Multifractional correlation

Multifractional correlation is proposed that is based on a new generalized fractional Fourier transform to which we refer as a multifractional Fourier transform. The multifractional correlation yields remarkable improvements in the correlation output peak intensity, peak sharpness, and light efficiency compared with convention correlation, which uses matched and phase-only filters, and still maintains better target discrimination capability and a reasonable robustness to noise. An optoelectronic hybrid system that can implement the multifractional correlation is also suggested.     

Optical color image hiding scheme by using Gerchberg–Saxton algorithm in fractional Fourier domain

We proposed an optical color image hiding algorithm based on Gerchberg–Saxton retrieval algorithm in fractional Fourier domain. The RGB components of the color image are converted into a scrambled image by using 3D Arnold transform before the hiding operation simultaneously and these changed images are regarded as the amplitude of fractional Fourier spectrum. Subsequently the unknown phase functions in fractional Fourier domain are calculated by the retrieval algorithm, in which the host RBG components are the part of amplitude of the input functions. The 3D Arnold transform is performed with different parameters to enhance the security of the hiding and extracting algorithm. Some numerical simulations are made to test the validity and capability of the proposed color hiding encryption algorithm.     

Image double encryption based on iteration Fourier and chaos system

According to the digital image encryption, a double encryption algorithm based on the iterative Fourier transform and chaotic transform is proposed. It uses iterative Fourier transform to encrypt image for the first time, then processes the encrypted image through the chaos replacement, which can change image pure phase distribution to realize double encryption. The simulated result shows that the algorithm can effectively resist the attacks of statistical analysis, and has higher encryption effect and safety which is very sensitive to secret key.     

Implementing compressive fractional Fourier transformation with iterative kernel steering regression in double random phase encoding

This paper proposes a novel approach in double random phase encryption based on compressive fractional Fourier transform along with the kernel steering regression. The method increases the complexity of the image by using fractional Fourier transform and taking fewer measurements from the image data. Numerical results are given to analyze the validity of this technique. Considering natural images to be sparse in some domain, we apply a compressive sensing (CS) approach by using a TwIST algorithm. The encryption process has kernel steering regression algorithm for denoising and compressive sensing technique for image compression along with the fractional Fourier transform that makes the image in more complex form.     

Optical image encryption based on the multiple-parameter fractional Fourier transform

A novel image encryption algorithm is proposed based on the multiple-parameter fractional Fourier transform, which is a generalized fractional Fourier transform, without the use of phase keys. The image is encrypted simply by performing a multiple-parameter fractional Fourier transform with four keys. Optical implementation is suggested. The method has been compared with existing methods and shows superior robustness to blind decryption.     

Image recovery from double amplitudes in fractional Fourier domain

The classical Gerchberg--Saxton algorithm is introduced into the image recovery in fractional Fourier domain after adaptation. When this algorithm is applied directly, its performance is good for smoothed image, but bad for unsmoothed image. Based on the diversity of fractional Fourier transform on its orders, this paper suggests a novel iterative algorithm, which extracts the information of the original image from amplitudes of its fractional Fourier transform at two orders. This new algorithm consists of two independent Gerchberg--Saxton procedures and an averaging operation in each circle. Numerical simulations are carried out to show its validity for both smoothed and unsmoothed images with most pairs of orders in the interval [0, 1].     

Triple image encryption scheme in fractional Fourier transform domains

We proposed a triple image encryption scheme by use of fractional Fourier transform. In this algorithm, an original image is encoded in amplitude part and other two images are encoded into phase information. The key of encryption algorithm is obtained from the difference between the third image and the output phase of transform. In general case, random phase encoding technology is not required in the proposed algorithm. Moreover, all information of images is preserved in theory when image are decrypted with correct key. The optical implementation of the algorithm is presented with an electro-optical hybrid structure. Numerical simulations have demonstrated the efficiency and the security of this algorithm. Based on this scheme a multiple image algorithm is expanded and designed.     

Determination of exact rotation angle and discrimination for rotated images

The complex frequency scaling property of Fourier transforms may be very effective for the determination of exact image rotation angle in application areas such as defense, manufacturing agriculture and commerce. In this paper, we exploit the complex frequency scaling property of Fourier transform to determine the exact angle of rotation of a target image with respect to reference image. We also investigate the validity of the developed algorithm using occluded target images. Further, we extend our algorithm to differentiate between different but similar rotated target images. We use both gray scale and DARPA's moving and stationary target recognition program's synthetic aperture radar images to validate our algorithm.     

Double image encryption based on iterative fractional Fourier transform

We present an image encryption algorithm to simultaneously encrypt two images into a single one as the amplitudes of fractional Fourier transform with different orders. From the encrypted image we can get two original images independently by fractional Fourier transforms with two different fractional orders. This algorithm can be independent of additional random phases as the encryption/decryption keys. Numerical results are given to analyze the capability of this proposed method. A possible extension to multi-image encryption with a fractional order multiplexing scheme has also been given.     

