Constrained Reconstruction Techniques for Diffuse Optical Tomography

Three-dimensional diffuse optical tomography (DOT) attempts to map in vivo tissue blood oxygenation and blood volume levels by reconstructing the spatial distribution of the optical absorption coefficient from intensity measurements on the surface of the body. This problem is typically ill-posed due to the large attenuation and scattering of the diffuse wave. In addition, certain applications, such as breast mapping from a planar array of optical sources and detectors, increase the ill-posedness of the problem by restricting the views of the sources and detectors. Also, unlike CT or MRI, the interaction of the diffuse wave with the medium can not be restricted to two dimensions. Thus all three spatial dimensions must be considered to accurately account for the diffuse wave propagation. This results in problems that are typically highly underdetermined as well. We first present a comparison of the currently employed linear model reconstruction techniques, to both identify the most promising class using a linear model approach and to provide a baseline for the comparison of the reconstruction performance of the additionally constrained algorithms. Our approach to improve the reconstruction fidelity of this highly underdetermined and ill-posed problem has been to incorporate a priori constraints on the solution. We have developed two types of constrained reconstruction algorithms. The first takes advantage of the necessity of collecting data at two optical wavelengths to implement a constraint on the boundaries and value of the absorption anomaly. The second algorithm is an admissible solution approach where we have examined a number of convex constraint functions on the solution. Using the admissible solution approach