Iterative Gauss-Seidel method improves image reconstruction in diffuse optical Tomography: A comparative study

Diffuse Optical Tomography is an adjunct imaging modality with the capability of providing functional characteristics of the soft-tissues under investigation. A stable solution can be obtained for the DOT inverse problem which entails the regularization because of its nonlinear, ill-posedness, and sometimes under-determined nature. The regularization parameter is usually selected heuristically or based on previous experience. Even though several algorithms for determining the optimal regularization have been devised, the Tikhonov-type regularization being the most common, the difficulty of making this estimation computationally efficient and accurate continues. The goal of this paper is to provide iterative based numerical approaches such as Method of Successive Displacement, Kaczmarz, and Modified Richardson schemes for estimating the appropriate regularization parameter as well as for inverse computing that leads to better image reconstruction. The existing inverse estimation approach, which uses the standard Levenberg–Marquardt (LM) inverse method to obtain the solution, has an expensive computational complexity for large problems. The investigation is carried out on the reconstruction performed with multiple number of anomalies placed at distinct positions in a coarser mesh using the Method of Successive Displacement numerical technique. Furthermore, the Method of Successive Displacement is expanded to estimate the optimal regularization parameter without repeated matrix inversion, considerably improving reconstructed image quality while reducing computation complexity. This technique can also be used to achieve spatially varying optimal regularization. The results of the reconstruction using numerical data reveals that the Method of Successive Displacement based (or Gauss-Seidel) iterative procedure can provide a better regularisation parameter in order to resolve the target with closely spaced anomalies with less computational complexity when compared to the results of the existing L-curve, GCV and MRM based regularisation estimation. The Method of Successive Displacement technique can reconstruct the absorption coefficient distribution at par with the standard Levenberg–Marquardt (LM) inverse method, and it is a good choice for computing the regularization parameter because it greatly reduces the computational complexity associated with automatically obtaining optimal regularization.