A Robust Public-key Image Watermarking Scheme Based on Weakness Signal Detection Using Chaos System

There are numerous studies showing that there is a constant increase in the ocean ambient noise level and the ever-growing demand for developing algorithms for detecting weak signals in ambient noise. In this study, we utilize dynamical and statistical complexity to detect the presence of weak ship noise embedded in ambient noise. The ambient noise and ship noise were recorded in the South China Sea. The multiscale entropy (MSE) method and the complexity-entropy causality plane (C-H plane) were used to quantify the dynamical and statistical complexity of the measured time series, respectively. We generated signals with varying signal-to-noise ratio (SNR) by varying the amplification of a ship signal. The simulation results indicate that the complexity is sensitive to change in the information in the ambient noise and the change in SNR, a finding that enables the detection of weak ship signals in strong background ambient noise. The simulation results also illustrate that complexity is better than the traditional spectrogram method, particularly effective for detecting low SNR signals in ambient noise. In addition, complexity-based MSE and C-H plane methods are simple, robust and do not assume any underlying dynamics in time series. Hence, complexity should be used in practical situations.

Weak signal detection has garnered considerable attention in numerous research fields, especially weak signal detection under strong noise, which is an urgent problem researches are concerned with. In this paper, a new criterion to select singular values using correlation coefficients is proposed for detecting weak exponential damped sinusoidal signals. This method has a wide variety of signal processing applications. The innovation of our method lies in selecting the most informative singular values of K rather than the most energetic singular values. The proposed method measures the similarity between component signals and useful signals via the autocorrelation function and correlation coefficient, which can preserve more information of the original signal and be more suitable for weak signal detection scenarios under strong noise. Numerical experiments and analysis are performed to verify the efficiency and effectiveness of our method, and indicate that the presented method is superior to the singular value selection methods based on energy or simple difference principle for correlation coefficients. Compared to stochastic resonance methods suitable for weak signal detection under strong background noise, our proposed method also offer significant advantages. Thus, it is beneficial for theoretical analysis and engineering applications.

The problem of distributed detection of a deterministic signal with unknown strength using a neural network approach is considered. Since the signal level Is not known there does not exist a uniformly powerful detection scheme for the problem. The neural network architecture used Is a two layer feedforward perceptron model with N Inputs M nodes In the hidden layer and two output nodes that correspond to the signal and noise hypotheses. The back propagation algorithm Is used to train the system with a known noise distribution. For fixed false alarm probabilities the performance of the trained network with regard to a set of test signals is estimated and compared to the performance of some known detection procedures such as Fisher''s method Tlppett''s method and the optimum test. Simulation results are presented for a network with two input nodes and three or four nodes In the hidden layer. When Laplace noise Is assumed the network performs better than the Tlppett method. For the detection of weak and moderate signals in Gaussian noise the network performs reasonably close to the optimum detection scheme. The decision regions for the neural network detection scheme is comparable to those of the Fisher''s and Tlppett''s methods. However unlike the Tippett''s method which has a fixed decision region regardless of the noise distribution the neural network''s decision region changes with the noise distribution. 1. SIGNAL DETECTION

Weak signal detection is a significant problem in modern detection such as mechanical fault diagnosis. The uniqueness of chaos and good learning ability of neural networks provide new ideas and framework for weak signal detection field. In this paper, Elman neural network is applied to detect and recover weak pulse signal in chaotic noise. For detection problem of weak pulse signal under chaotic noise, based on short-term predictability of chaotic observations, phase space reconstruction for observed signals is carried out. And Elman deep learning adaptive detection model (EDAD model) is established for weak pulse signal detection, and a hypothesis test is used to detect weak pulse signal from the prediction error. For the recovery of weak pulse signal under chaotic noise, a double-layer Elman deep neural network recovery model (DEDR model) is proposed, which is based on the Elman deep learning network model and single-point jump model for weak pulse signal, and it is optimized with goal of minimizing mean square prediction error of the Elman model. The profile least squares method is applied to estimate parameters of the DEDR model for difficult recovery of weak pulse signal because the DEDR model is essentially a semiparametric model with parametric and nonparametric parts. In the end, simulation experiments show that the model built in this paper can effectively detect and recover weak pulse signal in the background of chaotic noise.

