Showing papers on "Fractional Fourier transform published in 2020"

A novel chaos based optical image encryption using fractional Fourier transform and DNA sequence operation

Abstract: In this paper, we propose a new method for optical image encryption using fractional Fourier transform, DNA sequence operation and chaos theory. Random phase masks are generated using iterative Lorenz map and the plain image is transformed to a DNA matrix. This matrix is combined with the random phase mask and then transformed three times using the fractional Fourier transform. An Optical implementation of the encryption algorithm is proposed in our work. According to the experiment results and security analysis, we find that our algorithm has good encryption effect, larger secret key space and high sensitivity to the secret key. It can resist to most known attacks, such as statistical analysis and exhaustive attacks. All these features show that our encryption algorithm is very suitable for digital image encryption.

Arrhythmia Detection in ECG Signal Using Fractional Wavelet Transform with Principal Component Analysis

Abstract: Any significant alteration in the Electro-Cardio-Gram (ECG) signal wave components (P-QRS-T) for a time duration is detected as arrhythmia. In this paper, a novel fractional wavelet transform (FrWT) is used as a preprocessing tool. FrWT describes the given signal in time–frequency fractional domain using fractional Fourier transform and its denoising using wavelet transform. Because of this novel and intriguing property, it is broadly utilized as a noise removal tool in the fractional domain along with multiresolution analysis. Next, features are extracted using Yule–Walker autoregressive modeling. Dimensionality of the extracted features is to be reduced for proper detection of different types of arrhythmias. Principal component analysis has been applied for arrhythmia detection using variance estimation. The proposed method is evaluated on the basis of various performance parameters such as output SNR, mean squared error (MSE) and detection accuracy ( $$ {\text{DE}}_{\text{Acc}} $$ ). An output SNR of 33.41 dB, MSE of 0.1689% and Acc of 99.94% for real-time ECG database and output SNR of 25.25 dB, MSE of 0.1656%, $$ {\text{DE}}_{\text{Acc}} $$ of 99.89% for MIT-BIH Arrhythmia database are obtained.

Novel Short-Time Fractional Fourier Transform: Theory, Implementation, and Applications

Abstract: As a generalization of the classical Fourier transform (FT), the fractional Fourier transform (FRFT) has proven to be a powerful tool for signal processing and analysis. However, it is not suitable for processing signals whose fractional frequencies vary with time due to a lack of time localization information. A simple method to overcome this limitation is the short-time FRFT (STFRFT). There exist several different definitions of the STFRFT in the literature. Unfortunately, these existing definitions do not well generalize the classical result of the conventional short-time FT (STFT), which can be interpreted as a bank of FT-domain filters. The objective of this paper is to propose a novel STFRFT that preserves the properties of the conventional STFT and can be implemented easily in terms of FRFT-domain filter banks. We first present the novel STFRFT and then derive its inverse transform and basic properties. The time-fractional-frequency analysis of this transform is also presented. Moreover, the implementation of the proposed STFRFT is discussed. Finally, we provide several applications for the proposed STFRFT.

Discrete Transforms and Matrix Rotation Based Cancelable Face and Fingerprint Recognition for Biometric Security Applications.

Abstract: The security of information is necessary for the success of any system. So, there is a need to have a robust mechanism to ensure the verification of any person before allowing him to access the stored data. So, for purposes of increasing the security level and privacy of users against attacks, cancelable biometrics can be utilized. The principal objective of cancelable biometrics is to generate new distorted biometric templates to be stored in biometric databases instead of the original ones. This paper presents effective methods based on different discrete transforms, such as Discrete Fourier Transform (DFT), Fractional Fourier Transform (FrFT), Discrete Cosine Transform (DCT), and Discrete Wavelet Transform (DWT), in addition to matrix rotation to generate cancelable biometric templates, in order to meet revocability and prevent the restoration of the original templates from the generated cancelable ones. Rotated versions of the images are generated in either spatial or transform domains and added together to eliminate the ability to recover the original biometric templates. The cancelability performance is evaluated and tested through extensive simulation results for all proposed methods on a different face and fingerprint datasets. Low Equal Error Rate (EER) values with high AROC values reflect the efficiency of the proposed methods, especially those dependent on DCT and DFrFT. Moreover, a comparative study is performed to evaluate the proposed method with all transformations to select the best one from the security perspective. Furthermore, a comparative analysis is carried out to test the performance of the proposed schemes with the existing schemes. The obtained outcomes reveal the efficiency of the proposed cancelable biometric schemes by introducing an average AROC of 0.998, EER of 0.0023, FAR of 0.008, and FRR of 0.003.

