Numerical comparison of different penalty modified barrier functions for optical tomography problems

摘要

Fluorescent contrast agents have been proposed for near-infrared (NIR) diagnostic breast imaging problems as the most efficient process for inducing optical contrast. We have developed a penalty modified barrier function method (PMBF) with constrained truncated Newton and trust region methods (CONTN) for fluorescence-enhanced NIR diagnostic imaging for both noncontact (area illumination/collection) and contact (point illumination/collection) measurement techniques. A simple logarithmic penalty function has been used in the PMBF/CONTN algorithm with linear convergence. The motivation of this paper is to compare the efficiency and performance of this method with many alternative penalty barrier function methods, (a) hyperbolic penalty function, (b) quadratic-logarithm penalty function, (c) logarithmic exponential penalty function for proper selection of a penalty function that will be the most suitable for optical reconstruction problems. In this paper a numerical comparison of different penalty function methods has been made using experimental measured data in a clinically relevance volume in three-dimensions. Our objective is to continue development of sophisticated constrained optimization PMBF/CONTN method to provide high resolution three dimensional tomography a reality.