Fractional M-band dual tree complex wavelet transform for digital watermarking

In this paper, a novel digital watermarking scheme using fractional M-band dual tree complex wavelet transform (Fr-M-band-DT-CWT) is proposed. High frequency channels have wide bandwidth and low frequency channels have narrow bandwidth. These characteristics are suitable for analysing low frequency signal, but not for relatively high frequency signal. The images often contain many edges, which may cause rich middle and high frequency components in the 2-band wavelet domain. Therefore, the ordinary 2-band dual tree complex wavelet transform (DT-CWT) is not well-suited for analysing the image. So, the M-band DT-CWT with the FrFT called Fr-M-band-DT-CWT is proposed in this paper to address this problem. Further, we integrate the Fr-M-Band-DT-CWT with singular value decomposition (SVD) in order to enhance the performance. Experimental results of the proposed watermarking scheme are compared with the previously available watermarking algorithms, fractional Fourier transform (FrFT), fractional wavelet transform (FrWT). Further, the proposed watermark extraction scheme is also tested on different attacks. The results of the present investigations show that the proposed watermarking scheme is superior as compared to other existing watermarking schemes.     

Double-image encryption by iterative phase retrieval algorithm in fractional Fourier domain

A novel double-image encryption algorithm is proposed, which can simultaneously encrypt two images into a single one as the amplitude of a fractional Fourier transform with two different groups of fractional orders. The two original images can be retrieved independently by fractional Fourier transforms with two different groups of fractional orders, one public phase mask, and two different private phase masks. The proposed approach can enlarge the key space, achieve faster convergence in the iterative process, and avoid cross-talk between the two images in reconstruction. Numerical simulations are presented to verify its validity and efficiency.     

Efficient computation of joint fractional Fourier domain signal representation

A joint fractional domain signal representation is proposed based on an intuitive understanding from a time-frequency distribution of signals that designates the joint time and frequency energy content. The joint fractional signal representation (JFSR) of a signal is so designed that its projections onto the defining joint fractional Fourier domains give the modulus square of the fractional Fourier transform of the signal at the corresponding orders. We derive properties of the JFSR, including its relations to quadratic time-frequency representations and fractional Fourier transformations, which include the oblique projections of the JFSR. We present a fast algorithm to compute radial slices of the JFSR and the results are shown for various signals at different fractionally ordered domains.     

Image encryption scheme based on random fractional discrete cosine transform and dependent scrambling and diffusion

An image encryption scheme is proposed by combining the random fractional discrete cosine transform (RFrDCT) with the dependent scrambling and diffusion (DSD). The application of the randomization, irrational choice and vectorization of fractional orders and the randomization of generating sequences improves the key-sensitivity and thus enlarges the key space greatly. Both the locations and the values of RFrDCT transformed coefficients are changed during the stage of DSD to further enhance the security of image encryption scheme. Numerical simulations demonstrate that the proposed image encryption scheme is feasible, secure and capable of resisting common classical attacks.     

Fractional finite Fourier transform

We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.     

Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask

A single channel asymmetric color image encryption scheme is proposed that uses an amplitude- and phase- truncation approach with interference of polarized wavefronts. Instead of commonly used random phase masks, wavelength-dependent structured phase masks (SPM) are used in the fractional Fourier transform domain for image encoding. The primary color components bonded with different SPMs are combined into one grayscale image using convolution. We then apply the amplitude and phase truncation to the fractional spectrum, which helps generate unique decryption keys. The encrypted image bonded with a different SPM is then encoded into a polarization selective diffractive optical element. The proposed scheme alleviates the alignment problem of interference and does not need iterative encoding and offers multiple levels of security. The effect of a special attack to the proposed asymmetric cryptosystem has been studied. To measure the effectiveness of the proposed method, we calculated the mean square error between the original and the decrypted images. The computer simulation results support the proposed idea.     

