Regularization methods for diffuse optical tomography

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto. fi Author Petri Hiltunen Name of the doctoral dissertation Regularization methods for diffuse optical tomography Publisher School of Science Unit Department of Biomedical Engineering and Computational Science Series Aalto University publication series DOCTORAL DISSERTATIONS 98/2011 Field of research Computational Science Manuscript submitted 1 April 2011 Manuscript revised 9 June 2011 Date of the defence 8 November 2011 Language English Monograph Article dissertation (summary + original articles) Abstract Near-infrared light can be used as a three dimensional imaging tool, called diffuse optical tomography (DOT), in the study of human physiology. Due to differences in the extinction coefficients of oxygenated and deoxygenated haemoglobin at different wavelengths, concentrations of the haemoglobins can be resolved from measurements at a few wavelengths. Therefore, DOT is a fascinating modality for biomedical applications, such as functional brain imaging, breast cancer screening, etc. Moreover light is a safe tool, because it is non-ionizing and at intensity levels used in DOT, it does not cause burns at skin or in organs.Near-infrared light can be used as a three dimensional imaging tool, called diffuse optical tomography (DOT), in the study of human physiology. Due to differences in the extinction coefficients of oxygenated and deoxygenated haemoglobin at different wavelengths, concentrations of the haemoglobins can be resolved from measurements at a few wavelengths. Therefore, DOT is a fascinating modality for biomedical applications, such as functional brain imaging, breast cancer screening, etc. Moreover light is a safe tool, because it is non-ionizing and at intensity levels used in DOT, it does not cause burns at skin or in organs. There are a few different models to describe light propagation in tissue-like media. One of the simplest, called the diffusion approximation (DA), was used in this thesis. The optical properties, the absorption and the scattering coefficients, are the parameters which determine the light propagation in the DA model. When optical properties are known and one is interested in estimating the photon flux at the boundary, the problem is called a forward problem. Likewise, when the photon flux at the boundary is measured and the task is to find the optical properties, the problem is called an inverse problem. The inverse problem related to DOT is ill-posed, i.e., the solution might not be unique or the solution does not depend continuously on data. Due to ill-posedness of the inverse problem, some regularization methods should be used. In this thesis, regularization methods for a stationary and nonstationary inverse problems was considered. By the nonstationary inverse problem, it is meant that the optical properties are not static during the measurement and the whole evolution of the optical properties is reconstructed in contrast to the stationary problem, where the optical properties are assumed to be static during the measurement. The regularization for the inverse problem could be implemented as the Tikhonov regularization or using statistical inversion theory, also known as the Bayesian framework. In this thesis, two different regularization methods for the static reconstruction problem in DOT were studied. They both allow discontinuities in the optical properties that might occur at boundaries between organs. For the nonstationary reconstruction problem, an efficient regularization model is presented.