System response matrix is the numerical relation from excitation to response. Cause most medical image reconstruction employ forward projection and backward projection, system response matrix is one of the essential issues attracted many researchers'attention. It proposes a infinitesimalanalysis method for modeling the system response matrix. Accuracy of system response matrix is improved. Numerical experiment show that SNR ( Signal Noise Ratio) of forward projection is increased to more than 1 000 times via 64 pixel tiny block, and SNR( Signal Noise Ratio) of backward projection is raised by two orders of magnitude.%系统响应矩阵是以矩阵形式表征的从激励到响应的数值化关系.由于绝大多数正电子发射成像的重建算法都包含正投影和反投影的计算步骤,系统响应矩阵精度是研究者普遍关心的重要因素之一.通过对系统响应矩阵进行微元法建模,提高了系统响应矩阵的精度.数值结果显示,随着微元的尺寸变小,64点微元正投影的信噪比提高了100倍以上,16线微元反投影的信噪比提高了7个数量级.
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