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Integral transforms – the base of recent technologies. (English) Zbl 1340.44001

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, May 15–17, 2013. In honor of the 70th birthday of Karel Segeth. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-61-5). 158-167 (2013).
A historical outline of integral transforms is presented with attention devoted to Fourier, wavelet and Radon transforms. The definitions of the chosen transforms and their inverses are given and some basic properties are described. The author offers interesting applications and concrete examples of wavelets to image processing and a demonstration of how Radon transform is useful in computer tomography is shown.
For the entire collection see [Zbl 1277.00032].

MSC:

44A05 General integral transforms
44A12 Radon transform
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
92C55 Biomedical imaging and signal processing
65T50 Numerical methods for discrete and fast Fourier transforms
65T60 Numerical methods for wavelets

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