基于极坐标变换去除计算机层析图像环形伪影

探测器像元响应的不一致、光源能不稳定等因素使得计算机层析(CT)图像中含有较多的环形伪影,严重降低了图像质量,影响了图像的三维重建和量化分析,为此提出了基于极坐标变换与傅里叶变换后低通滤波的算法去除环形伪影。通过极坐标变换将直角坐标下的环形伪影转化为极坐标下的线性伪影,然后对线性伪影图像进行傅里叶变换获得频谱图像,进而设计二维低通滤波器进行滤波处理,最后通过傅里叶逆变换与坐标逆变换获得校正后的图像。利用Matlab软件,编写程序对算法进行验证,结果表明,该算法能够有效地去除环形伪影,使图像内部细节清晰可见,并且保护了图像边缘信息,提高了图像的信噪比;另外,使用该方法处理100张切片图像只需3.5min,可满足批量处理的需求。     

Image encryption based on double random amplitude coding in random Hartley transform domain

We propose an image encryption scheme based on double random amplitude coding technique by using random Hartley transform, which is defined according to the random Fourier transform. The significant feature of this algorithm is that the encrypted image is real and convenient for storage as well as transfer of the encrypted information. Moreover, the algorithm has enhanced security and the correct information of original image can be well protected under bare decryption, blind decryption and brute force attacks. Numerical simulation results are also presented in support of the proposed scheme.     

Random fractional Fourier transform

We propose a novel random fractional Fourier transform by randomizing the transform kernel function of the conventional fractional Fourier transform. The random fractional Fourier transform inherits the excellent mathematical properties from the fractional Fourier transform and can be easily implemented in optics. As a primary application the random fractional Fourier transform can be directly used in optical image encryption and decryption. The double phase encoding image encryption schemes can thus be modeled with cascaded random fractional Fourier transformers.     

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.     

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。     

Single Channel Quantum Color Image Encryption Algorithm Based on HSI Model and Quantum Fourier Transform

In order to obtain high-quality color images, it is important to keep the hue component unchanged while emphasize the intensity or saturation component. As a public color model, Hue-Saturation Intensity (HSI) model is commonly used in image processing. A new single channel quantum color image encryption algorithm based on HSI model and quantum Fourier transform (QFT) is investigated, where the color components of the original color image are converted to HSI and the logistic map is employed to diffuse the relationship of pixels in color components. Subsequently, quantum Fourier transform is exploited to fulfill the encryption. The cipher-text is a combination of a gray image and a phase matrix. Simulations and theoretical analyses demonstrate that the proposed single channel quantum color image encryption scheme based on the HSI model and quantum Fourier transform is secure and effective.     

Image encryption by using local random phase encoding in fractional Fourier transform domains

Based on fractional Fourier transform, an image encryption algorithm is proposed and researched. A local random phase encoding is introduced into this algorithm. The data at the local area of complex function is converted by fractional Fourier transform. The local random phase encoding is performed many times. Moreover only one set of random phase data is used in image encryption process. Compare to double random phase encoding, the parameter defining local area can be regarded as the additional key to increase the security of the encryption scheme. Some numerical simulations are achieved to demonstrate the performance of the image encryption scheme.     

Causes of the reconstructed cross appearing in lensless Fourier transform digital holography

Causes of the bright cross appearing in the reconstructed field of lensless Fourier transform digital hologram (LFDH) are presented. Firstly, as LFDH's reconstruction was directly performed by Fourier transform algorithm, the intensity distribution of reconstructed image plane was just LFDH's spectrum, and three parts of the reconstructed field are imaged in the spectral plane. Meanwhile their intensities were almost the same. Hence, the ratio of signal to noise of the reconstructed image was obviously lower than that of the conventional digital hologram. Further, non-uniformity of the background intensity and random noises usually existed in a practical LFDH. Meanwhile their spectra spread through the central and the edge areas; this also led to decrease in the ratio of signal to noise of the reconstructed image. Specially, as the two-dimensional Fourier transform algorithm was performed row by row, and then column by column, the low-frequency spectrum induced by the non-uniformity of the background and random noises along the directions of rows and columns would concentrate on the central column and row, respectively, and what is gotten looked like a cross. Therefore, the cross appearing in LFDH's reconstructed field should be attributed to the combination of the background and the Fourier transform algorithm itself.     

Double image encryption based on discrete multiple-parameter fractional Fourier transform and chaotic maps

A double image encryption method is proposed by utilizing discrete multiple-parameter fractional Fourier transform and chaotic maps. One of the two original images scrambled by one chaotic map is encoded into the amplitude of a complex signal with the other original image as its phase. The complex signal multiplied by another chaotic random phase mask is then encrypted by discrete multiple-parameter fractional Fourier transform. The parameters in chaotic map and discrete multiple-parameter fractional Fourier transform serve as the keys of this encryption scheme. Numerical simulations have been done to demonstrate the performance of this algorithm.     

Randomization of the Fourier transform

We have investigated the multiplicity and complexity in eigenvalues of the fractional Fourier transform and found that the ambiguity of the eigenvalues may indicate randomness. We have therefore proposed a method to randomize the Fourier transform. Such a random Fourier transform can be applied in the field of image encryption and decryption.     

分数傅里叶域数字水印算法

基于离散分数傅里叶变换(DFRFT)快速算法发展了一种分数傅里叶谱域图像水印算法.该算法根据分数傅里叶变换谱具有空域和频域双域信息表达能力,分别对原始图像和所加水印信息进行不同级次的分数傅里叶变换,提取水印分数傅里叶谱的低频成分并直接将其叠加到原始图像的分数傅里叶谱中的对角像元上,然后再进行逆变换得到水印图像.在JPEG压缩、图像旋转及剪切等攻击方式下,对该水印算法进行了鲁棒性分析,数值实验表明该水印算法具有良好的抗攻击性和安全性.