Bootstrap Empirical Mode Decomposition with Application to CIELAB Color Images

Mode Decomposition ◽

Local Mean ◽

The Mean ◽

Spatial Spectra ◽

Proof Of Convergence ◽

Cielab Color

This paper proposes an alternative optimization-based EMD based on the notions of: 1. <i>local mean points </i>that impose mode symmetry via a Tikhonov regularized least-square (RLS) problem, and 2. efficient <i>bootstrap sifting</i> that guarantees asymptotic convergence of the mean envelope to the local mean points, regardless of regularization. Mathematical proof of convergence and a straightforward extension to the 2D-multivariate setting and CIELAB color image sare presented. Performance is demonstrated with a univariate signal and two images. Spectral analysis confirms coordinated feature extraction among image components, and separation of spatial spectra among the intrinsic mode functions.

A NEW APPLICATION OF ENSEMBLE EMD AMELIORATING THE ERROR FROM INSUFFICIENT SAMPLING RATE

Advances in Adaptive Data Analysis ◽

10.1142/s179353691100088x ◽

2011 ◽

Vol 03 (04) ◽

pp. 493-508 ◽

Cited By ~ 3

Author(s):

DISHAN HUANG ◽

YULIN XU

Keyword(s):

Ball Bearing ◽

Broad Band ◽

Sampling Rate ◽

Vibration Signal ◽

Mode Decomposition ◽

Ensemble Mean ◽

Mixed Noise ◽

Bearing Vibration ◽

The Mean

The objective of this paper is to apply an assisted noise method for ameliorating the empirical mode decomposition (EMD) error from insufficient sampling rate for a vibration signal. When the intrinsic mode functions (IMFs) are extracted from a signal mixed noise at a certain level on the sifting algorithm, an extraordinary phenomenon, where noise submerges the EMD error, is discovered. Thus, noise-assisted data is proposed to disturb the EMD error in the sifting process. In order to cancel out noise after serving its purpose, the IMFs are processed with an ensemble mean. As a result, the noise-assisted data ameliorates the EMD error from insufficient sampling rate, and the method treats the mean as the final true result. An EMD example of ball bearing vibration is presented to illustrate the validity of the approach. This paper recommends implementing the noise-assisted method in the EMD on vibration and acoustic signals with broad band.

A Novel Shearer Cutting State Recognition Method Based on Improved Variational Mode Decomposition and LSSVM with Acoustic Signals

Shock and Vibration ◽

10.1155/2020/8835462 ◽

2020 ◽

Vol 2020 ◽

pp. 1-16

Author(s):

Zhongbin Wang ◽

Bin Liang ◽

Lei Si ◽

Kuangwei Tong ◽

Chao Tan

Keyword(s):

Search Algorithm ◽

Optimal Parameter ◽

Gravitational Search Algorithm ◽

Principal Component ◽

Least Square ◽

Support Vector ◽

Variational Mode Decomposition ◽

Recognition Method ◽

Mode Decomposition

The recognition of shearer cutting state is the key technology to realize the intelligent control of the shearer, which has become a highly difficult subject concerned by the world. This paper takes the sound signal as analytic objects and proposes a novel recognition method based on the combination of variational mode decomposition (VMD), principal component analysis method (PCA), and least square support vector machine (LSSVM). VMD can decompose a signal into various modes by using calculus of variation and effectively avoid the false component and mode mixing problems. On this basis, an improved gravitational search algorithm (IGSA) is designed by using the position update mechanism of Levy flight strategy to find the optimal parameter combination of VMD. Then, the feature extraction is achieved by calculating the envelope entropy and kurtosis of the decomposed intrinsic mode functions (IMFs). To avoid dimensional disasters and reinforce the classification performance, PCA is introduced to choose useful features, and the LSSVM-based classifier is reasonably constructed. Finally, the experimental results indicate that the proposed method is more feasible and superior in the recognition of shearer cutting states.

A Novel 4D Track Prediction Approach Combining Empirical Mode Decomposition with Nonlinear Correlation Coefficient

South Florida Journal of Development ◽

10.46932/sfjdv2n4-019 ◽

2021 ◽

Vol 2 (4) ◽

Author(s):

Zhiyuan Shen Shen ◽

Xiaowei Wang ◽

Qiuxiang Wu

Keyword(s):

