Overcoming ill-posedness in optical tomography

In optical tomography (OT) one attempts to reconstruct cross-sectional images of various body parts given data from near-infrared transmission measurements. The cross-sectional images display the spatial distribution of optical properties, such as the absorption coefficient μ_a, the reduced scattering coefficient μ_s′, or a combination thereof. One of the major problems of the novel imaging technology is that many different spatial distributions of optical properties inside the medium can lead to the same detector readings on the surface of the medium. Therefore, the reconstruction problem in optical tomography is ill posed. 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 image iterative reconstruction (GIIR) scheme. The image reconstruction is considered as 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. We present the underlying concepts in our approach to overcome ill-posedness in optical tomography and show how different penalty terms affects the performance of the image reconstruction.