Information theoretic regularization in diffuse optical tomography

Abstract

Diffuse optical tomography (DOT) retrieves the spatially distributed optical characteristics of a medium from external measurements. Recovering these parameters of interest involves solving a non-linear and severely ill-posed inverse problem. In this thesis we propose methods towards the regularization of DOT via the introduction of spatially unregistered, a priori information from alternative high resolution anatomical modalities, using the information theory concepts of joint entropy (JE) and mutual information (MI). Such functionals evaluate the similarity between the reconstructed optical image and the prior image, while bypassing the multi-modality barrier manifested as the incommensurate relation between the gray value representations of corresponding anatomical features in the modalities involved. By introducing structural a priori information in the image reconstruction process, we aim to improve the spatial resolution and quantitative accuracy of the solution.A further condition for the accurate incorporation of a priori information is the establishment of correct alignment between the prior image and the probed anatomy in a common coordinate system. However, limited information regarding the probed anatomy is known prior to the reconstruction process.In this work we explore the potentiality of spatially registering the prior image simultaneously with the solution of the reconstruction process.We provide a thorough explanation of the theory from an imaging perspective, accompanied by preliminary results obtained by numerical simulations as well as experimental data. In addition we compare the performance of MI and JE. Finally, we propose a method for fast joint entropy evaluation and optimization, which we later employ for the information theoretic regularization of DOT. The main areas involved in this thesis are: inverse problems, image reconstruction & regularization, diffuse optical tomography and medical image registration. Statement of intellectual contributionI, Christos Panagiotou, declare that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been properly indicated in the thesis.

Mono- and multimodal registration of optical breast images

“…[59][60][61] Information on theoretical measures have been considered, as well as a means to relate reconstructed images to prior knowledge from aligned anatomical images. 62 …”

“…Methods, not specific to the imaging modality used to determine prior knowledge, for including this information in reconstruction algorithms have been introduced by Intes et al 77 and Guven et al 78,79 In all of these methods, the reconstruction is posed as a Bayesian estimation problem where anatomical information is treated as a prior. Panagiotou et al 62 introduce an information theoretic regularization approach for incorporating anatomical data into the reconstruction. Finally, Jagannath and Yalavarthy 80 introduce an algorithm that relies on a 3-D patient breast model that is used to incorporate spatial variation in the refractive index into the reconstruction.…”

Region-based reconstruction method for fluorescent molecular tomography

“…Such prior information can either be obtained from other imaging modalities [24] or be incorporated in a manner by introducing penalty functions, as well as regularization terms such as in Eq. (14) [25,26]. An alternative way of improving the ill-posed nature of the FMT reconstruction is to reduce the number of unknowns involved in the reconstruction.…”

ET Bayesian reconstruction using automatic bandwidth selection for joint entropy optimization

“…For the last two decades there has been a considerable progress in maximum a-posteriori (MAP) image reconstruction for ET using prior knowledge about tracer distribution [1]- [7]. High resolution data available from anatomical scanning modalities, such as magnetic resonance (MR) and computed tomography (CT) can be employed in MAP reconstruction as prior.…”