实现Mellin变换的一种新方法

本文讨论了用光学系统实现Mellin变换的一种新方法,叙述了用计算机进行全息透镜的设计和用计算机产生二元式全息图的制造原理。实验上实现了由一组16个抽样点组成的一维Mellin变换,并可直接推广到二维情况。 关键词：     

精确到次带头项贡献的核子结构函数非单态分量的解析表达式

本文利用逆Mellin变换从非单态核子结构函数的矩得到了精确到次带头项贡献的核子结构函数非单态分量的解析表达式, 最后将理论预言与实验进行比较     

基于斑点噪声的拖尾Rayleigh分布的合成孔径雷达图像最大后验概率降噪

为了反映合成孔径雷达图像中斑点噪声尖峰厚尾的统计特征，使用拖尾Rayleigh分布来描述斑点噪声.基于Gamma先验分布和斑点噪声的拖尾Rayleigh分布，推导出了合成孔径雷达图像的最大后验概率滤波方程，并给出了它在特定特征参数时的解析形式.使用Mellin变换从观察图像估计拖尾Rayleigh分布的未知参数.给出了在斑点噪声的拖尾Rayleigh分布下的最大后验概率降噪试验和量化指标.为了消除滑动窗大小和噪声强度对降噪结果的影响，给出了降噪能力随滑动窗大小和噪声方差的动态变化关系.结果表明，拖尾Ray 关键词： 斑点噪声 拖尾Rayleigh分布 最大后验概率降噪 Mellin变换     

核磁共振实现基本量子逻辑门和量子分立付里叶变换

本文详细研究了利用核磁共振方法实现基本量子逻辑操作,提出了实现量子分立付里叶变换的实验方案,设计了可供实验的脉冲系列,为实验研究量子分立付里叶变换提供了具体方案。     

用多焦点全息透镜实现多重谱分数傅里叶变换

提出用多焦点全息透镜实现多重谱分数傅里叶变换.利用全息方法通过一次曝光制作出多焦点的全息透镜,分析了用此全息元件实现这种变换的条件,并在实验上实现了多重谱分数傅里叶变换. 实验结果表明这种变换方法简便可行,可广泛应用于多通道光学信息处理系统及多目标图像识别系统中.     

Ising耦合体系中量子傅里叶变换的优化

量子傅里叶变换是量子计算中一种重要的量子逻辑门. 任意量子位的傅里叶变换可以分解为一系列普适的单比特量子逻辑门和两比特量子逻辑门, 这种分解方式使得傅里叶变换的实验实现简单直观, 但所用的实验时间显然不是最短的. 本文利用优化控制和数值计算方法对Ising耦合体系中多量子位傅里叶变换的实验时间进行优化, 优化后的实现方法明显短于传统方法. 优化方法的核磁共振实验实现验证了其有效性.     

二维光学沃尔什—哈特曼变换

从光学变换的基本方程出发,分析了变换所需的空间横向调制型全息透镜的相位误差,提出用计算机产生全息图和光学全息相结合的方法产生高精度的二维变换全息透镜.在实验上实现了二维32序的光学沃尔什-哈特曼变换,实验结果与理论计算一致.     

用相干光实现Walsh变换

本文采用相干光方法对Walsh变换进行了具体的实验研究。设计了五平面的相干光变换装置,实现了一维八序的Walsh变换,给出了变换频谱。对于二维Walsh变换原则上也是适用的。 关键词：     

基于半导体光放大器交叉偏振调制效应实现正、反相波长变换

利用琼斯矩阵,对基于半导体光放大器中的交叉偏振调制效应实现全光波长变换进行了理论分析.结果表明,利用这种机制可以实现同相与反相波长变换.在实验上同时实现了10Gb/s归零信号的正相与反相波长变换,输出消光比分别达到了6.9 dB和8.1 dB.     

Gyrator变换全息图及其在图像加密中的应用

提出了gyrator变换全息图,利用gyrator变换快速算法模拟实现了gyrator变换全息图的产生和再现,并研究了基于相移数字全息的gyrator变换全息图.在此基础上提出了采用正弦相位光栅实现光学图像加密的新方法.该方法利用gyrator变换在相空间的旋转特性,将gyrator变换的角度、光栅的频率及光栅的旋转角度作为加密密钥,并利用两个或两个以上的gyrator变换系统的级联实现图像加密,增加了系统的安全性.依据相移数字全息进行的两个gyrator变换系统级联的仿真实验验证了该方法的可行性、有效性及其良好的安全性能.     

