Linear and nonlinear reconstruction for diffuse optical tomography in an inhomogeneous background

Diffuse Optical Tomography is a novel approach to imaging the body's optical properties non-invasively using non-ionizing electromagnetic radiation in the visible and near-infrared range. As spectral information at a number of measurement wavelengths can give important information about functional properties of tissue relatively deep withing the body, it is hoped that Optical Tomography will be clinically useful, particularly for detecting breast tumors and distinguishing between tumors and benign lesions. This paper formulates the fully three-dimensional linear and nonlinear inverse problems for Diffuse Optical Tomography and compares the linear and nonlinear reconstructions in a heterogeneous medium for a number of cases. In the first case, the background has a randomly varying lowpass structure. In the second case, the background has a layered structure with a sharp transition between layers, and, in the third case, the structure of the background is known, but not the corresponding optical properties.