二维Mellin变换的实现

本文分析了Mellin变换的光学实现问题,提出一种实现Mellin变换的新方法,并对此进行了实验研究和给出了实验结果。 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     

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.     

全息图压缩的小波分析方法

全息信息压缩是实现全息图通讯的重要工作之一.本文提出用小波变换的方法对全息图的信息进行压缩,理论分析和计算机模拟结果都表明这一方法的有效性和灵活性.     

用计算全息元件实现光学Perfect shuffle网络

本文介绍了一种实现光学perfect shuffie(PS)网络的方法,它是用计算机产生全息片(CGH)的方法制作的元件,该元件可以很简单地实现二维光学PS网络,实验结果表明,该方法是可行的,效果好,能推广到其它的变换网络。     

光学一般变换的傅里叶变换实验方法

本文利用傅里叶光学系统简化了光学一般变换全息透镜的设计,以一维八序Walsh-Hadamard变换为例,用计算机设计和产生了变换所需的透镜,并进行引了光学实验,得到了预定变换结果。     

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.     

菲涅耳数字全息图的Gabor小波变换再现法

提出了一种基于Gabor小波变换的菲涅耳全息图的数值再现方法,实现无需空间滤波处理,即可对物光波进行数值再现.给出Gabor小波变换以及小波变换脊的定义,并从理论上证明通过对全息图进行Gabor小波变换,提取小波变换脊对应的小波变换系数,包括幅值与相位信息,即可直接获得与+1级频谱相对应的被测物光在全息面上的强度与相位分布,并同时直接消除零级衍射像以及孪生像的影响.通过计算机模拟再现光波经全息图衍射后的传播规律实现数值再现,得到清晰的再现像.通过计算机模拟一相位型物体以及实验证明该方法的有效性.     

基于光学子波变换的SDF匹配滤波器

提出了一种基于光学子波变换的综合判别函数匹配滤波器(WFSDF),将光学子波变换和综合判别函数相结合,只用一个简单的4f系统就能实现输入图像和SDF子波变换的相关运算。采用计算全息的方法制作复数匹配滤波器。计算机模拟仿真结果表明,与传统的SDF匹配滤波器相比,WFSDF匹配滤波器,锐化了相关峰,提高了识别率,同时简化了光路,能够实现多目标的畸不变识别。     

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.     

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.     

Pionisation in a ø3 theory ladder model

The inclusive reaction a + b → c + X is calculated in a φ³ theory ladder model in the pionisation region. A Mellin transform method is used to obtain, without resorting to leading term approximations, a double Regge form for the $\text{<}\text{ab}\text{c}\text{bab}\text{c}$ > amplitude in this region, resulting in limiting pionisation. The Mellin transform method has to be applied with discretion here and is not a trivial extension of the same method as applied earlier to the fragmentation region. It is pointed out that these methods can also be applied to multiple-inclusive reactions, once again giving expected Regge-behaved results.     

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.     

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.     

深空光通信中的图像信标捕获技术

为实现深空光通信链路建立过程中精确的对准,提出了一种深空光通信系统扩展信标的捕获方案。该方案以可视地球图像作为信标,在航天器上存储一幅信标图像作为参考图像,采用天线扫描的方式在各点对所瞄准的区域成像,利用像素扫描的方式,使参考图像和实际探测图像进行相关,在天线扫描完成以后,找出相关性最大的位置,即可认为在该点捕获到地球图像。在计算两图像相关系数的过程中,由于傅里叶梅林变换幅度谱具有伸缩及旋转不变性,因此利用傅里叶梅林变换即可消除两图像相关系数因为旋转和伸缩的影响。利用蒙特卡罗方法随机产生1000个视场,仿真结果表明,3σ内正确捕获到信标图像的概率为99.6%,表明这是一种可行的方法。     

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.     

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