Computational Efficient Refocusing and Estimation Method for Radar Moving Target With Unknown Time Information

Abstract: In the real application scenario, the time information when a moving target enters/leaves the radar coverage is often unknown, which would lead to severe performance loss for target refocusing, parameter estimation and imaging. We address the refocusing and motion parameters estimation problem for a moving target with unknown entry/departure time, involving range cell migration (RCM) and Doppler frequency migration (DFM) within the coherent refocusing period. A computationally efficient refocusing method based on extended generalized Radon Fourier transform (EGRFT) and window Fractional Fourier transform (WFRFT), i.e., EGRFT-WFRFT, is proposed. By employing the four-dimensional searching in the parameter space, the proposed EGRFT-WFRFT method could extract and match the target signal very well, resulting in good refocusing output, where the target's entry time, radial acceleration, velocity and initial range could be estimated. Then the radar echoes corresponding to the “entry time” are extracted. After quadratic phase term compensation, WFRFT is performed on the extracted echoes to obtain the estimation of target's departure time. Numerical experiments and real radar dataset processing are carried out to evaluate the performance of the proposed method. The results show that EGRFT-WFRFT could achieve superior focusing performance.

Introduction of a new vortex cosine-hyperbolic-Gaussian beam and the study of its propagation properties in fractional Fourier transform optical system

Abstract: Based on the framework of the Huygens–Fresnel diffraction, we investigate theoretically the propagation properties of a new vortex beam, which is referred to as vortex-cosh-Gaussian beam (vChGB), through a paraxial ABCD optical system. A closed-form formula of vChGB passing through the above system is derived. We show by analytical and numerical calculations that the decentered parameter and the topological vortex charge affect strongly the characteristics of the considered beam upon propagating in free space. In a fractional Fourier transform system (FrFT), it is found that the intensity and the phase distributions of the propagating vChGB evolves gradually and periodically versus the order of the FrFT. The shape of the vChGB depends on the parameters of the beam and the fractional order of the FrFT system. The results obtained may be beneficial to applications in optical trapping, optical micromanipulation and beam shaping.

Fast Detection Method for Low-Observable Maneuvering Target via Robust Sparse Fractional Fourier Transform

Abstract: In this letter, a novel fast detection algorithm, known as robust sparse fractional Fourier transform (RSFRFT), is proposed for low-observable maneuvering target detection in a clutter background. The discrete FRFT (DFRFT)-based detection method is time-consuming for large data volumes and the detection performance of sparse FRFT (SFRFT)-based algorithm will be significantly degraded in a heavy clutter background. Using two levels of detection, the defects of DFRFT and SFRFT algorithms are overcome using the proposed algorithm. The first-level detection is performed on the subsampled spectrum to estimate the target frequencies. The second-level detection is carried out after reconstruction for target detection. The simulation analysis and experiments using marine radar data show that the proposed method can achieve a good detection performance for low-observable maneuvering target detection in the clutter background with lower computational complexity.

Color image encryption based on chaotic compressed sensing and two-dimensional fractional Fourier transform.

Abstract: Combining the advantages of structured random measurement matrix and chaotic structure, this paper introduces a color image encryption algorithm based on a structural chaotic measurement matrix and random phase mask. The Chebyshev chaotic sequence is used in the algorithm to generate the flip permutation matrix, the sampling subset and the chaotic cyclic matrix for constructing the structure perceptual matrix and the random phase mask. The original image is compressed and encrypted simultaneously by compressed sensing, and re-encrypted by two-dimensional fractional Fourier transform. Simulation experiments show the effectiveness and reliability of the algorithm.

