A fast reconstruction method for fluorescence molecular tomography based on improved iterated shrinkage

Fluorescence molecular tomography (FMT) has become a promising imaging modality for in vivo small animal molecular imaging, and has many successful applications. This is partly due to the wealth of the fluorescent probes. By labeling the regions of interest with fluorescent probes, FMT can achieve non-invasive investigation of the biological process by localizing the targeted probes based on certain inverse mathematical models. However, FMT is usually an ill-posed problem, and some form of regularization should be included to stabilize the problem, which can be considered as the a priori information of the fluorescent probe bio-distribution. When FMT is used for the early detection of tumors, an important characteristic is the sparsity of the fluorescent sources. This is because tumors are usually very small and sparse at this stage. Considering this, general sparsity-promoting Lp-norm regularization is utilized in this paper. The iterated shrinkage based reconstruction method is adopted to solve the general Lp regularization problem. However, the original iterated shrinkage method is proved to have a linear convergence rate, and a large number of iterations are needed to obtain satisfactory results. In this paper, an improved iterated shrinkage based FMT reconstruction algorithm is proposed. By using the solutions from two previous iterations to determine the current solution, the convergence rate can be greatly increased. Heterogeneous simulation experiment shows that the proposed method can obtain comparable results with greatly reduced number of iterations compared with the original iterated shrinkage based method, which makes it a practical reconstruction algorithm.