Laser & Optoelectronics Progress, Volume. 60, Issue 12, 1211001(2023)
Diffusion Optical Tomography Based on Convex-Nonconvex Finite Element Total Variation Regularization
Jinlan Li1, Zhaoyang Xie1, Guoqi Liu2, and Jian Zou1、*
Author Affiliations
1School of Information and Mathematics, Yangtze University, Jingzhou 434020, Hubei, China2College of Computer and Information Engineering, Henan Normal University, Xinxiang 453007, Henan, Chinashow less
A reconstruction model based on convex-nonconvex finite element total variation (CNC-FETV) regularization is proposed to avoid the biased estimation of regularization in diffuse optical tomography. First, the finite element method was used to divide the computational domain into a finite number of triangles, after which a continuous piecewise polynomial function was used to approximate the absorption coefficient value in each triangle. Then, the derived difference matrix was assembled element by element to obtain a representation of the FETV regularization. Subsequently, the CNC-FETV regularization was obtained by the construction method based on convex-nonconvex sparse regularization. Results theoretically proved that the nonconvex regularization term could maintain the overall convexity of the objective function under certain conditions. Finally, the alternating direction multiplier method was used to solve the proposed model. Numerical experiments show that compared with the Tikhonov and FETV regularization models, the proposed CNC-FETV regularization model has superior performances in both numerical criteria and visual effects for diffusion optical tomography reconstructions.