A Spectral–Spatial Anomaly Target Detection Method Based on Fractional Fourier Transform and Saliency Weighted Collaborative Representation for Hyperspectral Images

Abstract: Anomaly target detection methods for hyperspectral images (HSI) often have the problems of potential anomalies and noise contamination when representing background. Therefore, a spectral–spatial hyperspectral anomaly detection method is proposed in this article, which is based on fractional Fourier transform (FrFT) and saliency weighted collaborative representation. First, hyperspectral pixels are projected to the fractional Fourier domain by the FrFT, which can enhance the capability of the detector to suppress the noise and make anomalies to be more distinctive. Then, a saliency weighted matrix is designed as the regularization matrix referring to context-aware saliency theory and combined with the FrFT-based collaborative representation detector. The saliency-weighted regularization matrix assigns different pixels with different weights by using both spectral and spatial information, which can reduce the influence of the potential anomalous pixels embedded in the background when applying collaborative representation theory. Finally, to further improve the performance of the proposed method, a spectral–spatial detection procedure is employed to calculate final anomaly scores by using both spectral information and spatial information. The proposed method is compared with nine state-of-the-art hyperspectral anomaly detection methods on six HSI datasets, including two synthetic HSI datasets and four real-world HSI datasets. Extensive experimental results illustrate that the proposed method's detection performance outperforms other nine well-known compared methods in terms of area under the receiver operating characteristic (ROC) curve values, visual detection characteristics, ROC curve, and separability.

Optical image encryption scheme based on apertured fractional Mellin transform

Abstract: An optical image encryption scheme is proposed by utilizing an apertured nonlinear fractional Mellin transform (FrMT). Due to its nonlinear property, FrMT is utilized for eliminating potential insecurity in an image encryption system caused by known-plaintext and chosen-plaintext attacks. The aperture in the optical system makes it harder for attackers to collect optical signals in the transmission process. The apertured FrMT can be implemented by log-polar transform and Collins diffraction and the key space of the proposed image encryption algorithm is very large. The orders of the FrMT, the radii of the FrMT domains, the order of the FrFT, the phases generated in the further encryption process, wavelength, side-lengths of hard aperture, and the parameters of logistic map are used as cipher keys. Extensive simulation results demonstrate that the proposed algorithm is feasible, sensitive to the keys, and capable of resisting common classical attacks. The encryption effect changes with the size of apertures.

Adaptive piecewise re-scaled stochastic resonance excited by the LFM signal

Abstract: The piecewise re-scaled stochastic resonance method is proposed and thoroughly investigated in a bistable system, which is induced by the linear frequency-modulated (LFM) signal. At first, the theoretical formulation for piecewise re-scaled stochastic resonance is explained in detail. Then, several numerical simulations are carried out and the effects of some related parameters are discussed, in which the moment of the signal segmentation and the re-scaled coefficient are key factors. Meanwhile, the numerical results indicate that the proposed method manages to process the LFM signal submerged in the noise. After that, adaptive piecewise re-scaled SR is proposed to solve the problem of the parameter selection. At last, the comparison between fractional Fourier transform (FRFT) and the proposed method is present. Compared to the traditional FRFT, the method has a better performance, especially in amplification effect. The method in this paper may provide reference for processing other kinds of frequency-modulated signals besides the LFM signal.

Performance of Chirp Parameter Estimation in the Fractional Fourier Domains and an Algorithm for Fast Chirp-Rate Estimation

Abstract: This article addresses the problem of fast and accurate chirp signal parameter estimation in fractional Fourier domains. By employing a perturbation analysis, it is shown that the fractional Fourier transform can be used as an effective tool to yield an asymptotically minimum-variance unbiased estimator of the chirp parameters. Furthermore, it is shown that the asymptotic performance of the fractional-Fourier-transform-based chirp-rate estimator depends only on the actual chirp rate, not the initial frequency. Consequently, the chirp-rate estimation can be done in only one-dimensional search space, which greatly reduces the computational cost. In order to validate theoretical outcomes, we propose a fast and powerful method for the estimation of chirp rates in the fractional Fourier domains based on the golden section search. Extensive computer simulations confirm the theoretical results by demonstrating that the estimation performance of the chirp rate achieves the Cramer–Rao lower bound for both single- and multicomponent chirps. Consequently, we assert that the proposed method of chirp parameter estimation in the fractional Fourier domains is the minimum-variance unbiased estimator, requiring minimal computational cost.

