Adaptive mesh generation for diffuse optical tomography (Invited Paper)

In diffuse optical tomography (DOT), the discretization error in the numerical solutions of the forward and inverse problems results in error in the reconstructed optical images. In this work, based on the analysis presented by Guven, M et al., we present two theorems that constitute the basis for adaptive mesh generation for the forward and inverse DOT problems. The proposed discretization schemes lead to adaptively refined composite meshes that yield the desired level of imaging accuracy while reducing the size of the discretized forward and inverse problems. Our numerical experiments validate the error estimates developed by Guven, M et al. and show that the new adaptive mesh generation algorithms improve the accuracy of the reconstructed optical images