Reconstruction of Fluorescence Molecular Tomography Using a Neighborhood Regularization

In fluorescence molecular tomography, the highly scattering property of biological tissues leads to an ill-posed inverse problem and reduces the accuracy of detection and localization of fluorescent targets. Regularization technique is usually utilized to obtain a stable solution. Conventional Tikhonov regularization is based on singular value decomposition (SVD) and L-curve strategy, which attempts to find a tradeoff between the residual norm and image norm. It is computationally demanding and may fail when there is no optimal turning point in the L-curve plot. In this letter, a neighborhood regularization method is presented. It achieves a reliable solution by computing the geometric mean of multiple regularized solutions. These solutions correspond to different regularization parameters with neighbor orders of magnitude. The main advantages lie in three aspects. First, it can produce comparable or better results in comparison with the conventional Tikhonov regularization with L-curve routine. Second, it replaces the time-consuming SVD computation with a trace-based pseudoinverse strategy, thus greatly reducing the computational cost. Third, it is robust and practical even when the L-curve technique fails. Results from numerical and phantom experiments demonstrate that the proposed method is easy to implement and effective in improving the quality of reconstruction.