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On a problem in radiotherapy: Questions of non‐negativity
Author(s) -
Cormack A. M.,
Quinto Eric Todd
Publication year - 1989
Publication title -
international journal of imaging systems and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.359
H-Index - 47
eISSN - 1098-1098
pISSN - 0899-9457
DOI - 10.1002/ima.1850010203
Subject(s) - convolution (computer science) , series (stratigraphy) , fourier series , negativity effect , fourier transform , simple (philosophy) , mathematics , field (mathematics) , function (biology) , pure mathematics , mathematical analysis , computer science , geology , artificial intelligence , psychology , paleontology , social psychology , philosophy , evolutionary biology , artificial neural network , biology , epistemology
A well‐known result is used to show that if g is a non‐negative function and the radiation field, f , is its Radon transform, the dose field, f̂, is the convolution of g with (1/π r ) and is necessarily non‐negative. Simple series expansions of f and f̂ are given, and the series for f is written as a finite Fourier series. Known properties of finite Fourier series are used to seek, fruitlessly, for useful conditions on the coefficients to ensure the non‐negativity of f .
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