| Optical tomographic imaging plays an increasingly important role in many biomedical applications, including, for example, neural activity detection, disease diagnosis, and pharmaceutical evaluation. A major challenge remains the development and optimization of accurate and efficient algorithms for tomographic image reconstructions. Codes that employ the theory of radiative transfer (TRT) have attracted considerable research efforts in recent years due to their superior accuracy over the diffusion-theory-based algorithms. Their advantages are most prominent when small imaging geometries are considered, as the occur for example in the fast expanding field of small animal imaging to study cancer and other diseases. Over the past decade first TRT based algorithms have emerged and are now available for the time-independent case (so called steady-state domain) and the frequency-domain, in which light intensities are modulated in the MHz to GHZ range. However, the frequency-domain algorithms have not been optimized specifically for small-volume tissue imaging, which results in inconveniently time-consuming performance, requirement of large memory size, and poor stability in a number of practical applications.;In this thesis, I have developed and optimized a nonlinear inverse reconstruction algorithm with the aim to achieve enhanced image qualities and higher numerical efficiencies in respect to the existing frequency-domain algorithms. The methodology of the PDE-constrained optimization is adopted and customized to serves as an organizing theme, which leads to the application of the Quasi-Newton reduced-space sequential quadratic programming (QN-RSQP) method of the nonlinear inverse reconstruction algorithm. To further increase the speed of the reconstruction algorithm, I have implemented a domain decomposition method that allows to execute the QN-RSQP algorithm in parallel. In addition a parametric reconstruction technique was developed, which makes use of the Discrete Cosine Transform (DCT), to enhance both the stability of the inverse algorithm and the quality of recovered images. The codes developed were used to perform numerical sensitivity analysis, and optimal source-modulation frequency were determined for imaging small tissue volumes. Finally the algorithms were employed to study tumor growth and regression in small animals as well as looking at disease characteristics in finger joints affected by arthritis. Both simulation and tissue phantom study have shown that the new algorithms improve the image reconstruction speed and enhance the reconstructed image quality. The tumor monitoring study results reached our expectation, which further confirms the feasibility of the new algorithms for small animal imaging. |
