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

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Abstract
It is well known that the reconstruction problem in optical tomography is ill-posed. In other words, many different spatial distributions of optical properties inside the medium can lead to the same detector readings on the surface of the medium under consideration. Therefore, the choice of an appropriate method to overcome this problem is of crucial importance for any successful optical tomographic image reconstruction algorithm. In this work we approach the problem within a gradient-based iterative image reconstruction scheme. The image reconstruction is considered to be a minimization of an appropriately defined objective function. The objective function can be separated 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 objective function the gradient with respect to the spatial distribution of optical 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 penalty terms, can improve the reconstruction results.