Using Peano–Hilbert space filling curves for fast bidimensional ensemble EMD realization

In this paper, a statistical analysis of electroencephalogram (EEG) signals is carried out in the empirical mode decomposition (EMD) domain using a publicly available benchmark EEG database. First, the intrinsic mode functions (IMF) are extracted from the EEG signals in the EMD domain. Next, the investigation was carried whether the Bessel k-form (BKF) probability density function (pdf) can appropriately model the IMFs extracted in EMD domain of the EEG signals. It is shown that on an average, the BKF pdf is a suitable prior to model the first five IMFs extracted from various types of EEG recordings. After that, it is shown that the BKF parameters can distinguish among the EEG signals at those five IMF levels quite well. The analysis is further confirmed through the p-values obtained by one way analysis of variance (ANOVA). Thus, the BKF parameters in the EMD domain may be used to characterize EEG signals and help the electroencephalographers in developing fast and effective classifiers for seizure seizure detection.

Empirical mode decomposition (EMD) is a powerful tool for the non-stationary and nonlinear signal analysis and has attracted considerable attention recently. However, one of primary problems existing in the EMD is the mode mixing, which makes the physical meaning of decomposition results obscure. The ensemble EMD (EEMD) is presented to alleviate the shortcoming. The EEMD is a noise-added method and can extract the components with truly physical meaning from the signal. Firstly, a simulation signal is used to test the performance of the EEMD; compared with the EMD, the EEMD illustrates the superiority over the EMD. Then, the fault diagnosis method based on the EEMD is applied to diagnose the faults of the gearbox with multiple faults and successfully extracts the multiple faults information from the collected signal. The results show that the fault diagnosis method based on the EEMD is a promising method for the fault diagnosis of gearboxes.

Various faults inevitably occur in mechanical systems and may result in unexpected failures. Hence, fault detection is critical to reduce unscheduled downtime and costly breakdowns. Empirical mode decomposition (EMD) is an adaptive time-frequency domain signal processing method, potentially suitable for nonstationary and/or nonlinear processes. However, the EMD method suffers from several problems such as mode mixing, defined as intrinsic mode functions (IMFs) with incorrect scales. In this paper, an ensemble noise-reconstructed EMD method is proposed to ameliorate the mode mixing problem and denoise IMFs for enhancing fault signatures. The proposed method defines the IMF components as an ensemble mean of EMD trials, where each trial is obtained by sifting signals that have been reconstructed using the estimated noise present in the measured signal. Unlike traditional denoising methods, the noise inherent in the input data is reconstructed and used to reduce the background noise. Furthermore, the reconstructed noise helps to project different scales of the signal onto their corresponding IMFs, instrumental in alleviating the mode mixing problem. Two critical issues concerned in the method, i.e., the noise estimation strategy and the number of EMD trials required for denoising are discussed. Furthermore, a comprehensive noise-assisted EMD method is proposed, which includes the proposed method and ensemble EMD (EEMD). Numerical simulations and experimental case studies on accelerometer data collected from an industrial shaving process are used to demonstrate and validate the proposed method. Results show that the proposed method can both detect impending faults and isolate multiple faults. Hence, the proposed method can act as a promising tool for mechanical fault detection.

Automatic patient monitoring for cardiac diseases requires the detection of various abnormal electrical activities occurring in the heart. Pseudo-pacemaker activities by cardiac cells or non-standard electrical impulses in the atria or ventricle cause various types of arrhythmia. Atrial fibrillation (AF) is the most important irregularity that occurs due to electrical malfunctioning in the atria. Unsynchronized pumping of the atria and ventricle causes different volumes of blood flow at different rhythms. In this paper, a method for the automatic detection of AF in the empirical mode decomposition (EMD) domain is proposed. Being a completely data-adaptive technique, EMD can be applied to all kinds of electrocardiogram signals. Selective reconstruction eliminates the requirement of conventional preprocessing for denoising the raw data. A combination of temporal and statistical features is used to characterize abnormal rhythms. A novel SQ time deviation feature is introduced, which is proved to be a good choice for AF classification. A nonlinear-kernel-based support vector machine classifier is used for classification. Sensitivity, specificity, and accuracy comparable to those of previous works are achieved for the MIT-BIH Arrhythmia Database.

