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

Mošová, Vratislava

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].

Reviewer: Leandro Farina (Porto Alegre)

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

Keywords:

integral transforms; sound processing; image processing; Radon transform; wavelet; Fourier transform; inverses; computer tomography

Software:

JPEG2000