Compton scattering tomography reconstruction algorithm combined with transmission CT

The Compton scattering tomography (CST) reconstruction is a nonlinear inverse problem due to the attenuation. One of the solutions is to combine the attenuation coefficients achieved by transmission CT data. However, the CST reconstruction is ill-posed, and its solution would be sensitive to the noise and the projection matrix errors brought by the attenuation coefficients. In order to solve the problem, this paper proposes a novel reconstruction algorithm for CST based on the compressive sensing theory. The novel method comes down the CST reconstruction to a problem for minimizing the images total variation (TV), and then solves it using the Split-Bregman method based on the alternating direction method. Numerical experiments show that the reconstruction quality and the anti-noise performance of the proposed method are improved compared to the algebraic reconstruction technique (ART).