Recursive pruning of the 2D DFT with 3D signal processing applications

Author

Knudsen, Knud Steven ; Bruton, Leonard T.

Author_Institution

Dept. of Electr. & Comput. Eng., Calgary Univ., Alta., Canada

Volume

41

Issue

3

fYear

1993

fDate

3/1/1993 12:00:00 AM

Firstpage

1340

Lastpage

1356

Abstract

A recursively pruned radix-(2×2) two-dimensional (2D) fast Fourier transform (FFT) algorithm is proposed to reduce the number of operations involved in the calculation of the 2D discrete Fourier transform (DFT). It is able to compute input and output data points having multiple and possibly irregularly shaped (nonsquare) regions of support. The computational performance of the recursively pruned radix-(2×2) 2D FFT algorithm is compared with that of pruning algorithms based on the one-dimensional (1D) FFT. The former is shown to yield significant computational savings when employed in the combined 2D DFT/1D linear difference equation filter method to enhance three-dimensional spatially planar image sequences, and when employed in the MixeD moving object detection and trajectory estimation algorithm

Keywords

fast Fourier transforms; image sequences; recursive functions; signal processing; stereo image processing; 2D DFT; 3D signal processing; MixeD moving object detection and trajectory estimation algorithm; discrete Fourier transform; fast Fourier transform; recursively pruned radix-(2×2) 2D FFT algorithm; three-dimensional spatially planar image sequences; Difference equations; Discrete Fourier transforms; Fast Fourier transforms; Flow graphs; Helium; Image sequences; Least squares approximation; Signal processing; Signal processing algorithms; Two dimensional displays;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.205734

Filename

205734