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 -