Wireless Device Identification Based on Radio Frequency Fingerprint Features.

Abstract: With the development of the Internet of Things (IoT) technology and the rapid deployment of 5G wireless, more and more radiation devices are appearing in the increasingly complex electromagnetic environment. To be able to manage these devices in a unified manner, accurate identification of the devices has become a top priority. Specific emitter identification (SEI) is to effectively solve this problem. In this paper, both power spectral density (PSD) and fractional Fourier transform (FrFT) methods are used to extract the characteristics of transient signals. The characteristics of steady-state signals are analyzed by the bispectrum method. The SEI system model in this paper is constructed based on these techniques. Our experiments results show that when the SNR is 16dB, the SEI system can achieve a recognition accuracy of over 97% by exploiting the characteristics of the transient signal. Since the characteristics of the steady-state signal can better suppress noise, the SEI system can achieve a nearly 90% classification recognition accuracy under extremely low SNR.

Multidimensional fractional Fourier transform and generalized fractional convolution

Abstract: In this paper, we prove inversion theorems and Parseval identity for the multidimensional fractional Fourier transform. Analogous to the existing fractional convolutions on functions of single vari...

Image Compression and Encryption Scheme Based on Compressive Sensing and Fourier Transform

Abstract: An image compression and encryption scheme based on compressive sensing (CS) and Fourier transform is proposed to achieve image encryption and compression with reconstruction robustness and high security. Making use of the property of CS, encryption and compression are combined. In order to avoid the security limitations of revealing the energy information of the plaintext from ciphertext and reusing of measurement matrix to improve security, chaos system and two-dimensional fractional Fourier transform (2D-FRT) are used to perform encryption. Moreover, double random phase encryption based on 2D-FRT can avoid the loss of reconstruction robustness in diffusion encryption. The test results indicate that the proposed method has high security, good compression performance and reconstruction robustness.

Fractional Fourier Transform Based Adaptive Filtering Techniques for Acoustic Emission Signal Enhancement

Abstract: Acoustic emission technique (AET) is a well-known non-destructive testing method used for the detection of crack growth and monitoring structural integrity of components. The main limitation in the application of AET is the fact that acoustic emission (AE) signal is often affected by background noise. A new approach is proposed in this paper to reduce the background noise and to improve the accuracy of AE signal detection. Various noise reduction methods have been applied and studied for AE signal enhancement so far. Some of the studies proved that self-adaptive noise cancellation (SANC) and adaptive noise cancellation (ANC) are better techniques for denoising the AE signal. This paper proposes the use of ANC and SANC schemes based on Fractional Fourier Transform (FrFT) for AE signal enhancement. FrFT is the generalization of the classical Fourier Transform (FT). The use of FrFT gives an advantage of an additional degree of freedom (angle of rotation in time–frequency plane) over the traditional Fourier transform and could provide improved performance. In this method, the noisy signal is rotated in time- frequency plane to extract the signal in Fractional Fourier domain (FrFD). Two adaptive filters viz. least mean squares and normalized least mean squares are studied for FrFD based ANC approach. The performance of the proposed method is validated using real AE signals acquired from three different experiments: pencil lead break test, composite drilling test and concrete compression test. Results are compared with the time and frequency domain adaptations. Moreover, the results have also been compared with the frequency domain adaptation techniques. Results have demonstrated that FrFD based ANC approach outperforms the conventional time domain and frequency domain adaptive filtering with an improved signal to noise ratio and significantly reduces mean square error.

A family of convolution-based generalized Stockwell transforms

Abstract: The main purpose of this paper is to introduce a family of convolution-based generalized Stockwell transforms in the context of time-fractional-frequency analysis. The spirit of this article is completely different from two existing studies (see D. P. Xu and K. Guo [Appl. Geophys. 9 (2012) 73–79] and S. K. Singh [J. Pseudo-Differ. Oper. Appl. 4 (2013) 251–265]) in the sense that our approach completely relies on the convolution structure associated with the fractional Fourier transform. We first study all of the fundamental properties of the generalized Stockwell transform, including a relationship between the fractional Wigner distribution and the proposed transform. In the sequel, we introduce both the semi-discrete and discrete counterparts of the proposed transform. We culminate our investigation by establishing some Heisenberg-type inequalities for the generalized Stockwell transform in the fractional Fourier domain.

