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

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。

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.