Pattern classification using optical Mellin transform and circular photodiode array

Scale-invariant pattern classification using a hybrid system combining the optical Mellin transform and a digital signal processing technique is discussed. We accomplish the optical Mellin transform by a logarithmic coordinate transformation using a computer-generated hologram, followed by an optical Fourier transform. Mellin transform patterns are detected with a circular photodiode array, whose output signals are processed by a micro-computer. A new criterion is discussed, in which circular or periodic correlation is employed. Experimental examples are presented.     

Covariant Mellin transforms and the Weyl group quantization

The outline of the formalism with diagonalized dilation generator is presented. The covariant Mellin transform defining quanta with definite dimensionality and SL(2, C) quantum numbers is proposed.     

New transformation for optical signal processing

The use of the optical Mellin transform in several novel optical signal processing applications using the frequency plane correlator and joint transform correlator is discussed.     

Mellin Transform of the Limit Lognormal Distribution

The technique of intermittency expansions is applied to derive an exact formal power series representation for the Mellin transform of the probability distribution of the limit lognormal multifractal process. The negative integral moments are computed by a novel product formula of Selberg type. The power series is summed in general by means of its small intermittency asymptotic. The resulting integral formula for the Mellin transform is conjectured to be valid at all levels of intermittency. The conjecture is verified partially by proving that the integral formula reproduces known results for the positive and negative integral moments of the limit lognormal distribution and gives a valid characteristic function of the Lévy-Khinchine type for the logarithm of the distribution. The moment problem for the logarithm of the distribution is shown to be determinate, whereas the moment problems for the distribution and its reciprocal are shown to be indeterminate. The conjecture is used to represent the Mellin transform as an infinite product of gamma factors generalizing Selberg’s finite product. The conjectured probability density functions of the limit lognormal distribution and its logarithm are computed numerically by the inverse Fourier transform.     

Meblin transforms associated with Julia sets and physical applications

We introduce the Mellin transform of the balanced invariant measure associated to the Julia set generated by a rational transformation. We show that its analytic continuation is a meromorphic function, the poles of which are on a semi-infinite periodic lattice. This allows one to have an understanding of the behavior of the measure near a repulsive fixed point. Trace identities corresponding to the fact that the analytically continued Mellin transform vanishes at negative integers are derived for the polynomial case. The quadratic map is first analyzed in detail, and the analytic properties of the inverse of the Green's function are exhibited. Of interest is the appearance of a dense set of spikes at dyadic points when the Julia set is disconnected. These results are used to study the residues of the Mellin transform. A certain number of physically interesting consequences are derived for the spectral dimensionality of quantum mechanical systems, the excitation spectrum of which displays unusual oscillations. The appearance of complex critical indices for thermodynamical systems is also discussed in the conclusion.Supported in part by a N.A.T.O. Postdoctoral fellowship.     

Image encryption algorithm based on the multi-order discrete fractional Mellin transform

A multi-order discrete fractional Mellin transform (MODFrMT) is constructed and directly used to encrypt the private images. The MODFrMT is a generalization of the fractional Mellin transform (FrMT) and is derived by transforming the image with multi-order discrete fractional Fourier transform (MODFrFT) in log-polar coordinates, where the MODFrFT is generalized from the closed-form expression of the discrete fractional Fourier transform (DFrFT) and can be calculated by fast Fourier transform (FFT) to reduce the computation burden. The fractional order vectors of the MODFrMT are sensitive enough to be the keys, and consequently key space of the encryption system is enlarged. The proposed image encryption algorithm has significant ability to resist some common attacks like known-plaintext attack, chosen-plaintext attack, etc. due to the nonlinear property of the MODFrMT. Additionally, Kaplan-Yorke map is employed in coordinate transformation process of the MODFrMT to further enhance the security of the encryption system. The computer simulation results show that the proposed encryption algorithm is feasible, secure and robust to noise attack and occlusion.     

Calculation of a Certain Determinant

The n×n determinant det[(a+j−i)Γ(b+j+i)] is evaluated. This completes the calculation of the Mellin transform of the probability density of the determinant of a random quaternion self-dual matrix taken from the gaussian symplectic ensemble. The inverse Mellin transform then gives the later probability density itself. Received: 30 August 1999 / Accepted: 29 March 2000     

A clarification on the use of the Mellin transform in optical pattern recognition

The necessity of translating a scaled input function in the logarithmic coordinates necessary to perform an optical Mellin transform is demonstrated. The implications of this requirement in the processing of two dimensional inputs for pattern recognition are discussed.