分数傅里叶变换计算全息

在计算全息和分数傅里叶变换的基础上提出了不对称分数傅里叶变换计算全息和双随机相位不对称分数傅里叶变换计算全息。在这种方法中,首先用一随机相位函数乘以输入图像信息,然后沿x方向实施α级次的一维分数傅里叶变换,再乘以第二个随机相位函数,最后,沿y方向实施β级次的一维分数傅里叶变换。采用迂回位相编码法对变换后的结果编码,绘出计算全息图。为了恢复原始图像,需要知道变换级次和随机相位函数。利用这种方法进行图像加密,使加密图像的密钥由原来两重增加到四重,从而提高了系统的保密性能。     

基于随机分数傅里叶变换的双图像加密算法

利用光学随机分数傅里叶变换设计了一种双图像加密算法,并给出了相应的光学实现.加密算法中,将两幅原始图像分别作为加密系统输入复函数的振幅和位相分布函数,利用随机分数傅里叶变换进行加密,所得复函数的振幅即为加密图像,而位相部分是变换的输出相位,随机位相作为加密算法的密码.在数值模拟中,二值文本图像和灰度图像分别被作为原始图像用于加密结果分析和加密安全测试,结果表明该加密算法具有很好的安全性.     

基于变形分数傅里叶变换的六重密钥图像加密

提出一种利用变形分数傅里叶变换和双随机相位编码对图像加密的方法.对要加密的图像分别进行两次变形分数傅里叶变换和两次随机相位函数调制,使加密图像的密钥由原来两重增加到六重.利用全息元件,可以用光学系统实现这种加密和解密变换.计算机模拟结果表明,只有当六重密钥都完全正确时,才能准确地重建原图像,这种六重密钥加密方法提高了图像信息的安全保密性.     

光学图像加密与多参数加权类分数傅里叶变换

为了提高图像加密的安全性, 提出了一种多参数加权类分数傅里叶变换。此类多参数加权类分数傅里叶变换是C.C.Shih提出的四项加权类分数傅里叶变换的一种扩展, 除了分数阶数, 还有四个在四项加权系数之中的自由参数, 称其为向量参数。同时给出此多参数加权类分数傅里叶变换的离散形式, 并把这种算法应用到光学图像加密中。此算法在应用一次二维分数傅里叶变换可以有十个密键：一类为阶数参数; 另一类为向量参数, 因此这种加密算法在增加了安全性的同时, 加密过程的复杂度降低。数值仿真验证了此算法的有效性和可靠性。     

用全息透镜记录多重分数傅里叶变换全息图

提出一种全息透镜记录多重分数傅里叶变换全息图的新方法，它能在三维空间不同位置和不同方向上分别再现所记录的多个物体的图象，分析了利用全息透镜记录多重分数傅里叶变换全息图的原理及特点，制作了多重分数傅里叶变换全息图，并获得了满意的再现结果。     

利用分数傅里叶变换相关实现散斑相关测量

提出了一种在匹配滤波相关中利用分数傅里叶变换代替傅里叶变换实现散斑相关测量的方法.利用分数傅里叶变换的指数性质,采用把移变后的散斑图像先进行相位调制,再进行分数傅里叶变换的方法,有效地解决了分数傅里叶变换的移变性带来的谱移问题.编程模拟和拉伸试件位移场测量的结果表明,只要选择合适的分数傅里叶变换级次和相位调制函数,可以得到优于傅里叶变换相关的理想输出.     

基于光学相关的多目标检测

运用傅里叶变换相关识别技术实现了无畸变、有平移多目标的检测。在此基础上讨论了图像边缘信息和非边缘信息对相关性能的影响。运用分数傅里叶变换相关识别技术实现了目标图像存在尺度、旋转畸变而无平移变化时的目标检测。结果表明,分数傅里叶变换的级次选择对目标图像的旋转和尺度畸变有一定的补偿作用。在分数傅里叶变换相关中,通过简单的级次调节可实现一定范围内的旋转、尺度畸变不变识别。     

傅里叶变换的局限性及其改进方法

从对傅里叶变换的局限性分析入手 ,揭示了窗口傅里叶变换、小波变换和分数傅里叶变换的出现是傅里叶变换本身发展的必然 ,阐明了其改进方法产生的原因及其优缺点 ,分析了其改进方法与傅里叶变化的关系 ,这些有助于加深对傅里叶变换的认识。     

基于分频域和菲涅耳域的光学图像加密方法

结合分数傅里叶变换及菲涅耳变换,在光学图像加密系统中分别具有多密钥性和无透镜性的优点,提出了基于分频域和菲涅耳域的光学图像加密方法。基于分数傅里叶变换的光学加密系统,引入菲涅耳变换及全息技术,使原有的加密系统在不增加光学元件的基础上提高了系统的安全性。理论分析和计算机仿真模拟证明了这种方法的可行性。     

基于分数傅里叶变换的分数相关峰值特性

本文通过理论分析和计算机仿真研究了分数傅里叶变换的级次对分数相关峰值特性的影响并优化了分数相关的级次。结果表明分数相关输出在旁辩和峰值宽度方面与传统相关相比有了较大的改善,因而可以提高目标探测的灵敏性。     

