A trust region method in adaptive finite element framework for bioluminescence tomography

Bioluminescence tomography (BLT) is an effective molecular imaging (MI) modality. Because of the ill-posedness, the inverse problem of BLT is still open. We present a trust region method (TRM) for BLT source reconstruction. The TRM is applied in the source reconstruction procedure of BLT for the first time. The results of both numerical simulations and the experiments of cube phantom and nude mouse draw us to the conclusion that based on the adaptive finite element (AFE) framework, the TRM works in the source reconstruction procedure of BLT. To make our conclusion more reliable, we also compare the performance of the TRM and that of the famous Tikhonov regularization method after only one step of mesh refinement of the AFE framework. The conclusion is that the TRM can get faster and better results after only one mesh refinement step of AFE framework than the Tikhonov regularization method when handling large scale data. In the TRM, all the parameters are fixed, while in the Tikhonov method the regularization parameter needs to be well selected.