Image reconstruction based on total variation minimization and alternating direction method for Compton scatter tomography

Compton scatter tomography measures samples electron densities utilizing the scattered photons. Compared to traditional transmission imaging models, Compton scatter tomography has the following characteristics, i.e. freedom in construction systems, greater sensitivity for low-density materials, and lower radiation dose. It has been applied in non-destructive testing, medical, and security inspections, and other fields. However, Compton scatter tomography reconstruction is a nonlinear inverse problem, common is ill-posed, and its solutions are very sensitive to noise and erroneous measurements. To tackle the problem, in this paper we propose a novel Compton scatter tomography reconstruction algorithm based on the total variation minimization and alternating direction method. The main idea of our method is to reformulate the reconstruction problems TV function as an optimization with constrains where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method to solve the sub-problems. Numerical experiments shows that the reconstruction quality and efficiency of the proposed method are improved compared to the adaptive-steepest-descent-projection onto convex sets method.