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

In part I (Guven et al 2007 Inverse Problems 23 1115–33), we analysed the error in the reconstructed optical absorption images resulting from the discretization of the forward and inverse problems. Our analysis led to two new error estimates, which present the relationship between the optical absorption imaging accuracy and the discretization error in the solutions of the forward and inverse problems. In this work, based on the analysis presented in part I, we develop new adaptive discretization schemes for the forward and inverse problems in order to reduce the error in the reconstructed images resulting from discretization. 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. We present numerical experiments to validate the error estimates developed in part I and show the improvement in the accuracy of the reconstructed optical images with the new adaptive mesh generation algorithms. (Some figures in this article are in colour only in the electronic version)