Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review
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TY - GEN
T1 - Superfast algorithms of multidimensional discrete k-wave transforms and Volterra filtering based on superfast radon transform
T2 - book chapter
AU - Labunets, Valeri
AU - Labunets-Rundblad, Ekaterina
AU - Astola, Jaakko T.
PY - 2001
Y1 - 2001
N2 - Fast algorithms for a wide class of non-separable n-dimensional (nD) discrete unitary K-transforms (DKT) are introduced. They need less 1D DKTs than in the case of the classical radix-2 FFT-type approach. The method utilizes a decomposition of the nD K-transform into the product of a now nD discrete Radon transform and of a set of parallel/independ 1D K-transforms. If the nD K-transform has a separable kernel (e.g., the case of the discrete Fourier transform) our approach leads to decrease of multiplicative complexity by the factor of n comparing to the classical row/column separable approach. It is well known that an nth order Volterra filter of one dimensional signal can be evaluated by an appropriate nD linear convolution. This work describes new superfast algorithm for Volterra filtering. New approach is based on the superfast discrete Radon and Nussbaumer Polynomial Transforms.
AB - Fast algorithms for a wide class of non-separable n-dimensional (nD) discrete unitary K-transforms (DKT) are introduced. They need less 1D DKTs than in the case of the classical radix-2 FFT-type approach. The method utilizes a decomposition of the nD K-transform into the product of a now nD discrete Radon transform and of a set of parallel/independ 1D K-transforms. If the nD K-transform has a separable kernel (e.g., the case of the discrete Fourier transform) our approach leads to decrease of multiplicative complexity by the factor of n comparing to the classical row/column separable approach. It is well known that an nth order Volterra filter of one dimensional signal can be evaluated by an appropriate nD linear convolution. This work describes new superfast algorithm for Volterra filtering. New approach is based on the superfast discrete Radon and Nussbaumer Polynomial Transforms.
UR - https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=tsmetrics&SrcApp=tsm_test&DestApp=WOS_CPL&DestLinkType=FullRecord&KeyUT=000174396200006
UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=0035763162
U2 - 10.1117/12.449740
DO - 10.1117/12.449740
M3 - Conference contribution
SN - 0-8194-4186-4
VL - 4472
T3 - Proceedings of SPIE
SP - 53
EP - 64
BT - APPLICATIONS OF DIGITAL IMAGE PROCESSING XXIV
A2 - Tescher, A.G.
PB - SPIE
ER -
ID: 42978206