An adaptive Tikhonov regularization method for fluorescence molecular tomography

The high degree of absorption and scattering of photons propagating through biological tissues makes fluorescence molecular tomography (FMT) reconstruction a severe ill-posed problem and the reconstructed result is susceptible to noise in the measurements. To obtain a reasonable solution, Tikhonov regularization (TR) is generally employed to solve the inverse problem of FMT. However, with a fixed regularization parameter, the Tikhonov solutions suffer from low resolution. In this work, an adaptive Tikhonov regularization (ATR) method is presented. Considering that large regularization parameters can smoothen the solution with low spatial resolution, while small regularization parameters can sharpen the solution with high level of noise, the ATR method adaptively updates the spatially varying regularization parameters during the iteration process and uses them to penalize the solutions. The ATR method can adequately sharpen the feasible region with fluorescent probes and smoothen the region without fluorescent probes resorting to no complementary priori information. Phantom experiments are performed to verify the feasibility of the proposed method. The results demonstrate that the proposed method can improve the spatial resolution and reduce the noise of FMT reconstruction at the same time.