Correlation Coefficient ◽

Nearest Neighbor ◽

Rapid Development ◽

Least Square ◽

Nonlinear Correlation ◽

Air Transport Industry ◽

Mode Decomposition ◽

Prediction Approach

The accuracy of 4D track prediction plays an important role to solve the prominent contradiction between the rapid development of air transport industry and the limited resources of airspace. The conventional 4D track prediction based on the aerospace dynamic model is usually inaccurate since of weather influence and air traffic controller (ATC) factor. In this paper, an entirely data-driven nominal flight height profile prediction approach combing empirical mode decomposition (EMD) with nonlinear correlation coefficient (NCC) is proposed. Firstly, the historical tracks are implemented on EMD individually. Then according to a procedure similar to leave-one-out cross validation (LOOCV), the physical meanings of different intrinsic mode functions (IMFs) obtained by EMD are analyzed to corresponding to the various flight information. For a specified flight, the similarities between different dates are measured by NCC. Finally, a predicted nominal trajectory is obtained by summing a series of selected IMFs with a regression weight under least square optimization framework. It is demonstrated that the proposed method shows a higher prediction performance when comparing with the state of the art method named as nearest neighbor classification with dynamic time warping (DTW). La precisión de la predicción de la pista 4D desempeña un papel importante para resolver la importante contradicción entre el rápido desarrollo de la industria del transporte aéreo y los recursos limitados del espacio aéreo. La predicción convencional de la pista 4D basada en el modelo dinámico aeroespacial suele ser inexacta debido a la influencia de las condiciones meteorológicas y el factor del controlador de tráfico aéreo (ATC). En este trabajo, se propone un enfoque de predicción del perfil de altura de vuelo nominal totalmente basado en datos que combina la descomposición empírica de modos (EMD) con el coeficiente de correlación no lineal (NCC). En primer lugar, las pistas históricas se implementan en la EMD individualmente. A continuación, de acuerdo con un procedimiento similar al de la validación cruzada sin intervención (LOOCV), se analizan los significados físicos de las diferentes funciones de modo intrínseco (IMF) obtenidas por la EMD para que correspondan a las diversas informaciones de vuelo. Para un vuelo específico, se miden las similitudes entre las distintas fechas mediante NCC. Por último, se obtiene una trayectoria nominal predicha mediante la suma de una serie de FMI seleccionadas con un peso de regresión en el marco de la optimización de mínimos cuadrados. Se demuestra que el método propuesto muestra un mayor rendimiento de predicción en comparación con el método más avanzado denominado clasificación de vecinos más cercanos con deformación temporal dinámica (DTW).

AN IMPROVED ONLINE PARADIGM FOR SCREENING OF DIABETIC PATIENTS USING RR-INTERVAL SIGNALS

Journal of Mechanics in Medicine and Biology ◽

10.1142/s0219519416400030 ◽

2016 ◽

Vol 16 (01) ◽

pp. 1640003 ◽

Cited By ~ 16

Author(s):

RAM BILAS PACHORI ◽

MOHIT KUMAR ◽

PAKALA AVINASH ◽

KORA SHASHANK ◽

U. RAJENDRA ACHARYA

Keyword(s):

Kernel Function ◽

Morlet Wavelet ◽

Least Square ◽

Support Vector ◽

Svm Classifier ◽

Diabetic Patients ◽

Rr Interval ◽

Mode Decomposition

Diabetes Mellitus (DM) which is a chronic disease and difficult to cure. If diabetes is not treated in a timely manner, it may cause serious complications. For timely treatment, an early detection of the disease is of great interest. Diabetes can be detected by analyzing the RR-interval signals. This work presents a methodology for classification of diabetic and normal RR-interval signals. Firstly, empirical mode decomposition (EMD) method is applied to decompose the RR-interval signals in to intrinsic mode functions (IMFs). Then five parameters namely, area of analytic signal representation (AASR), mean frequency computed using Fourier-Bessel series expansion (MFFB), area of ellipse evaluated from second-order difference plot (ASODP), bandwidth due to frequency modulation (BFM) and bandwidth due to amplitude modulation (BAM) are extracted from IMFs obtained from RR-interval signals. Statistically significant features are fed to least square-support vector machine (LS-SVM) classifier. The three kernels namely, Radial Basis Function (RBF), Morlet wavelet, and Mexican hat wavelet kernels have been studied to obtain the suitable kernel function for the classification of diabetic and normal RR-interval signals. In this work, we have obtained the highest classification accuracy of 95.63%, using Morlet wavelet kernel function with 10-fold cross-validation. The classification system proposed in this work can help the clinicians to diagnose diabetes using electrocardiogram (ECG) signals.

Automated detection of circinate exudates in retina digital images using empirical mode decomposition and the entropy and uniformity of the intrinsic mode functions

Biomedical Engineering / Biomedizinische Technik ◽

10.1515/bmt-2013-0082 ◽

2014 ◽

Vol 59 (4) ◽

Cited By ~ 12

Author(s):

Salim Lahmiri ◽

Mounir Boukadoum

Keyword(s):

Digital Images ◽

Color Image ◽

Detection System ◽

Histogram Equalization ◽

Automated System ◽

Support Vector ◽

Clinical Environment ◽

Mode Decomposition

AbstractThis work presents a new automated system to detect circinate exudates in retina digital images. It operates as follows: the true color image is converted to gray levels, and contrast-limited adaptive histogram equalization (CLAHE) is applied to it before undergoing empirical mode decomposition (EMD) as intrinsic mode functions (IMFs). The entropies and uniformities of the first two IMFs are then computed to form a feature vector that is fed to a support vector machine (SVM) for classification. The experimental results using a set of 45 images (23 normal images and 22 images with circinate exudates taken from the STARE database) and tenfold cross-validation indicate that the proposed approach outperforms previous works found in the literature, with perfect classification. In addition, the image processing time was <4 min, making the presented circinate exudate detection system fit for use in a clinical environment.

