Fluorescence diffuse optical tomography: a wavelet-based model reduction

Abstract

Fluorescence diffuse optical tomography is becoming a powerful tool for the investigation of molecular events in small animal studies for new therapeutics developments. Here, the stress is put on the mathematical problem of the tomography, that can be formulated in terms of an estimation of physical parameters appearing as a set of Partial Differential Equations (PDEs). The Finite Element Method has been chosen here to resolve the diffusion equation because it has no restriction considering the geometry or the homogeneity of the system. It is nonetheless well-known to be time and memory consuming, mainly because of the large dimensions of the involved matrices. Our principal objective is to reduce the model in order to speed up the model computation. For that, a new method based on a multiresolution technique is chosen. All the matrices appearing in the discretized version of the PDEs are projected onto an orthonormal wavelet basis, and reduced according to the multiresolution method. With the first order resolution, this compression leads to the reduction of a factor 2×2 of the initial dimension, the inversion of the matrices is approximately 4 times faster. A validation study on a phantom was conducted to evaluate the feasibility of this reduction method.