18,672 research outputs found
Noise Corruption of Empirical Mode Decomposition and Its Effect on Instantaneous Frequency
Huang's Empirical Mode Decomposition (EMD) is an algorithm for analyzing
nonstationary data that provides a localized time-frequency representation by
decomposing the data into adaptively defined modes. EMD can be used to estimate
a signal's instantaneous frequency (IF) but suffers from poor performance in
the presence of noise. To produce a meaningful IF, each mode of the
decomposition must be nearly monochromatic, a condition that is not guaranteed
by the algorithm and fails to be met when the signal is corrupted by noise. In
this work, the extraction of modes containing both signal and noise is
identified as the cause of poor IF estimation. The specific mechanism by which
such "transition" modes are extracted is detailed and builds on the observation
of Flandrin and Goncalves that EMD acts in a filter bank manner when analyzing
pure noise. The mechanism is shown to be dependent on spectral leak between
modes and the phase of the underlying signal. These ideas are developed through
the use of simple signals and are tested on a synthetic seismic waveform.Comment: 28 pages, 19 figures. High quality color figures available on Daniel
Kaslovsky's website: http://amath.colorado.edu/student/kaslovsk
Ensemble Empirical Mode Decomposition: Image Data Analysis with White-noise Reflection
During the last decade, Zhaohua Wu and Norden E. Huang announced a new improvement of the original Empirical Mode Decomposition method (EMD). Ensemble Empirical Mode Decomposition and its abbreviation EEMD represents a major improvement with great versatility and robustness in noisy data filtering. EEMD consists of sifting and making an ensemble of a white noise-added signal, and treats the mean value as the final true result. This is due to the use of a finite, not infinitesimal, amplitude of white noise which forces the ensemble to exhaust all possible solutions in the sifting process. These steps collate signals of different scale in a proper intrinsic mode function (IMF) dictated by the dyadic filter bank. As EEMD is a time–space analysis method, the added white noise is averaged out with a sufficient number of trials. Here, the only persistent part that survives the averaging process is the signal component (original data), which is then treated as the true and more physically meaningful answer. The main purpose of adding white noise was to provide a uniform reference frame in the time–frequency space. The added noise collates the portion of the signal of comparable scale in a single IMF. Image data taken as time series is a non-stationary and nonlinear process to which the new proposed EEMD method can be fitted out. This paper reviews the new approach of using EEMD and demonstrates its use on the example of image data analysis, making use of some advantages of the statistical characteristics of white noise. This approach helps to deal with omnipresent noise
Empirical mode decomposition-based facial pose estimation inside video sequences
We describe a new pose-estimation algorithm via integration of the strength in both empirical mode decomposition (EMD) and mutual information. While mutual information is exploited to measure the similarity between facial images to estimate poses, EMD is exploited to decompose input facial images into a number of intrinsic mode function (IMF) components, which redistribute the effect of noise, expression changes, and illumination variations as such that, when the input facial image is described by the selected IMF components, all the negative effects can be minimized. Extensive experiments were carried out in comparisons to existing representative techniques, and the results show that the proposed algorithm achieves better pose-estimation performances with robustness to noise corruption, illumination variation, and facial expressions
Data-driven time-frequency analysis of multivariate data
Empirical Mode Decomposition (EMD) is a data-driven method for the decomposition
and time-frequency analysis of real world nonstationary signals. Its main advantages over
other time-frequency methods are its locality, data-driven nature, multiresolution-based
decomposition, higher time-frequency resolution and its ability to capture oscillation of
any type (nonharmonic signals). These properties have made EMD a viable tool for real
world nonstationary data analysis.
Recent advances in sensor and data acquisition technologies have brought to light
new classes of signals containing typically several data channels. Currently, such signals are almost invariably processed channel-wise, which is suboptimal. It is, therefore,
imperative to design multivariate extensions of the existing nonlinear and nonstationary
analysis algorithms as they are expected to give more insight into the dynamics and the
interdependence between multiple channels of such signals.
To this end, this thesis presents multivariate extensions of the empirical mode de-
composition algorithm and illustrates their advantages with regards to multivariate non-
stationary data analysis. Some important properties of such extensions are also explored,
including their ability to exhibit wavelet-like dyadic filter bank structures for white Gaussian noise (WGN), and their capacity to align similar oscillatory modes from multiple
data channels. Owing to the generality of the proposed methods, an improved multi-
variate EMD-based algorithm is introduced which solves some inherent problems in the
original EMD algorithm. Finally, to demonstrate the potential of the proposed methods,
simulations on the fusion of multiple real world signals (wind, images and inertial body
motion data) support the analysis
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