Analysis of finite-element-based methods for reducing the ill-posedness in the reconstruction of fluorescence molecular tomography

The major issue in reconstruction of optical imaging might be the ill-posedness of the problem. In this paper, four different algorithms, including singular value decomposition (SVD), the truncated SVD, Tikhonov regularization and adaptive regularization, are analyzed and applied for solving the matrix equation generated from diffuse equation based on finite-element method in fluorescence molecular tomography. Results illustrate the need for either imposition of regularization term or elimination of too small singular values in reducing the ill-posedness. The results also suggest that the adaptive-regularization method offers superior performance in the reconstruction among the four methods in most cases even if the initially selected regularization parameter is not optimal, thus providing the convenience for the reconstruction.