Bayesian sampling methods constitute a powerful tool for signal detection and estimation. They exploit the virtues of Bayesian estimation, concise modeling of the problem and efficient use of all prior information available, while being computationally feasible and apt for efficient implementation. Therefore they offer practical solutions to a wide field of problems in statistical signal processing.
This thesis describes the application of a Bayesian sampling method, the Gibbs sampler, on signals from the domain of Optical Coherence Tomography (OCT). OCT is a state-of-the-art imaging technology, which is used for high-resolution imaging of the outer layer of biological tissue. The task of extracting the relevant information from OCT images is described as a joint detection and estimation problem by formulating a statistical system model which represents the physical processes involved in the generation of OCT images, as well as the known statistical properties of the tissue.
With the help of this model, a Gibbs sampler is developed with the purpose of locating and quantifying steps in the depth profile of the tissue's refractive index, based on the distorted observed signal, i.e. the OCT image. The system model and the respective algorithms for synthesis as well as detection and estimation of OCT signals are gradually refined in order to achieve more realistic OCT signals.
In order to compare the estimator's performance with an existing method, the Single Most Likely Replacement (SMLR) algorithm, which has been used successfully in the domain of OCT, is adapted to the newly defined system model.
All algorithms derived and discussed in the course of this thesis are applied to synthetic as well as real OCT signals to compare their outcome.