NOISE-MODULATED EMPIRICAL MODE DECOMPOSITION

Advances in Adaptive Data Analysis ◽

10.1142/s1793536910000410 ◽

2010 ◽

Vol 02 (01) ◽

pp. 25-37 ◽

Cited By ~ 6

Author(s):

PO-HSIANG TSUI ◽

CHIEN-CHENG CHANG ◽

NORDEN E. HUANG

Keyword(s):

Hilbert Spectrum ◽

Hilbert Huang Transform ◽

The Core ◽

Mode Decomposition ◽

Threshold Amplitude ◽

The Mean ◽

Mixing Problem ◽

Emd Method

The empirical mode decomposition (EMD) is the core of the Hilbert–Huang transform (HHT). In HHT, the EMD is responsible for decomposing a signal into intrinsic mode functions (IMFs) for calculating the instantaneous frequency and eventually the Hilbert spectrum. The EMD method as originally proposed, however, has an annoying mode mixing problem caused by the signal intermittency, making the physical interpretation of each IMF component unclear. To resolve this problem, the ensemble EMD (EEMD) was subsequently developed. Unlike the conventional EMD, the EEMD defines the true IMF components as the mean of an ensemble of trials, each consisting of the signal with added white noise of finite, not infinitesimal, amplitude. In this study, we further proposed an extension and alternative to EEMD designated as the noise-modulated EMD (NEMD). NEMD does not eliminate mode but intensify and amplify mixing by suppressing the small amplitude signal but the larger signals would be preserved without waveform deformation. Thus, NEMD may serve as a new adaptive threshold amplitude filtering. The principle, algorithm, simulations, and applications are presented in this paper. Some limitations and additional considerations of using the NEMD are also discussed.

An Improved Empirical Mode Decomposition Based on Local Integral Mean and Its Application in Signal Processing

Mathematical Problems in Engineering ◽

10.1155/2021/8891217 ◽

2021 ◽

Vol 2021 ◽

pp. 1-30

Author(s):

Xiao-dong Niu ◽

Li-rong Lu ◽

Jian Wang ◽

Xing-cheng Han ◽

Xuan Li ◽

...

Keyword(s):

Real Data ◽

Ensemble Empirical Mode Decomposition ◽

Mean Value ◽

Orthogonal Decomposition ◽

Improved Method ◽

Mode Decomposition ◽

The Mean ◽

Mode Mixing

Empirical mode decomposition (EMD) is an effective method to deal with nonlinear nonstationary data, but the lack of orthogonal decomposition theory and mode-mixing are the main problems that limit the application of EMD. In order to solve these two problems, we propose an improved method of EMD. The most important part of this improved method is to change the mean value by envelopes of signal in EMD to the mean value by the definite integral, which enables the mean value to be mathematically expressed strictly. Firstly, we prove that the signal is orthogonally decomposed by the improved method. Secondly, the Monte Carlo method of white noise is used to explain that the improved method can effectively alleviate mode-mixing. In addition, the improved method is adaptive and does not need any input parameters, and the intrinsic mode functions (IMFs) generated from it is robust to sifting. We have carried out experiments on a series of artificial and real data, the results show that the improved method is the orthogonal decomposition method and can effectively alleviate mode-mixing, and it has better decomposition performance and physical meaning than EMD, ensemble EMD (EEMD), and complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). In addition, the improved method is generally more time-consuming than EMD, but far less than EEMD and CEEMDAN.

A Novel Gaussian Window Approach for Empirical Mode Decomposition

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.457-458.274 ◽

2012 ◽

Vol 457-458 ◽

pp. 274-277

Author(s):

Shuen De Wu ◽

Chiu Wen Wu ◽

Cha Lin Liu ◽

Yan Hao Huang ◽

Kung Yen Lee

Keyword(s):

Numerical Analysis ◽

Averaging Method ◽

Gaussian Window ◽

Mode Decomposition ◽

The Mean ◽

Algorithmic Construction ◽

Window Approach ◽

Mode Mixing

Empirical mode decomposition (EMD) is an algorithmic construction for decomposing multi-component signals into a series of intrinsic mode functions (IMFs). However, traditional EMD may encounter the difficulty of mode mixing when a signal contains intermittency. To solve the difficulty, a Gaussian window averaging method is proposed to construct the mean envelope of a given signal in each sifting process. The numerical analysis also demonstrates promising reliability with the proposed algorithm.