The inverse problem of a Gaussian convolution and its application to the finite size of the measurement chambers/detectors in photon and proton dosimetry
The inverse problem of a Gaussian convolution and its application to the finite size of the measurement chambers/detectors in photon and proton dosimetry
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DOI：
10.1088/0031-9155/48/6/302
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发表时间：
2003-03-21
影响因子：
3.5
通讯作者：
Kaissl, W
中科院分区：
文献类型：
--
作者：
Ulmer, W;Kaissl, W
高斯卷积核 K 被推导为李算子级数的格林函数。高斯核的反卷积是由逆格林函数 K-1 开发的。实际应用是对有限探测器尺寸的光子和质子的测量轮廓 D-m(x) 进行反卷积，以确定点探测器的轮廓 D-p(x) 或质子的蒙特卡洛布拉格曲线。如果 D-m(x) 是解析函数或仅以数值形式给出，则所提出的算法有效。比较了反卷积的一些近似方法（微分算子扩展至 2 x 2 cm(2) 和 4 x 4 cm(2) 轮廓的分析适应，Hermite 扩展至测量的 6 x 6 cm(2) 和 20 x 20 cm(2) 轮廓以及 80/180 MeV 质子的布拉格曲线，FFT 至分析 4 x 4 cm(2) 轮廓）。逆问题可能意味着不适定问题，特别是 FFT 的使用可能容易受到这些问题的影响。
A Gaussian convolution kernel K is deduced as a Green's function of a Lie operator series. The deconvolution of a Gaussian kernel is developed by the inverse Green's function K-1. A practical application is the deconvolution of measured profiles D-m(x) of photons and protons with finite detector size to determine the profiles D-p(x) of point-detectors or Monte Carlo Bragg curves of protons. The presented algorithms work if D-m(x) is either an analytical function or only given in a numerical form. Some approximation methods of the deconvolution are compared (differential operator expansion to analytical adaptations of 2 x 2 cm(2) and 4 x 4 cm(2) profiles, Hermite expansions to measured 6 x 6 cm(2) and 20 x 20 cm(2) profiles and Bragg curves of 80/180 MeV protons, FFT to an analytical 4 x 4 cm(2) profile). The inverse problem may imply ill-posed problems, and, in particular, the use of FFT may be susceptible to them.