Electroencephalograph (EEG) is brain activity measurement technique that it is widely used by placing electrode on the scalp. The EEG recording signals are vulnerably contaminated by noise. Thus, it can lead to misperception in analyzing EEG signals. One of the noise that has major influence on the recorded EEG signals is ocular artifacts (OAs). In this paper, a new method to remove OAs automatically is proposed by combining between Complete Ensemble Empirical Mode Decomposition (CEEMD) and Independent Component Analysis (ICA). CEEMD-ICA-OD removes OAs based on the concentration of noise that is calculated by calculating entropy for every CEEMD decomposition. Every selected decomposition of CEEMD will be used as input to the ICA method. Then, ICA will decompose selected CEEMD decomposition into independent components (ICs). Then, Chauvenet Criterion (CC) as Outlier Detection (OD) method is used to detect OAs pattern. Every detected OAs pattern will be eliminated by zeroing process on OAs pattern so that the EEG signal information remains secure. The proposed method were compared with Empirical Mode Decomposition (EMD), Ensemble EMD (EEMD) and Complete EEMD (CEEMD) with zeroing ICA combination for every comparison method. The performance measure of the proposed method and the benchmark method is calculated by using Root Mean Square Error (RMSE) and Signal to Noise Ratio (SNR) to show the performance quality in eliminating OAs. The experiment results show that the proposed method is successfully removing OAs better than the other methods with RMSE value and SNR value are 0.2491 and -0.3449, respectively.

An empirical signal separation algorithm for multicomponent signals based on linear time-frequency analysis

This paper deals with the image quality assessment (IQA) task using a natural image statistics approach. A reduced reference (RRIQA) measure based on the bidimensional empirical mode decomposition is introduced. First, we decompose both, reference and distorted images, into intrinsic mode functions (IMF) and then we use the generalized Gaussian density (GGD) to model IMF coefficients of the reference image. Finally, we measure the impairment of a distorted image by fitting error between the IMF coefficients histogram of the distorted image and the estimated IMF coefficients distribution of the reference image, using the Kullback–Leibler divergence (KLD). Furthermore, to predict the quality, we propose a new support vector machine-based (SVM) classification approach as an alternative to logistic function-based regression. In order to validate the proposed measure, three benchmark datasets are involved in our experiments. Results demonstrate that the proposed metric compare favorably with alternative solutions for a wide range of degradation encountered in practical situations.

Recently, ensemble empirical mode decomposition (EEMD) method has been developed for non-linear and non-stationary signal analysis. The method can work on nature signals (non-linear and nonstationary signals) and reduce the speckle noise. With the EEMD method, the signal is decomposed into several intrinsic mode functions (IMFs) and the frequencies of IMFs are arranged in decrease order (high to low) after the EEMD processing. The scaling mode of the EEMD method is similar to wavelet transform, but the signal resolutions in different frequency domains do not decrease by down-sampling. There are a large population and a developed economy in Weihe watershed, the disasters of droughts and floods caused by the autumn precipitation (here is precipitation in September and October) less or more than normal cause great loss and serious influence. In this paper, we propose the EEMD method to decompose the autumn precipitation series in the Weihe river basin during last 50 years into several IMFs, then extract the information including in the precipitation series and get the characteristics of multi-scales. The result shows that it is well response to the autumn precipitation series in the Weihe river basin and to the abrupt climate change in late 1970s and early 1980s of last century. The response appears earlier for high time scales than for low time scales In addition, the expression of the response for high time scales is the form of variability, but it is the amplitude of variability for low time scales.

Empirical mode decomposition (EMD) is an adaptive, data-driven algorithm that decomposes any time series into its intrinsic modes of oscillation, which can then be used in the calculation of the instantaneous phase and frequency. Ensemble EMD (EEMD), where the final EMD is estimated by averaging numerous EMD runs with the addition of noise, was an advancement introduced by Wu and Huang (2008) to try increasing the robustness of EMD and alleviate some of the common problems of EMD such as mode mixing. In this work, we test the performance of EEMD as opposed to normal EMD, with emphasis on the effect of selecting different stopping criteria and noise levels. Our results indicate that EEMD, in addition to slightly increasing the accuracy of the EMD output, substantially increases the robustness of the results and the confidence in the decomposition.

Emotion feature extraction is the key to speech emotional recognition. And ensemble empirical mode decomposition(EEMD) is a newly developed method aimed at eliminating emotion mode mixing present in the original empirical mode decomposition(EMD). To evaluate the performance of this new method, this paper investigates the effect of a parameters pertinent to EEMD: speech emotional envelope. Firstly, a speaker emotional envelope features extraction based on EEMD is proposed in the paper. Using the piecewise power function in speech emotional envelope has a better effect in emotional identification. At the same time, the proposed technique has been utilized for classification of fo ur kinds of emotional(angry, happy, sad and neutral) speech signals. Emotional intrinsic mode functions(IMFe) are obtained by empirical mode decomposition on emotional speech signals, the fast fourier transform(FFT) of each intrinsic mode function is extracte d as the emotional feature coefficient which is used in speaker emotional identification applying by vector quantization. MATLAB is used to ca lculate the characteristic of emotional speech signals using empirical mode decomposition (EEMD). We obtain an emotional envelope by transforming the IMFe of emotional speech signals, and obtain a new method of emotion recognition according to different emotional envelop feature vectors. The results indicate the proposed method works well in speaker emotional identification.

