7 December 2001 Superfast algorithms of multidimensional discrete k-wave transforms and Volterra filtering based on superfast radon transform
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Abstract
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 new 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 n-th 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.
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Valeri G. Labunets, Ekaterina V. Labunets-Rundblad, Jaakko T. Astola, "Superfast algorithms of multidimensional discrete k-wave transforms and Volterra filtering based on superfast radon transform", Proc. SPIE 4472, Applications of Digital Image Processing XXIV, (7 December 2001); doi: 10.1117/12.449740; https://doi.org/10.1117/12.449740
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