基于改进的自适应无参经验小波变换的滚动轴承故障诊断

为实现滚动轴承故障周期冲击特征的有效提取,解决经验小波变换Fourier谱分割存在的问题,提出了一种改进的自适应无参经验小波变换方法。首先,利用自适应无参经验小波变换对信号Fourier谱进行自适应分割;然后,利用峭度指标对谱边界进行合并,并重构滤波器组对信号进行分解;最后,选取峭度值最大的分量进行包络解调提取故障特征。仿真和工程应用验证了所提方法的有效性,分析结果表明该方法的性能优于集合经验模态分解和经典经验小波变换。     

Image encryption based on interference that uses fractional Fourier domain asymmetric keys

We propose an image encryption technique based on the interference principle and phase-truncation approach in the fractional Fourier domain. The proposed scheme offers multiple levels of security with asymmetric keys and is free from the silhouette problem. Multiple input images bonded with random phase masks are independently fractional Fourier transformed. Amplitude truncation of obtained spectrum helps generate individual and universal keys while phase truncation generates two phase-only masks analytically. For decryption, these two phase-only masks optically interfere, and this results in the phase-truncated function in the output. After using the correct random phase mask, universal key, individual key, and fractional orders, the original image is retrieved successfully. Computer simulation results with four gray-scale images validate the proposed method. To measure the effectiveness of the proposed method, we calculated the mean square error between the original and the decrypted images. In this scheme, the encryption process and decryption keys formation are complicated and should be realized digitally. For decryption, an optoelectronic scheme has been suggested.     

基于小波分解的时变信道盲辨识

针对传统的信道盲辨识算法很难适应时变信道模型的问题，提出了一种基于小波多分辨率分解的时变信道盲辨识算法．该算法首先应用小波多分辨率分解原理来近似建模时变信道；然后，利用信道输出序列的二阶统计量对时变信道的小波分解模型的小波系数进行两级盲辨识；最后，应用估计的小波系数即可重构时变信道的冲激响应．仿真结果表明，该算法可很好地完成周期时变信道的盲辨识与盲均衡任务．     

水中目标辐射噪声调制谱提取方法

分析了小波多分辨率分解方法引起的频率混叠的问题,提出了直接采用窄带FIR滤波的方法提取感兴趣的数据,然后利用Morlet复解析小波变换方法提取螺旋桨轴频。通过设置合适的中心频率和带宽,提取调制信号的包络,对包络信号进行谱分析,提取螺旋桨的轴频等信息,对于推算目标速度具有重要价值。     

Fractional Fourier transformer of variable order based on a modular lens system

The fractional Fourier transform is a new topic in optics. To make use of the fractional Fourier transform as an experimental tool, I design a fractional Fourier transformer of variable order: I introduce a lens system that is able to perform equidistant fractional Fourier transforms that cover the whole range of orders and that consist of a minimum number of modules. By module, I mean an elementary fractional Fourier transform of certain order that consists of a lens between two free-space lengths. Because of the commutative additivity of the transform, various fractional orders can be achieved by means of different constellations of the modules. It is possible to perform a large variety of fractional Fourier transforms with a small number of modules.     

Optical image encryption system using nonlinear approach based on biometric authentication

A nonlinear image encryption scheme using phase-truncated Fourier transform (PTFT) and natural logarithms is proposed in this paper. With the help of the PTFT, the input image is truncated into phase and amplitude parts at the Fourier plane. The phase-only information is kept as the secret key for the decryption, and the amplitude distribution is modulated by adding an undercover amplitude random mask in the encryption process. Furthermore, the encrypted data is kept hidden inside the face biometric-based phase mask key using the base changing rule of logarithms for secure transmission. This phase mask is generated through principal component analysis. Numerical experiments show the feasibility and the validity of the proposed nonlinear scheme. The performance of the proposed scheme has been studied against the brute force attacks and the amplitude-phase retrieval attack. Simulation results are presented to illustrate the enhanced system performance with desired advantages in comparison to the linear cryptosystem.     

An automated methodology for the classification of focal and nonfocal EEG signals using a hybrid classification approach

The uncertainty in human brain leads to the formation of epilepsy disease in human. The automatic detection and severity analysis of epilepsy disease is proposed in this article using a hybrid classification algorithm. The proposed method consists of decomposition stage, feature extraction, and classification stages. The electroencephalogram (EEG) signals are decomposed using dual-tree complex wavelet transform and then features are extracted from these coefficients. These features are then classified using the neural network classification approach in order to classify the EEG signals into either focal or nonfocal EEG signals. Furthermore, severity of the focal EEG signal is analyzed using an adaptive neuro-fuzzy inference system classification approach. The proposed hybrid classification method for the classification of focal signals and nonfocal signals achieved 98.6% of sensitivity, 99.1% of specificity, and 99.4% of accuracy. The average detection rate for both focal and nonfocal dataset is about 98.5%.     

