Elastic-optical tomography for breast cancer imaging.

摘要

This dissertation is devoted to studies of elastic-optical tomography for breast cancer imaging. Efforts are made to exploration of development and application of numerical optimization methods to the inverse problem which have a great stability and accuracy on the reconstructed images. Elastic-optical tomography model has been created and evaluated to account for the compression-induced changes in optical tomography. The major accomplishments in the study are summarized in the following.First, an improved Levenberg-Marquardt method is developed for diffuse optical tomography problems to take into account the magnitude variation and reasonable range of the optical coefficients. A scaling matrix scheme is introduced to reduce the effect of poor scaling by using an ellipsoidal trust region instead of a spherical trust region. A lower bound is imposed to avoid non-positive results. The proposed approach is capable of detecting inclusions in different shapes with high object to background optical contrast even under the impact of noise.We also applied quasi-Newton methods (BFGS and lm-BFGS methods) to solve the inverse problems in the diffuse optical tomography. A more efficient inexact line search strategy is employed in the method. For large-scale problems, lm-BFGS can help reduce the memory requirement. Good reconstruction can be achieved in terms of inclusion location and size in both numerical and experimental studies.A hybrid method is then proposed by combining the improved Levenberg-Marquardt method and quasi-Newton method. The hybrid method can switch between the above mentioned two methods based on the iteration results to avoid slow convergence. Studies show that the hybrid method can improve the quality of the reconstructed optical images compared to Levenberg-Marquardt method and quasi-Newton method.A very important portion in this dissertation is the development of elastic-optical tomography to predict how optical properties change according to the externally applied compression for breast cancer imaging. Both the mechanical and optical properties of the breast tissue are incorporated into the model. Results show that the proposed model can be used to interpret the possible misleading information caused by compression induced changes in optical images and recover the actual optical contrast, location and size of the malignant tumors.