Novel Fractional Wavelet Packet Transform: Theory, Implementation, and Applications

Abstract: The fractional wavelet transform (FRWT), which generalizes the classical wavelet transform and the well-known fractional Fourier transform, has recently been demonstrated as a powerful analytical tool for signal and image processing. However, this transform suffers from a relatively poor resolution in the high fractional frequency region, which results in difficulties in discriminating signals containing close high fractional frequency components. A simple but effective method to overcome this deficiency is the fractional wavelet packet transform (FRWPT). There exist several different definitions of the FRWPT in the literature. Unfortunately, these existing definitions do not generalize well the classical results for the conventional wavelet packet transform. The objective of this paper is to obtain a novel FRWPT that preserves the properties of its conventional counterpart. We first define the novel FRWPT and then discuss its related properties. Fractional wavelet packet subspaces are also constructed. Moreover, a recursive algorithm for implementing the proposed FRWPT is presented. Finally, we discuss potential applications of the proposed FRWPT.

Sparsely Localized Time-Frequency Energy Distributions for Multi-Component LFM Signals

Abstract: This letter presents a high resolution method which separates close components of a multi-component linear frequency modulated (LFM) signal and eliminates their Cross-Terms (CTs). We first investigate the energy distribution of the Auto-Terms (ATs) and CTs in ambiguity plane. This reveals that the energy of the CTs of parallel close components is significant around the origin. We propose to mask the samples in which the CTs may have interferences with the ATs. This mask is signal-dependent and its directions are determined using the relationship between the radial slices of ambiguity function (AF) and the fractional Fourier transform (FrFT). Exploiting sparsity in time-frequency (TF) domain and by solving an $\ell _1$ -norm minimization problem, the localized time-frequency distribution (TFD) is extracted from the acquired samples of the AF. Simulation results reveal significant improvements in the efficiency compared to previous works.

An MTRC-AHP Compensation Algorithm for Bi-ISAR Imaging of Space Targets

Abstract: For bistatic inverse synthetic aperture radar (Bi-ISAR) imaging of space targets, the impacts of scatterers’ migration through resolution cell (MTRC) and azimuth high-order phase (AHP) are becoming more severe, especially for a long coherent processing interval (CPI). In this paper, the movement of a scatterer is modeled as a quartic function under the restriction of the space target orbit, then an MTRC-AHP compensation algorithm is proposed. A fourth-order keystone transform is introduced to remove the MTRC firstly, then the residual AHP terms are compensated gradually via the azimuth compensation phase and fractional Fourier transform (FRFT). The impact of the orbit prediction error of the space target on the algorithm is analyzed theoretically. Numerical simulations illustrate the effectiveness of the proposed method and validation of the theoretical analysis.

Optical color image encryption based on chaotic fingerprint phase mask in various domains and comparative analysis.

Abstract: Random phase masks serve as secret keys and play a vital role in double random phase encoding architecture. In this paper, we propose a new, to the best of our knowledge, method to generate the random phase masks using the chaotic Henon map and fingerprint. We then extend the generated chaotic fingerprint phase masks to the Fourier transform domain, fractional Fourier transform domain, Fresnel transform domain, and Gyrator transform domain to encrypt color images. In these four color image encryption schemes, the fingerprint and chaotic parameters serve as secret keys directly, and the chaotic fingerprint phase masks are just used as interim variables and functions. If the sender and receiver share the fingerprint, only the chaotic parameters are needed to transmit over the network. Thus, the management and transmission of the secret keys in these four encryption schemes are convenient. In addition, the fingerprint keys which are strongly linked with the sender or receiver can enhance the security of these four encryption schemes greatly. Extensive numerical simulations have been carried out to verify the feasibility, security, and robustness of these four color image encryption schemes.