Generalized conditional gradient method with adaptive regularization parameters for fluorescence molecular tomography.

Fluorescence molecular tomography (FMT) is an optical imaging technology with the ability of visualizing the three-dimensional distribution of fluorescently labelled probes in vivo. However, due to the light scattering effect and ill-posed inverse problems, obtaining satisfactory FMT reconstruction is still a challenging problem. In this work, to improve the performance of FMT reconstruction, we proposed a generalized conditional gradient method with adaptive regularization parameters (GCGM-ARP). In order to make a tradeoff between the sparsity and shape preservation of the reconstruction source, and to maintain its robustness, elastic-net (EN) regularization is introduced. EN regularization combines the advantages of L-norm and L-norm, and overcomes the shortcomings of traditional L-norm regularization, such as over-sparsity, over-smoothness, and non-robustness. Thus, the equivalent optimization formulation of the original problem can be obtained. To further improve the performance of the reconstruction, the L-curve is adopted to adaptively adjust the regularization parameters. Then, the generalized conditional gradient method (GCGM) is used to split the minimization problem based on EN regularization into two simpler sub-problems, which are determining the direction of the gradient and the step size. These sub-problems are addressed efficiently to obtain more sparse solutions. To assess the performance of our proposed method, a series of numerical simulation experiments and in vivo experiments were implemented. The experimental results show that, compared with other mathematical reconstruction methods, GCGM-ARP method has the minimum location error (LE) and relative intensity error (RIE), and the maximum dice coefficient (Dice) in the case of different sources number or shape, or Gaussian noise of 5%-25%. This indicates that GCGM-ARP has superior reconstruction performance in source localization, dual-source resolution, morphology recovery, and robustness. In conclusion, the proposed GCGM-ARP is an effective and robust strategy for FMT reconstruction in biomedical application.