Research On Sparse Algorithm Reconstruction Based On L _1/2 Norm X - Ray Luminescence Tomography

X-ray Luminescence Computed Tomography (XLCT) is a new modality of optical molecular imaging. XLCT has several advantages compared to other optical molecular imaging modalities:the anatomy and the nanophosphors can be imaged in one scan; The use of x-ray excitation eliminates the autofluorescence in optical fluorescence imaging; The straight line propagation of x-ray means a localized and deep probing capability. However, the high ill-posedness makes the reconstruction of XLCT a great challenge. Therefore, an effective and robust algorithm is proposed to figure out the reconstruction problem of XLCT.During the XLCT problem, the luminescent target is always sparse. The widely used L1-norm regularization method is usually not the sparsest one. Although the Lo-norm regularization can yield the sparest solution in most conditions, it faces the problem of combinatory optimization. Consequently, a method based on L1/2regularization is proposed in this contribution. Compared with L1regularization, L1/2regularization can yield a more sparse solution and it is easier to solve in contrast with the Lo regularization. Nevertheless, the L1/2regularization is a non-convex optimization problem which is difficult to solve, thus a reweighted iterative algorithm is proposed so that the solution of L1/2regularization can be solved through transforming it into the solution of a series of L1regularization, and then we can use the efficient L1-Homotopy to solve the problem. In order to validate the effectiveness of the proposed method, the L1/2regularization and L1regularization combined with Homotopy were employed respectively for the reconstruction of single target and double targets numerical experiments to compare with each other, the results suggest that the reconstruction of L1/2regularization is more accurate and sparser. The robustness of the proposed method is verified by experiments with adding noise. Moreover, we further validate the effectiveness of the proposed method through small animal experiments.To further improve the reconstruction results, the adaptive finite element optimizes is adopted which has good performance in our experiments. We mainly analyze the method to choose feasible region and refine mesh. Finally, basing on the results of coarse mesh, the adaptive finite element method is applied to obtain optimization results. The experiment results suggest that this method could improve the results greatly and the effectiveness of this method is verified.To obtain sparser results, in this paper, a L1/2regularization method is proposed. The effectiveness of this method is verified by numerical and in vivo experiments, the robustness of this method is validated through experiments with adding noise, the adaptive finite element method is applied to further improve the results, which provide a reference for future researches.