FDOT reconstruction and setting optimization using singular value analysis with automatic thresholding

Abstract

Fluorescence Enhanced Diffuse Optical Tomography (FDOT) retrieves 3D distributions of fluorophore concentration in small animals, non-invasively and in vivo. The FDOT problem can be formulated as a system of equations, d=Wf, where W is a weight matrix that couples the measurements (d) to the unknown spatial distribution (f) of the fluorophore concentration (forward problem). The Singular Value Decomposition (SVD) of W has been previously employed to solve the inverse problem (image reconstruction) and to study the imaging performance of FDOT. To achieve good image quality it is necessary to determine the number of useful singular values to retain. We use an automatic method that analytically calculates a threshold to select the significant singular values for SVD reconstruction of FDOT experiments previously validity in our laboratory. Afterwards, this work appraises the effect of different settings of the acquisition parameters (distribution of mesh points, density of sources and detectors) of a parallel-plate noncontact FDOT, in order to achieve the best possible imaging performance, i.e., minimum number of singular values of W, maximum information content in acquired measurements and minimum computational cost. We conclude that the use of a mesh with lower density in the direction perpendicular to the plates achieves better performance than the usual isotropic mesh points distribution. Any increase in the number of mesh points, sources and detectors at distances shorter than the photon mean free path leads to slight improvements in image quality while increasing computational burden.