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Towards a Bayesian Framework for Optical Tomography

Kwee, Ivo W; (2000) Towards a Bayesian Framework for Optical Tomography. Doctoral thesis (Ph.D), UCL (University College London). Green open access

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Maximum likelihood (ML) is a well established method for general parameter estimation. However in its original formulation, ML applied to the image reconstruction problem in Optical Tomography has two serious inadequacies. One is that ML is incapable of distinguishing noise in the data, leading to spurious artifact in the image. The other drawback is that ML does not provide a way to include any prior information about the object that might be available. Noise regularisation is a major concern in imaging and ill-posed inverse problems in general. The aim of this research is to improve the existing imaging algorithm for Optical Tomography. In this thesis we have taken two approaches to the problem. In the first approach we introduce a full maximum likelihood (FML) method which estimates the noise level concurrently. We show that FML in combination with a proposed method of hold-out validation is able to determine a nearly optimal estimate without overfitting to the noise in the data. In the second approach, we will propose a Bayesian method that uses the so-called normal- Wishart density as a parametric prior. We will show that for low degrees of freedom this choice of prior has robust imaging properties and that in some cases the prior can even increase the image resolution (compared to the ML image) but still retain good suppression of noise. We show how graphical modelling can assist in building complex probabilistic models and give examples for the implementation using a developed C++ library. Throughout the thesis, methods are validated by reconstruction examples using simulated data. In the final chapter, we will also present images from real experimental data.

Type: Thesis (Doctoral)
Qualification: Ph.D
Title: Towards a Bayesian Framework for Optical Tomography
Open access status: An open access version is available from UCL Discovery
Language: English
Additional information: Thesis digitised by ProQuest.
Keywords: Applied sciences; Medical physics; Optical Tomography
URI: https://discovery.ucl.ac.uk/id/eprint/10099273
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