Diffusion Optical Tomography Based On Convex-Nonconvex Total Variation Regularization Model

Diffusion optical tomography(DOT)is a promising medical imaging technique.By means of the interaction between near infrared light and the imaging tissue,the anatomical and physiological function information of the tissue can be expressed in the way of image,which can provide the basis for judging the health status of the tissue.An important factor limiting the application of diffusion optical tomography technology is the representation of computational domain.In diffusion optical tomography,the corresponding computational domain of tissue is usually a geometry with complex shape and structure,which is difficult to be represented effectively in Cartesian grid,resulting in modeling errors and affecting the image quality.In addition,due to the limitation of imaging equipment and the scattering characteristics of light,image reconstruction of diffusion optical tomography is an ill-conditioned inverse problem,which brings challenges to model solving.In order to improve the representation quality of reconstructed images and solve the problem of underquality,this paper combines finite element method(FEM),graph signal processing(GSP)and convex-nonconvex(CNC)sparse regularization to construct an DOT model.FEM divides the computational domain into a series of non-overlapping elements,uses simple graphics to fit complex boundaries,and uses simple elementary functions to simulate the properties of elements.It is a powerful tool for modeling complex geometry.GSP maps irregular data onto graphs and uses graph structure to depict the correlation between graph signals.It is a powerful framework for processing high dimensional and irregular data.Regularization is an effective method to solve the ill-determined linear inverse problem.In recent years,the the emerging CNC sparse regularization method can maintain the global convexity of the objective function and reduce the reconstruction deviation,and has a wide range of applications in image reconstruction,image denoising,fault detection and other fields.Based on the FEM and GSP theory and CNC sparse regularization,this paper conducts in-depth research on the image reconstruction of DOT.The main contributions are as follows:(1)Based on the CNC sparse regularization construction method,the convexnonconvex finite element total variation(CNC-FETV)regularization and convex-nonconvex graph total variation(CNC-GTV)regularization term are constructed,and CNC-FETV and CNC-GTV regularization reconstruction models are proposed.(2)It is theoretically proved that the total variation regularization reconstruction model of CNC-FETV and CNC-GTV can maintain the overall convexity of the objective function under certain conditions,and the alternating direction multiplier method(ADMM)is applied to solve the problem.(3)The proposed reconstructed model is applied to the reconstruction of DOT.In numerical experiments,we compare the proposed model with the existing model in different spatial resolution grids and different noise levels,and the experimental results show that the proposed model is superior to the existing model in numerical results and visual effects.