Accurate inversion of absorption and scattering in diffuse optical tomography without iterative Green´s function update

Diffuse optical tomography (DOT) reconstructs optical properties of a highly scattering medium such as tissue in a non-invasive and relatively low-cost manner. However, the inverse problem of DOT is a severely ill-posed nonlinear inverse problem, and the conventional methods usually require iterative Green´s function update to obtain accurate reconstruction. Recently, by exploiting the joint sparsity of absorption parameter perturbation, we showed that accurate reconstruction of absorption parameter variation can be obtained without Green´s function update. However, the method cannot be applied for the simultaneous reconstruction of both absorption and scattering parameters. In this paper, we reveal a general principle showing that support information found using the joint sparsity can convert the nonlinear inverse problem to a linear inverse problem with internal data, which naturally allows simultaneous reconstruction of absorption and scattering parameters. The proposed method is validated using various simulation studies, which produce improved reconstruction and reduction of the cross-talk artifacts compared to the conventional methods.