基于分数阶Fourier变换的数字图像实值加密方法

构造了一种新的保实化的分数阶Fourier变换,提出了一种基于该变换的数字图像实值加密方法。利用保实分数阶Fourier变换的保实特性和阶数可加性等完成了数字图像的加密与解密,明文和密文分别位于空域和由密钥决定的保实分数阶Fourier变换域中,具有较强的抗统计破译能力。密图是一个实值图像,便于显示和存储。仿真实验结果表明,该加密方法密钥简单,无数据膨胀,对参数敏感度高,具有一定的鲁棒性和安全性。在信息安全领域具有良好的研究前景和实用价值。     

Optical image encryption with redefined fractional Hartley transform

A new method for optical image encryption is introduced on the basis of two-dimensional (2-D) generalization of 1-D fractional Hartley transform that has been redefined recently in search of its inverse transform. We encrypt the image by two fractional orders and random phase codes. It has an advantage over Hartley transform, for its fractional orders can also be used as additional keys, and that, of course, strengthens image security. Only when all of these keys are correct, can the image be well decrypted. The optical realization is then proposed and computer simulations are also performed to confirm the possibility of the proposed method.     

Image encryption and decryption using fractional Fourier transform and radial Hilbert transform

A technique for image encryption using fractional Fourier transform (FRT) and radial Hilbert transform (RHT) is proposed. The spatial frequency spectrum of the image to be encrypted is first segregated into two parts/channels using RHT, and image subtraction technique. Each of these channels is encrypted independently using double random phase encoding in the FRT domain. The different fractional orders and random phase masks used during the process of encryption and decryption are the keys to enhance the security of the proposed system. The algorithms to implement the proposed encryption and decryption scheme are discussed, and results of digital simulation are presented.     

基于分数阶傅里叶变换的光学加密影片

随着通信与网络的快速发展,能够包含大容量信息的影片得到了广泛应用。利用分数阶傅里叶变换的特点,提出了一种全光学加密解密影片的方法。将现有的影片加密密钥从二重变为了四重,显著增加了影片的安全性。通过改变振幅型正弦光栅的作用位置,将影片的加密解密次数由现有的每帧各一次减小为总共一次,优化了算法。仿真结果验证了该方法的有效性。     

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.     

Image encryption based on the multiple-parameter discrete fractional Fourier transform and chaos function

In recent years, the chaos-based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques. In this paper, we propose a new approach for image encryption based on the multiple-parameter discrete fractional Fourier transform and chaotic logistic maps in order to meet the requirements of the secure image transmission. In the proposed image encryption scheme, the image is encrypted by juxtaposition of sections of the image in the multiple-parameter discrete fractional Fourier domains and the alignment of sections is determined by chaotic logistic maps. This method does not require the use of phase keys. The new method has been compared with several existing methods and shows comparable or superior robustness to blind decryption.     

双重分数傅里叶变换计算全息

提出了双重分数傅里叶变换计算全息，在这种方法中，将两个图像的信息分别经不同阶的分数傅里叶变换后，记录在同一张分数傅里叶变换计算全息图上，它需要两个特定的分数傅里叶变换系统才能再现出所记录的图像信息，利用其再现方式的特殊性，可制成一种新的安全认证系统。     

Asymmetric multiple-image hiding using phase retrieval technique based on amplitude- and phase-truncation in fractional Fourier domain

We propose a multiple-image hiding scheme based on the amplitude- and phase-truncation approach, and phase retrieval iterative algorithm in the fractional Fourier domain. The proposed scheme offers multiple levels of security with asymmetric keys. Multiple input images multiplied with random phase masks are independently fractional Fourier transformed with different orders. The individual keys and common keys are generated by using phase and amplitude truncation of fractional spectrum. After using two fractional Fourier transform, the resultant encrypted image is hided in a host image with phase retrieval iterative algorithm. Using the correct universal keys, individual keys, and fractional orders, one can recover the original image successfully. Computer simulation results with four gray-scale images support the proposed method. To measure the validity of the scheme, we calculated the mean square error between the original and the decrypted images. In this scheme, the encryption process and generation of decryption keys are complicated and should be realized using computer. For decryption, an optoelectronic setup has been suggested.     

Double image encryption based on phase-amplitude hybrid encoding and iterative phase encoding in fractional Fourier transform domains

A new method for double image encryption is proposed that is based on amplitude-phase hybrid encoding and iterative random phase encoding in fractional Fourier transform (FrFT) domains. In the iterative random phase encoding operation, a binary random matrix is defined to encode two original images to a single complex-valued image, which is then converted into a stationary white noise image by the iterative phase encoding with FrFTs. Compared with the previous schemes that uses fully phase encoding, the proposed method reduces the difference between two original images in key space and sensitivity to the FrFT orders. The primitive images can be retrieved exactly by applying correct keys with initial conditions of chaotic system, the pixel scrambling operation and the FrFT orders. Computer simulations demonstrate that the encryption method has impressively high security level and certain robustness against data loss and noise interference.