Real-time diffuse optical tomography using reduced-order light propagation models based on a priori anatomical and functional information

This paper proposes a new fast 3D image reconstruction algorithm for Diffuse Optical Tomography using reduced order polynomial mappings from the space of optical tissue parameters into the space of flux measurements at the detector locations. The polynomial mappings are constructed through an iterative estimation process involving structure detection, parameter estimation and cross-validation using data generated by simulating a diffusion approximation of the radiative transfer equation incorporating a priori anatomical and functional information provided by MR scans and prior psychological evidence. Numerical simulation studies demonstrate that reconstructed images are remarkably similar in quality as those obtained using the standard approach, but obtained at a fraction of the time

Optimizing the geometrical accuracy of curvilinear meshes

This paper presents a method to generate valid high order meshes with optimized geometrical accuracy. The high order meshing procedure starts with a linear mesh, that is subsequently curved without taking care of the validity of the high order elements. An optimization procedure is then used to both untangle invalid elements and optimize the geometrical accuracy of the mesh. Standard measures of the distance between curves are considered to evaluate the geometrical accuracy in planar two-dimensional meshes, but they prove computationally too costly for optimization purposes. A fast estimate of the geometrical accuracy, based on Taylor expansions of the curves, is introduced. An unconstrained optimization procedure based on this estimate is shown to yield significant improvements in the geometrical accuracy of high order meshes, as measured by the standard Haudorff distance between the geometrical model and the mesh. Several examples illustrate the beneficial impact of this method on CFD solutions, with a particular role of the enhanced mesh boundary smoothness.Comment: Submitted to JC

A Comparison Study of Two Methods for Elliptic Boundary Value Problems

In this paper, we perform a comparison study of two methods (the embedded boundary method and several versions of the mixed finite element method) to solve an elliptic boundary value problem