Preconditioned iterative methods for high-resolution image reconstruction with multisensors

We study the problem of reconstructing a high-resolution image from multiple undersampled, shifted, degraded frames with subpixel displacement errors. The corresponding reconstruction operator H is a spatially variant operator. In this paper, instead of using the usual zero boundary condition (corresponding to a dark background outside the scene), the Neumann boundary condition (corresponding to a reflection of the original scene at the boundary) is imposed on the images. The resulting discretization matrix of H is a block-Toeplitz-Toeplitz-block-like matrix. We apply the preconditioned conjugate gradient (PCG) method with cosine transform preconditioners to solve the discrete problems. Preliminary results show that the image model under the Neumann boundary condition gives better reconstructed high-resolution images than that under the zero boundary condition, and the PCG method converges very fast.