| This thesis addresses the super-resolution problem---creating a single high-resolution image from a sequence of low-resolution images of the same scene. A challenging version of this problem is considered in which the observed low-resolution images are misregistered, noisy, degraded by either a known, partially known, or unknown blur, and corrupted by aliasing as a result of sampling below the Nyquist rate. The super-resolution problem is posed as an estimation problem, and five solutions are presented.; The first solution, which is considered a baseline solution in this thesis, is derived using the maximum a posteriori (MAP) estimation framework. The presented method employs a stationary image model known as the simultaneously autoregressive (SAR) image prior. The main novelty of the approach is that all model parameters are estimated jointly from the observations.; Next, a Bayesian solution based on the Expectation-Maximization (EM) algorithm is presented. In this solution, the unknown high-resolution image is treated as a hidden variable and is marginalized over the prior probability density function. The image is modeled using the stationary SAR image prior. Numerical simulation results demonstrate that the Bayesian approach offers a fundamental estimation advantage over the baseline MAP method.; The third and fourth approaches employ a novel hierarchical non-stationary image prior. In these approaches, the solution is adapted to the local statistics of the image. The third method is based on a MAP formulation, whereas the fourth method is based on a hybrid Bayesian/MAP formulation in which the unknown parameters of the image prior are marginalized. Results show that these solutions provide a visual improvement over solutions based on a stationary image statistics.; The final presented approach addresses the blind super-resolved image deconvolution problem in which the solution includes an estimate of the high-resolution image and the unknown blurring function. The proposed solution is based on an approximate Bayesian technique known as the variational method.{09}Simulation results demonstrate that by treating the unknown point spread function as a hidden variable that the blur can be estimated without precise knowledge of its shape or support. |