Empirical mode decomposition (EMD) method based on HHT has exhibited unique advantages such as adaptability and highly efficiency in many nonlinear, nonstationary signals processing applications. It breaks the uncertainty principle limit, but the traditional EMD still has its deficiencies. In this article, we construct a new wavelet which has excellent decomposing-frequency performance and energy concentration, and then an improved EMD method based on this wavelet is presented. Results of numerical simulation show the validity and efficiency of the method proposed in paper are better than traditional one. Furthermore, some foreseeable trends of time-frequency distribution technologies are described. The systems in reality, strictly speaking, tend to non-linear, so most practical signals are non-stationary random signals. Nonlinear, nonstationary signals analysis is a very significant and difficult problem in almost all technical fields such as automation, communication, aerospace- engineering, biomedicine, structural fault diagnosis and so on. Owed to the rapid development of large scale integrated circuit technology and artificial intelligence, the exploration of signal processing theories have got a sharply impetus. A series of new modern signal processing theories and methods have appeared to meet the need of time-frequency joint analysis of nonlinear, non-Gaussian and non-stationary signals, including discrete short-time Fourier transform, wavelet transform, Hilbert-Huang transform and so on. Time-frequency joint analysis can observe the evolution of the signal in the time domain and the frequency domain simultaneously, provide local time-frequency characteristics of the signal.

The existence of coherent and incoherent (random) noises in the ground penetration radar (GPR) signals using high-frequency electromagnetic waves is inevitable; therefore, the elimination of noise from GPR data before performing any additional analysis is of great importance to increase the efficiency of the interpretations. We apply the Total Variation De-noising (TVD) and Savitzky-Golay (SG) filter, on the synthetic and real GPR data. For a better perception, we compare the same trace of the data before and after the experiences. The results indicate that the TVD method is more effective than common adaptive filtering in the time domain for reducing noise such as the SG filter which acts as a low-pass filter for smoothing data based on a polynomial least-squares approximation; however, due to the visibility of staircase artifacts using the TVD method, GPR data is first transferred to the empirical mode decomposition (EMD) frame which is useful for non-linear and non-stationary signal processing, then the TVD method is applied on it; ultimately, noise reduction using TVD is compared in the time and EMD domains. The comparison of the outputs shows that the TVD algorithm in the EMD domain, based on the sequential extraction of the energy belonging to the different intrinsic time scales of the signal, provides better noise attenuation than the other algorithms. In addition, TVD-EMD preserves the event forms, signal forms and improves the continuity in sections.

In this paper window empirical mode decomposition (WEMD) is proposed and is used to do texture segmentation. Empirical mode decomposition (EMD) can decompose the nonstationary and nonlinear signals by sifting into a few intrinsic mode functions (IMFs) which represent a simple oscillatory mode of local data. However, the traditional bidimensional EMD (BEMD) has two drawbacks of the gray spots in IMF image and the slow computation speed. WEMD can solve such problems. Based on the characteristic of WEMD and local time/space-frequency analysis of structure multivector, the renovate technique of texture segmentation is also presented. Characterized by the local amplitude and the local frequency of every IMF component, the texture image can be segmented by k-means clustering algorithm. The subsequent experimental results indicate this method's effectiveness.

The acquisition of ballistocardiogram (BCG) signals during sleeping always presents all kinds of high-frequency noise, which causes the problem to extract effective signals. This article proposes a new method to extract heartbeat and respiration signals by combining the whale optimization algorithm (WOA) and variational mode decomposition (VMD). Firstly, the sample entropy and energy difference ratio are used as the fitness function of WOA to optimize the penalty factor in the variational mode decomposition a and the number of decomposition layers K;Then the original signal was decomposed into multiple modal components (IMF) by optimized VMD; Finally, respiration and heartbeat signals were reconstructed, and their frequencies got calculated. Compared with the experimental results of empirical mode decomposition (EMD) and ensemble empirical mode decomposition (EEMD), the average respiratory rate error obtained by this algorithm is 0.097 and 0.013 lower than EMD and EEMD respectively, and the average heart rate error is 0.03 and 0.006 lower than EMD and EEMD respectively, it is proved that the algorithm can extract breath and heartbeat signals more effectively and accurately.

Empirical mode decomposition (EMD) is a widely used adaptive signal processing method, which has shown some shortcomings in engineering practice, such as sifting stop criteria of intrinsic mode function (IMF), mode mixing and end effect. In this paper, an improved sifting stop criterion based on the valid data segment is proposed, and is compared with the traditional one. Results show that the new sifting stop criterion avoids the influence of end effects and improves the correctness of the EMD. In addition, a novel AEMD method combining the analysis mode decomposition (AMD) and EMD is developed to solve the mode-mixing problem, in which EMD is firstly applied to dispose the original signal, and then AMD is used to decompose these mixed modes. Then, these decomposed modes are reconstituted according to a certain principle. These reconstituted components showed mode mixing phenomena alleviated. Model comparison was conducted between the proposed method with the ensemble empirical mode decomposition (EEMD), which is the mainstream method improved based on EMD. Results indicated that the AEMD and EEMD can effectively restrain the mode mixing, but the AEMD has a shorter execution time than that of EEMD.