixel displacements so as to provide enough independent information in the low resolution images to reconstruct the high resolution image. The reconstruction problem can be viewed as a deconvolution problem where many methods are available.

In this paper, we extend the method of tight frame to video clips to enhance the resolution of one specified frame. Video clips typically consists of 25 to 30 frames per second. Most frames nearby can be considered as small perturbations of the specified reference frame. More precisely, consider a sequence of frames {fk}k=-KK in a given video clip, where k is the order corresponding to the time stamp of the frames. We will call f0 the reference frame and aim to improve its resolution by incorporating information from frames {fk}k ¹0. The frames taken close to f0 in time can be considered as small perturbations of frame f0, i.e., images obtained by displacing the sensors in a sensor array. We assume that the frames {fk}k=-KK are related to f0 by a coordinate transform,

fk(Rkx+rk)» f0(x),     k = -K,...,K

where x are the coordinates of the pixels in the region of interest, which may be the entire image or part of the image.
A low resolution image of size N1-by-N2 is a function f(x),   x Î{0,1,...,N1-1}×{0,1,...,N2-1}. And the high resolution image corresponding to f is an image of size 2N1-by-2N2.



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