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Frontiers of Information Technology & Electronic Engineering

ISSN 2095-9184 (print), ISSN 2095-9230 (online)

2017 Vol.18 No.8 P.1131-1141

Sparse fast Clifford Fourier transform

Rui Wang, Yi-xuan Zhou, Yan-liang Jin, Wen-ming Cao

School of Communication and Information Engineering, Shanghai University, Shanghai 200444, China; College of Information Engineering, Shenzhen University, Shenzhen 518060, China; Department of Electrical and Computer Engineering, University of Missouri, Columbia 65211, USA

wmcao@szu.edu.cn

Abstract: The Clifford Fourier transform (CFT) can be applied to both vector and scalar fields. However, due to problems with big data, CFT is not efficient, because the algorithm is calculated in each semaphore. The sparse fast Fourier transform (sFFT) theory deals with the big data problem by using input data selectively. This has inspired us to create a new algorithm called sparse fast CFT (SFCFT), which can greatly improve the computing performance in scalar and vector fields. The experiments are implemented using the scalar field and grayscale and color images, and the results are compared with those using FFT, CFT, and sFFT. The results demonstrate that SFCFT can effectively improve the performance of multivector signal processing.

Key words: Sparse fast Fourier transform (sFFT); Clifford Fourier transform (CFT); Sparse fast Clifford Fourier transform (SFCFT); Clifford algebra

Chinese Summary  <1037> 稀疏快速Clifford傅里叶变换

概要：Clifford傅里叶变换（Clifford Fourier transform, CFT）可以应用于矢量场和标量场，但无法有效解决大数据问题，因为该算法是基于每个信号量计算的。稀疏快速傅里叶变换（sparse fast Fourier transform, sFFT）理论通过选择性地使用输入数据来处理大数据问题。受之启发，我们提出一个称为稀疏快速Clifford傅里叶变换（sparse fast CFT, SFCFT）的算法，该算法能够大幅度提高在标量场和矢量场中的计算性能。实验对标量场、灰度图和彩色图像数据进行处理，通过与FFT，CFT和sFFT进行比较，表明SFCFT可以有效提升多矢量信号处理的性能。

关键词组：稀疏快速傅里叶变换（sFFT）；Clifford傅里叶变换（CFT）；稀疏快速Clifford傅里叶变换（SFCFT）；Clifford代数


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DOI:

10.1631/FITEE.1500452

CLC number:

TP391

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On-line Access:

2017-09-08

Received:

2015-12-09

Revision Accepted:

2016-08-23

Crosschecked:

2017-08-24

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