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11.
The Two-Dimensional Clifford-Fourier Transform 总被引:1,自引:0,他引:1
Fred Brackx Nele De Schepper Frank Sommen 《Journal of Mathematical Imaging and Vision》2006,26(1-2):5-18
Recently several generalizations to higher dimension of the Fourier transform using Clifford algebra have been introduced,
including the Clifford-Fourier transform by the authors, defined as an operator exponential with a Clifford algebra-valued
kernel.
In this paper an overview is given of all these generalizations and an in depth study of the two-dimensional Clifford-Fourier
transform of the authors is presented. In this special two-dimensional case a closed form for the integral kernel may be obtained,
leading to further properties, both in the L
1 and in the L
2 context. Furthermore, based on this Clifford-Fourier transform Clifford-Gabor filters are introduced.
AMS subject classification numbers: 42B10, 30G35
Fred Brackx received a diploma degree in mathematics from Ghent University, Belgium, in 1970 and a Ph.D. degree in mathematics from the
same university in 1973. Since 1984 he is professor for mathematical analysis at Ghent University and currently he is leading
the Clifford Research Group. His main interests are function theory and functional analysis for functions with values in quaternion
and Clifford algebras. The research covers Clifford distributions, generalized Fourier, Radon and Hilbert transforms, orthogonal
polynomials and multi-dimensional wavelets.
Nele De Schepper received a diploma degree in mathematics from Ghent University, Belgium, in 2001. Since then she holds an assistantship at
the Department of Mathematical Analysis of Ghent University and is a member of the Clifford Research Group. Her main interests
are function theory and functional analysis for functions with values in Clifford algebras. The research covers generalized
Fourier transforms, orthogonal polynomials and multi-dimensional wavelets.
Frank Sommen received a diploma degree in mathematics from Ghent University, Belgium, in 1978, a Ph.D. degree in mathematics from the
same university in 1980, and a habilitation degree in mathematical analysis in 1984. From 1978 until 1999 he was at the National
Fund for Scientific Research (Flanders). Since 2000 he holds a Research professorship at Ghent University. His main interests
are function theory and functional analysis for functions with values in quaternion and Clifford algebras. The research covers
Clifford distributions, generalized Fourier, Radon and Hilbert transforms, orthogonal polynomials and multi-dimensional wavelets,
algebraic analysis, hyperfunctions and radial algebra. 相似文献
12.
13.
基于子波域空间相关的多分辨图像滤波方法 总被引:2,自引:1,他引:1
从静态子波变换入手,提出了一种有效的图像滤波算法。通过计算相邻尺度下细节信号的空间相关性来区分噪声和信号,如果子波系数的空间相关性大,则认为此位置的系数含有特征及边缘信息予以保留。实现这种理论的完整方法包括两部分:空间滤波和子波收缩。仿真结果表明这个算法有很好的降噪性能。 相似文献
14.
从图像的二维谱可以得出现行广播电视图像为什么不能满足人眼的视觉匹配以及现行电视制度的不足 ,从而对未来的高清晰度电视发展提出要求。 相似文献
15.
电力系统谐波检测的现状与发展 总被引:7,自引:0,他引:7
准确、实时地对电力系统谐波进行检测有着重要的意义。本文根据电力系统谐波测量的基本方法,对近年来电力系统谐波检测的新方法进行了分析和评述。最后对电力系统的谐波测量进行了总结并提出了看法。 相似文献
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Javier Ramírez Antonio García Uwe Meyer-Bäse Fred Taylor Antonio Lloris 《The Journal of VLSI Signal Processing》2003,33(1-2):171-190
Currently there are design barriers inhibiting the implementation of high-precision digital signal processing (DSP) objects with field programmable logic (FPL) devices. This paper explores overcoming these barriers by fusing together the popular distributed arithmetic (DA) method with the residue number system (RNS) for use in FPL-centric designs. The new design paradigm is studied in the context of a high-performance filter bank and a discrete wavelet transform (DWT). The proposed design paradigm is facilitated by a new RNS accumulator structure based on a carry save adder (CSA). The reported methodology also introduces a polyphase filter structure that results in a reduced look-up table (LUT) budget. The 2C-DA and RNS-DA are compared, in the context of a FPL implementation strategy, using a discrete wavelet transform (DWT) filter bank as a common design theme. The results show that the RNS-DA, compared to a traditional 2C-DA design, enjoys a performance advantage that increases with precision (wordlength). 相似文献
20.