零点分布更均匀的广义极谐复指数变换

doi:10.11772/j.issn.1001-9081.2022071020

《计算机应用》唯一官方网站 ›› 2023, Vol. 43 ›› Issue (8): 2499-2504.DOI: 10.11772/j.issn.1001-9081.2022071020

• 先进计算 • 上一篇

零点分布更均匀的广义极谐复指数变换

曾泽芝, 杨建伟()

南京信息工程大学数学与统计学院，南京 210044

收稿日期:2022-07-13 修回日期:2022-11-06 接受日期:2022-11-11 发布日期:2023-01-15 出版日期:2023-08-10
通讯作者: 杨建伟
作者简介:曾泽芝（1998—），男，江苏南京人，硕士研究生，主要研究方向：模式识别；
基金资助:
国家自然科学基金资助项目(61572015)

Generalized polar complex exponential transform with more uniform zeros distribution

Zezhi ZENG, Jianwei YANG()

School of Mathematics and Statistics，Nanjing University of Information Science and Technology，Nanjing Jiangsu 210044，China

Received:2022-07-13 Revised:2022-11-06 Accepted:2022-11-11 Online:2023-01-15 Published:2023-08-10
Contact: Jianwei YANG
About author:ZENG Zezhi， born in 1998， M. S. candidate. His research interests include pattern recognition.
Supported by:
National Natural Science Foundation of China(61572015)

摘要/Abstract

摘要：

针对极谐复指数变换（PCET）因自身径向函数实部和虚部的零点分布不均匀而存在的信息抑制问题，提出了一种零点分布更均匀的广义PCET。首先，改造了PCET，将PCET径向函数的指数推广为更一般的构造函数，而近来出现的指数傅里叶矩（EFM）、分数阶极谐变换、广义极谐变换、修正的广义极谐变换等都是所提广义PCET的特例；其次，选取了构造函数，使得所构造的广义PCET的径向函数实部和虚部的零点分布更均匀，并给出了这一特性的证明。在所取的汉字图像库、Coil-20库和COREL库上进行了图像重构实验，同时测试了广义PCET的旋转不变性及抗噪性能。当噪声强度为0时，PCET和广义PCET的识别率均为100%，这验证了PCET和广义PCET的旋转不变性。相较于PCET，所提广义PCET具有更低的重构误差及更高的识别率。理论分析和实验结果表明，零点分布比PCET更均匀的广义PCET同样具有旋转不变性和正交性，且其重构性能和抗噪性能均优于PCET，一定程度上解决了PCET的信息抑制问题，并在原点处数值稳定。

关键词: 极谐复指数变换, 径向函数, 零点分布, 图像重构, 信息抑制

Abstract:

In order to address the information suppression problem of Polar Complex Exponential Transform （PCET）， which is caused by nonuniform zeros distribution in the real part and imaginary part of PCET’s radial function， a generalized PCET with more uniform zeros distribution was proposed. First， PCET was modified， and the exponential part of PCET’s radial function was generalized to a more general constructor. And recently proposed Exponent-Fourier Moment （EFM）， fractional-order polar harmonic transform， generic polar complex exponential transform and the modified generic polar complex exponential transform are all the special cases of the proposed generalized PCET. Second， a constructor was chosen to make the zeros distribution in the real part and imaginary part of radial function of generalized PCET more uniform. And the proof of this property was given. Image reconstruction experiments were conducted on the selected Chinese character image， Coil-20 and COREL databases， and the rotation invariance and anti-noise performance of generalized PCET were tested. When the noise intensity is 0， both the recognition rates of PCET and generalized PCET are 100%， verifying the rotation invariance of PCET and generalized PCET. Compared with PCET， the proposed generalized PCET has lower reconstruction error and higher recognition rate. Theoretical analysis and experimental results show that the proposed generalized PCET with zeros distribution more uniform than PCET also has rotation invariance and orthogonality， and its reconstruction performance and anti-noise performance are better than those of PCET， which solves the information suppression problem of PCET to a certain extent， and is numerically stable at the origin.

Key words: Polar Complex Exponential Transform (PCET), radial function, zeros distribution, image reconstruction, information suppression

中图分类号:

TP391.41

曾泽芝, 杨建伟. 零点分布更均匀的广义极谐复指数变换[J]. 计算机应用, 2023, 43(8): 2499-2504.

Zezhi ZENG, Jianwei YANG. Generalized polar complex exponential transform with more uniform zeros distribution[J]. Journal of Computer Applications, 2023, 43(8): 2499-2504.

图/表 11

图1 n=7时，PCET与广义PCET的径向函数对比

Fig. 1 Comparison of radial functions of PCET and generalized PCET with n=7

图2 30幅二值测试图像

Fig. 2 Thirty binary test images

图3 二值图像重构示例

Fig. 3 Examples of reconstruction results of binary image

图4 灰度图像重构示例（Coil-20库）

Fig. 4 Examples of reconstruction results of gray-scale image （Coil-20 database）

图5 灰度图像重构示例（COREL库）

Fig. 5 Examples of reconstruction results of gray-scale image （COREL database）

图6 二值图像与灰度图像的平均重构误差曲线

Fig. 6 Curves of average reconstruction error of binary images and gray-scale images

图7 30幅汉字图像在不同强度椒盐噪声下的识别率

Fig. 7 Recognition rates of 30 Chinese character images with different intensities of salt-and-pepper noise

图8 20幅灰度图像（Coil-20库）在不同强度高斯噪声下的识别率

Fig. 8 Recognition rates of 20 gray-scale images （Coil-20 database） with different intensities of Gaussian noise

图9 20幅灰度图像（Coil-20库）在不同强度椒盐噪声下的识别率

Fig. 9 Recognition rates of 20 gray-scale images （Coil-20 database） with different intensities of salt-and-pepper noise

图10 100幅灰度图像（COREL库）在不同强度高斯噪声下的识别率

Fig. 10 Recognition rates of 100 gray-scale images （COREL database） with different intensities of Gaussian noise

图11 100幅灰度图像（COREL库）在不同强度椒盐噪声下的识别率

Fig. 11 Recognition rates of 100 gray-scale images （COREL database） with different intensities of salt-and-pepper noise

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零点分布更均匀的广义极谐复指数变换

Generalized polar complex exponential transform with more uniform zeros distribution

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