Parametric Reconstruction Method in Optical Tomograhy

Optical tomography consists of reconstructing the spatial of a medium´s optical properties from measurements of transmitted light on the boundary of the medium. Mathematically this problem amounts to parameter identification for the radiative transport equation (ERT) or diffusion approximation (DA). However, this type of boundary-value problem is highly ill-posed and the image reconstruction process is often unstable and non-unique. To overcome this problem, we present a parametric inverse method that considerably reduces the number of variables being reconstructed. In this way the amount of measured data is equal or larger than the number of unknowns. Using synthetic data, we show examples that demonstrate how this approach leads to improvements in imaging quality