基于信号奇异性分析的轴承故障检测方法

针对轴承振动信号利用小波单奇异点检测无法克服噪声影响的不足,提出利用小波模极大值分析信号奇异性变化进而进行轴承故障检测的方法。实验中对信号的模极大分形指数,模极大分形指数熵,Lipschitz指数以及Lipschitz指数熵等奇异特征进行分析比较,实验结果表明这些特征都能有效克服噪声影响实现故障检测,但模极大曲线数最能体现故障特征且检测效果最好。将该方法同基于小波包能量谱特征和小波单奇异点检测的方法进行比较,结果表明本文建议的方法在检测时间及检测率上都有显著提高。     

散斑分数傅里叶联合变换相关测量研究

提出数字散斑联合变换分数相关测量方法,利用分数相关可以锐化相关峰的作用,在数字散斑联合变换相关运算中用分数傅里叶变换代替傅里叶变换,提高测量精度。通过对散斑图像进行相位调制,有效地解决了分数傅里叶变换的移变性带来的谱移问题。编程模拟和对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,可以使相关峰的半宽度从4～5pixel锐化到仅1pixel,得到优于傅里叶变换相关的理想输出。     

Optical illustration of a varied fractional Fourier-transform order and the Radon-Wigner display

Based on an all-optical system, a display of a fractional Fourier transform with many fractional orders is proposed. Because digital image-processing terminology is used, this display is known as the Radon-Wigner transform. It enables new aspects for signal analysis that are related to time- and spatial-frequency analyses. The given approach for producing this display starts with a one-dimensional input signal although the output signal contains two dimensions. The optical setup for obtaining the fractional Fourier transform was adapted to include only fixed free-space propagation distances and variable lenses. With a set of two multifacet composite holograms, the Radon-Wigner display has been demonstrated experimentally.     

An improved multimodal medical image fusion scheme based on hybrid combination of nonsubsampled contourlet transform and stationary wavelet transform

This research proposes an improved hybrid fusion scheme for non-subsampled contourlet transform (NSCT) and stationary wavelet transform (SWT). Initially, the source images are decomposed into different sub-bands using NSCT. The locally weighted sum of square of the coefficients based fusion rule with consistency verification is used to fuse the detailed coefficients of NSCT. The SWT is employed to decompose approximation coefficients of NSCT into different sub-bands. The entropy of square of the coefficients and weighted sum-modified Laplacian is employed as the fusion rules with SWT. The final output is obtained using inverse NSCT. The proposed research is compared with existing fusion schemes visually and quantitatively. From the visual analysis, it is observed that the proposed scheme retained important complementary information of source images in a better way. From the quantitative comparison, it is seen that this scheme gave improved edge information, clarity, contrast, texture, and brightness in the fused image.     

Hybrid structured phase mask in frequency plane for optical double image encryption in gyrator transform domain

This paper proposes a method of double image encryption based on hybrid structured phase mask (HSPM) in the gyrator transform (GT) domain. The scheme becomes more secure by parameters used in the HSPM. These HSPMs are generated by using the combination of the optical vortex phase masks and secondary images after taking Fourier transform (FT). The input images are encrypted and recovered with correct values of HSPMs, rotation angles of GT and their keys used during the encryption. The use of an HSPM-based phase mask increases the security and key space for encryption. It can also be implemented opto-electronically. The mean square error calculated between the input and retrieved images shows the efficacy of scheme. The proposed method has also been investigated for its sensitivity to encryption parameters and its security against occlusion and noise attacks under a number of iterations. A set of numerical simulation results support the feasibility and security of the proposed scheme.     

Influence of Hall current on the flows of a generalized Oldroyd-B fluid in a porous space

Summary Exact analytical solutions for the magnetohydrodynamic (MHD) flows of an Oldroyd-B fluid through a porous space are developed. The fractional calculus approach is used to describe the constitutive model of a generalized Oldroyd-B fluid. The porous space is taken into account using modified Darcy's law for fractional viscoelastic fluid. The effect of Hall current is taken into account. Some interesting flows induced due to certain special oscillations are given. In each case, the analytical solutions are obtained using Fourier transform for fractional calculus. The present analysis with fractional calculus approach seems a first attempt for the study of MHD viscoelastic flows in a porous medium.