| In this dissertation the problem of signal recovery from a partially-known (random) linear degradation operators is studied in the framework of image restoration. This situation arises in many real-life applications, such as tomographic reconstructions from projections, inverse scattering problems, and in displacement-vector-field (DVF) estimation applications. The actual degradation is modeled by a linear space-invariant (LSI) impulse response, which is the sum of a deterministic and a random component. Two approaches are proposed based on this model. The first approach is based on the Expectation-Maximization (EM) algorithm, and the second algorithm utilizes the Empirical Bayesian (EB) analysis. In both approaches two commonly used image prior models were studied in full; the Gaussian image model and the conditional autoregressive (CAR) image model. As an extension to the proposed EM and EB approaches the prior knowledge on the unknown parameters is incorporated into those algorithms. All proposed algorithms, unlike all previous work on this problem, have the capability to simultaneously restore the image and identify the unknown parameters of the observation and image models. The proposed algorithms are demonstrated experimentally in the image restoration simulations and for the problem of tomographic reconstructions from projections. |