The measurement of multiphase flow parameters is of great importance in a wide range of industries. In the measurement of multiphase, the signals from the sensors are extremely weak and often buried in strong background noise. It is thus desirable to develop effective signal processing techniques that can detect the weak signal from the sensor outputs. In this paper, two methods, i.e., lock-in-amplifier (LIA) and improved Duffing chaotic oscillator are compared to detect and process the weak signal. For sinusoidal signal buried in noise, the correlation detection with sinusoidal reference signal is simulated by using LIA. The improved Duffing chaotic oscillator method, which based on the Wigner transformation, can restore the signal waveform and detect the frequency. Two methods are combined to detect and extract the weak signal. Simulation results show the effectiveness and accuracy of the proposed improved method. The comparative analysis shows that the improved Duffing chaotic oscillator method can restrain noise strongly since it is sensitive to initial conditions.

In order to extract the fault feature frequency of weak bearing signals, we put forward a local mean decomposition (LMD) method combining with the second generation wavelet transform. After performing the second generation wavelet denoising, the spline-based LMD is used to decompose the high-frequency detail signals of the second generation wavelet signals into a number of production functions (PFs). Power spectrum analysis is applied to the PFs to detect bearing fault information and identify the fault patterns. Application in inner and outer race fault diagnosis of rolling bearing shows that the method can extract the vibration features of rolling bearing fault. This method is suitable for extracting the fault characteristics of the weak fault signals in strong noise.

Delayed feedback and detection of weak periodic signals in a stochastic Hodgkin–Huxley neuron

The weak vital periodic signals are easy to be submerged by strong noise as human body is keeping still, whose frequencies are hard to be detected. A new method based on the combination of wavelet de-noising and chaotic oscillator is presented in order to solve this problem. The proposed method make use of the wavelet de-noising to remove some noise primarily, and then employ improved chaotic oscillator array to detect the respiration and heart beat signal. Simulation validates the feasibility of the detection method. The respiration and heart beat signal can be detected under strong noisy background, and the accuracy is quite acceptable. The methods presented can be applied to signal processor mounted on the life detection radar, which will improve the radar's performance in earthquake rescue and other life-saving missions.

Underground magnetic resonance sounding (MRS) low signal-noise ratio (SNR) weak signal is hard to manage with traditional de-noising method such as fitting and filter.In view of this, this article makes use of both transient electromagnetic method (TEM) data and MRS data obtained from integrated detecting equipment.The goal is to extract weak MRS signal based on TEM under strong background noise.At first, underground electrical distribution can be acquired from TEM data, which is processed by equivalent conductive plane method.Then, the initial model of moisture content distribution was constructed on geological information and 3D MRS forwarding was made with finite element method.At last, the correlation coefficient series and deviations between forwarding data and measured data were calculated.The initial model would be corrected until the result is satisfying.Model calculation shows that this method can effectively extract the weak nuclear magnetic signals in tunnel under strong background noise.

At present, commonly used methods of weak signal detection such as the wavelet threshold denoising method, digital filtering method, the Fourier frequency domain transformation etc. can achieve the lowest detection of signal-to-noise ratio (SNR) of -10 dB, and the bidirectional ring coupled Duffing oscillator can reach the lowest detected SNR of -20 dB. But the discharge pulse signal with a lower SNR often appears in on-site testing, so the existing detection methods are difficult to meet the practical requirements of weak signal detection. In order to effectively solve the problem, a new method for weak pulse signal detection is proposed based on an extended-Duffing oscillator. The main idea of this method is to make the Duffing oscillator model transform to an extended-Duffing oscillator model by using the general time scale transformation. This approach can effectively expand the frequency detection range for weak signal detection. In addition, because the critical amplitude of the Duffing system depends on various parameters, such as system parameters, initial values, driving signal frequency, and calculation step of Runge - Kutta method etc.. However, the Melnikov method is an approximate analytical method, which does not take into account the factors such as initial values and calculation step, therefore, the Melnikov method is not suitable for numerical simulations, and lack of practicality. For this, the critical amplitude of chaos with high accuracy is determined only through the simulation experiment. Experimental results show that the critical amplitude is equal to 0.825010 when the incentive angular frequency of the extended-Duffing oscillator equals 10000 rad/s, and the extended-Duffing oscillator changes from the critical chaotic state to the large scale cycle state for small changes (10-6) of the driving amplitude. The simulation results show that the extended-Duffing oscillator not only has a good noise immunity performance, but also can effectively detect weak partial discharge pulse signal so that the signal-to-noise ratio can be lower than -40 dB. This method further expands the detection range and application fields of weak signals.

