The main aim of this paper is to employ the total variation (TV) inpainting model to superresolution imaging problems. We focus on the problem of reconstructing a high-resolution image from several decimated, blurred and noisy low-resolution versions of the high-resolution image. We propose a general framework for multiple shifted and multiple blurred low-resolution image frames which subsumes several well-known superresolution models. Moreover, our framework allows an arbitrary pattern of missing pixels and in particular missing frames. The proposed model combines the TV inpainting model with the framework to formulate the superresolution image reconstruction problem as an optimization problem. A distinct feature of our model is that in regions without missing pixels, the reconstruction process is regularized by TV minimization whereas in regions with missing pixels or missing frames, they are reconstructed automatically by means of TV inpainting. A fast algorithm based on fixed-point iterations and preconditioning techniques is investigated to solve the associated Euler-Lagrange equations. Experimental results are given to show that the proposed TV superresolution imaging model is effective and the proposed algorithm is efficient.

We study the problem of reconstruction of a high-resolution image from several blurred low-resolution image frames. The image frames consist of blurred, decimated, and noisy versions of a high-resolution image. The high-resolution image is modeled as a Markov random field (MRF), and a maximum a posteriori (MAP) estimation technique is used for the restoration. We show that with the periodic boundary condition, a high-resolution image can be restored efficiently by using fast Fourier transforms. We also apply the preconditioned conjugate gradient method to restore high-resolution images in the aperiodic boundary condition. Computer simulations are given to illustrate the effectiveness of the proposed approach.