Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography

It is well known that the reconstruction problem in optical tomography is i ll-posed. In other words, many different spatial distributions of optical p roperties inside the medium can lead to the same detector readings on the s urface of the medium under consideration. Therefore, the choice of an appro priate method to overcome this problem is of crucial importance for any suc cessful optical tomographic image reconstruction algorithm. In this work we approach the problem within a gradient-based iterative image reconstructio n scheme. The image reconstruction is considered to be a minimization of an appropriately defined objective function. The objective function can be se parated into a least-square-error term, which compares predicted and actual detector readings, and additional penalty terms that may contain a priori information about the system. For the efficient minimization of this object ive function the gradient with respect to the spatial distribution of optic al properties is calculated. Besides presenting the underlying concepts in our approach to overcome ill-posedness in optical tomography, we will show numerical results that demonstrate how prior knowledge, represented as pena lty terms, can improve the reconstruction results. (C) 2001 society of Phot o-Optical Instrumentation Engineers.