完全最小二乘下的康普顿散射图像重建

Total Least Square Reconstruction of Compton Scattering Image

由康普顿散射能谱重建密度图像的问题是一个非线性的逆问题 ,这给重建带来很大困难。解决问题的一种方法是结合透射测量所得的衰减系数用以消除问题的非线性。但是 ,用这种方法所得到的投影矩阵却存在误差。为了减小这种误差对重建结果的影响 ,提出用完全最小二乘法来重建康普顿散射图像。数值模拟实验证明 ,这种方法极大地改善了重建图像的质量。

The reconstruction of density images from Compton scattered energy spectral data is a nonlinear inverse problem. The non-linearity brings serious problems in the reconstruction. One of the method eliminating the non-linearity is to combine the transmission CT for the determination of the attenuation coefficients. However, errors exist in the projection matrix determined in this way. In order to reduce the erroneous effects on the reconstruction results, the total least square algorithm is proposed for the reconstruction.Simulation results have proved that this reconstruction method improved greatly the reconstruction results.