Comparing Two Regularization Techniques for Diffuse Optical Tomography

Two techniques to regularize the diffuse optical tomography inverse problem were compared for a variety of simulated test domains. One method repeats the single-step Tikhonov approach until a stopping criteria is reached, regularizing the inverse problem by scaling the maximum of the diagonal of the inversion matrix with a factor held constant throughout the iterative reconstruction. The second method, a modified Levenberg-Marquardt formulation, uses an identical implementation but reduces the factor at each iteration. Four test geometries of increasing complexity were used to test the performance of the two techniques under a variety of conditions including varying amounts of data noise, different initial parameter estimates, and different initial values of the regularization factor. It was found that for most cases tested, holding the scaling factor constant provided images that were more robust to both data noise and initial homogeneous parameter estimates. However, the results for a complex test domain that most resembled realistic tissue geometries were less conclusive.