An adaptive multigrid algorithm for region of interest diffuse optical tomography

Due to diffuse nature of light photons, diffuse optical tomography (DOT) image reconstruction is a challenging 3D problem with a relatively large number of unknowns and limited measurements. As a result, the computational complexity of the existing DOT image reconstruction algorithms remains prohibitive. In this work, we investigate an adaptive multigrid approach to improve the computational efficiency and the quantitative accuracy of DOT image reconstruction. The key idea is based on locally refined grid structure for region of interest (ROI). The ROI may be defined as diagnostically significant regions, strong background heterogeneities and/or deep optical edges, A 2-level mesh is generated to provide high resolution for ROI and sufficiently high resolution for the rest of the image. A least squares (LS) solution is formulated for the inverse problem. Fast adaptive composite (FAC) 2-grid algorithm is employed to solve the inverse problem. Conjugate gradient (CG) is used at the relaxation stage of FAC 2-grid. Same problem is also solved using direct CG and standard 2-grid method for globally fine grid structure. Our numerical studies demonstrate that the proposed FAC based adaptive 2-grid approach provides up to 90% reduction in computational requirements as compared to the direct iterative and standard 2-grid methods while providing better image quality. The fundamental ideas introduced in this study are directly applicable to other linear and nonlinear inverse problems with Newton type global linearization.