Effect of discretization error and adaptive mesh generation in diffuse optical absorption imaging: I

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 first part of our work, we analyse the error in the reconstructed optical absorption images, resulting from the discretization of the forward and inverse problems. Our analysis identifies several factors which influence the extent to which the discretization impacts on the accuracy of the reconstructed images. For example, the mutual dependence of the forward and inverse problems, the number of sources and detectors, their configuration and their orientation with respect to optical absorptive heterogeneities, and the formulation of the inverse problem. As a result, our error analysis shows that the discretization of one problem cannot be considered independent of the other problem. While our analysis focuses specifically on the discretization error in DOT, the approach can be extended to quantify other error sources in DOT and other inverse parameter estimation problems.