Convergence estimates of the Tikhonov-type regularized solutions for the time-domain fluorescence diffuse optical tomography

In this work, we investigate the Tikhonov-type regularized solutions and their finite element solutions to the time-domain fluorescence diffuse optical tomography. Firstly, we analyze the finite element method for solving the direct problem and give its error estimates. With the classical source condition, we further establish the convergence estimates of the regularized solutions and their finite element solutions. The error estimates present explicit dependence on the critical parameters like noise level, regularization parameter, mesh size and time step size.