Fast and robust three-dimensional fluorescence source reconstruction based on separable approximation and adaptive regularization

In this study, a fast and robust reconstruction method based on the separable approximation and the adaptive regularization is presented for fluorescence molecular tomography. The subproblems can be established and solved efficiently through separable approximation, and the convergence process can be also accelerated by adaptive regularization. As is well known, the regularization parameter has an important impact on the results, and finding the optimal or near-optimal regularization parameter automatically is an challenging task. To solve this problem, the regularization parameter in the proposed method is updated heuristically instead of being determined manually or empirically. This adaptive regularization strategy of the proposed method can perform accurate reconstruction almost without worrying about the choice of the regularization parameter. By contrast, improper choice of the regularization parameter may cause larger location errors for the three contrasting methods. The proposed method is proved robust and insensitive to parameters, which can improve the reconstruction accuracy. Moreover, the proposed method was about 1-2 orders of magnitude faster than the contrasting methods commonly used in fluorescence tomography reconstruction. Furthermore, reliable performance on different initial unknown values and different noise levels was also investigated. Finally, the potential of the proposed method in a practical application was further validated by the physical experiment with a mouse model.