| Multiframe super-resolution is the problem of reconstructing a single high-resolution (HR) image from several low-resolution (LR) versions of it. We assume that the original HR image undergoes different linear transforms that can be approximated as a set of linear shift-invariant transforms over different subregions of the HR image. The linearly transformed HR image is then downsampled, resulting in different LR images. Under the assumption of linearity, these LR images can form a basis that spans the set of the polyphase components (PPCs) of the HR image. We propose sampling diversity, where a reference PPC, of different sampling, is used to make known portions (subpolyphase components) of the PPCs of the HR image. To estimate the reference PPC, LR images are acquired using two imaging sensors with different sensor densities. This setup allows for blind reconstruction of the polyphase components of the HR image by solving a few small linear systems of equations where the number of unknowns is equal to the number of available LR images. The parameters we estimate are the expansion coefficients of the PPCs in terms of the LR basis, using the subpolyphase components. Both synthetic and real data sets are used to test the algorithm. The major features of our approach arc: (1) it is blind, so that unknown motion and blurs can both be incorporated; (2) it is fast, in that only small linear systems of equations need to be solved; and (3) it is robust, in that it avoids the problem of system model errors by treating the LR images as basis for reconstructing the polyphase components of the HR image. |
