在康普顿散射成像(CST)技术中可以结合透射成像重建出衰减系数来消除散射重建的非线性, 但这样得到的投影矩阵带有误差。而CST重建问题的不适定性对噪声和投影矩阵的误差非常敏感, 重建结果会有较大误差。针对此问题, 基于压缩感知理论提出了一种新的CST重建算法。新方法将图像重建问题归结为一个图像的全变分(TV)最小化问题, 并使用收敛速度较快的基于交替方向法的Split-Bregman方法进行求解。在仿真实验中, 通过与代数重建技术(ART)进行比较, 在测量数据充足和测量数据不足两种情况下, 本文算法都具有更好的重建质量, 证明了所提算法在重建精度和抗噪性能方面的优势。

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 image’s 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).