The inverse problem of a Gaussian convolution and its application to the finite size of the measurement chambers/detectors in photon and proton dosimetry.
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 Dm(x) of photons and protons with finite detector size to determine the profiles Dp(x) of point-detectors or Monte Carlo Bragg curves of protons. The presented algorithms work if Dm(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 cm2 and 4 x 4 cm2 profiles, Hermite expansions to measured 6 x 6 cm2 and 20 x 20 cm2 profiles and Bragg curves of 80/180 MeV protons, FFT to an analytical 4 x 4 cm2 profile). The inverse problem may imply ill-posed problems, and, in particular, the use of FFT may be susceptible to them.
Ulmer
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W
VARIAN Medical Systems, Neuenhoferstr. 107 CH-5400 Baden, Switzerland.
Kaissl
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W
D000465:Algorithms; D005583:Fourier Analysis; D008954:Models, Biological; D016011:Normal Distribution; D017785:Photons; D011522:Protons; D011874:Radiometry / Q000295:instrumentation* / Q000379:methods*; D011878:Radiotherapy / Q000379:methods; D011879:Radiotherapy Dosage; D013223:Statistics as Topic; D013269:Stochastic Processes; D014159:Transducers
D011522:Protons