Digital averaging technique is widely used in weak signal detection. The weak signal buried in strong noise is normally digitized with a multi-bit analog-to-digital converter (ADC) before the averaging. When using large number of averaging, the digitization can be accomplished by a 2-level comparator, instead of a multi-bit ADC. In this paper, we studied the statistical properties of ADCs with additive white Gaussian noise (AWGN) input. Our analysis shows that, with low signal-to-noise ratio (SNR) input, a comparator introduces 20% amplitude SNR loss compared with a fine multi-bit ADC, which can be mostly recovered with a post filter. It also shows that the comparator is linear and insensitive to input offset with low SNR input and AWGN.

In this paper, chaotic system is applied to identify and extract the weak signals of bearing early fault which are often submerged in strong background noise. Chaotic system is an effective method in weak signal detection because of its properties of noise immunity and sensitivity to the weak periodic signal. However, chaotic system is not completely immune to noise in critical chaotic state. Aiming at this problem, four indicators are used to evaluate the detection performance of Duffing oscillators. Then, the influence of Duffing oscillator parameters on the four indicators is studied in detail and a new method is proposed to improve the detection performance of Duffing oscillator. The simulation and experimental results show that the proposed method can accurately obtain the characteristic signals of early bearing fault in a lower signal-to-noise ratio (SNR) situation.

This research work concentrates on developing new methodologies for weak signal detection, which are further used in the watermark detection application. The proposed detectors perform comparable to or better than most of the state-of-the-art techniques. Stochastic resonance plays a significant role in weak signal detection. Injection of precalculated noise is a big concern for us. Noises i.e., symmetric and asymmetric have been utilized for getting an improved version of the weak signal detector. With equality and non-equality constraints, we use the particle swarm optimization method to optimize the objective function. After that, we investigate a new detector based on the fractional operator. The noisy signal is convolved with the coefficients of fractional order filter. The proposed method has been tested with different standard performance parameters. The results of the proposed detector have been compared with state-of-the-art detectors such as a threshold detector (TD), neural network-based detector etc. The robustness of the proposed detector with respect to the parameters of signal and noise has also been explored. The problem of weak DC signal detection present in non-Gaussian noise is always a troublesome because of the non-linearity of the test statistic. We have used the concept of stochastic resonance in a conventional neural network-based detector. A predefined noise is injected during the back-propagation algorithm in order to minimize the error. The reduction in errors (in terms of enhancement in the probability of detection, $$P_D$$ at a constant value of the probability of false alarm, $$P_{FA}$$ ) and faster convergence give a right justification to use the concept of stochastic resonance in the neural network-based detector.

LFM signals are widely applied in radar, communication, sonar and many other fields. LFM signals received by these systems contain a lot of noise and outliers. In order to suppress the interference of strong impulse noise on target signals and realize the accurate estimation of LFM signal parameters, the impulse noise of echo signals need to be filtered. In this paper, to solve the problem of poor performance of LFM signal parameter estimation based on fractional Fourier transform in impulse noise, alpha stable distribution is used to establish the mathematical model of impulse noise. The proposed fastest tracking differentiator with an adaptive tracking factor is used to suppress the strong impulse noise, and fractional Fourier transform is used to estimate the parameter of the LFM signals. The experimental results show that the proposed fastest tracking differentiator with an adaptive tracking factor has a good filtering performance. It can effectively filter the impulse noise in the echo signal and allows the FrFT method to accurate estimate the parameters of the LFM signals in strong impulse noise.

This paper introduces the use of chaotic Duffing oscillators to ballistocardiograph system for detection of weak signal. A ballistocardiograph (BCG) is an instrument that records the motions of the body imparted to it by the heart beat. It has been found that digital filters are not suitable for processing the BCG signals in noise. So in this paper, we propose a chaotic oscillators algorithm to detect information from BCG. The principles of using it to detect weak cycle sinusoidal signals are presented firstly. Then, the experimental results have shown that this algorithm is quite effective for detecting BCG signal and improving the ratio of signal to noise.