Bivariate Empirical Mode Decomposition

10 pages, 3 figures. Submitted to Signal Processing Letters, IEEE. Matlab/C codes and additional material are downloadable from http://perso.ens-lyon.fr/patrick.flandrinThe Empirical Mode Decomposition (EMD) has been introduced quite recently to adaptively decompose nonstationary and/or nonlinear time series. The method being initially limited to real-valued time series, we propose here an extension to bivariate (or complex-valued) time series which generalizes the rationale underlying the EMD to the bivariate framework. Where the EMD extracts zero-mean oscillating components, the proposed bivariate extension is designed to extract zero-mean rotating components. The method is illustrated on a real-world signal and properties of the output components are discussed. Free Matlab/C codes are available at http://perso.ens-lyon.fr/patrick.flandrin

Univariate and bivariate empirical mode decomposition for postural stability analysis

The aim of this paper was to compare empirical mode decomposition (EMD) and two new extended methods of Open image in new windowEMD named complex empirical mode decomposition (complex-EMD) and bivariate empirical mode decomposition (bivariate-EMD). All methods were used to analyze stabilogram center of pressure (COP) time series. The two new methods are suitable to be applied to complex time series to extract complex intrinsic mode functions (IMFs) before the Hilbert transform is subsequently applied on the IMFs. The trace of the analytic IMF in the complex plane has a circular form, with each IMF having its own rotation frequency. The area of the circle and the average rotation frequency of IMFs represent efficient indicators of the postural stability status of subjects. Experimental results show the effectiveness of these indicators to identify differences in standing posture between groups

ISAR imaging Based on the Empirical Mode Decomposition Time-Frequency Representation

International audienceThis work proposes an adaptation of the Empirical Mode Decomposition Time-Frequency Distribution (EMD-TFD) to non-analytic complex-valued signals. Then, the modified version of EMD-TFD is used in the formation of Inverse Synthetic Aperture Radar (ISAR) image. This new method, referred to as NSBEMD-TFD, is obtained by extending the Non uniformly Sampled Bivariate Empirical Mode Decomposition (NSBEMD) to design a filter in the ambiguity domain and to clean the Time-Frequency Distribution (TFD) of signal. The effectiveness of the proposed scheme of ISAR formation is illustrated on synthetic and real signals. The results of our proposed methods are compared to other Time-Frequency Representation (TFR) such as Spectrogram, Wigner-Ville Distribution (WVD), Smoothed Pseudo Wigner-Ville Distribution (SPWVD) or others methods based on EMD

An Optimization Based Empirical Mode Decomposition Scheme for Images

Bidimensional empirical mode decompositions (BEMD) have been developed to decompose any bivariate function or image additively into multiscale components, so-called intrinsic mode functions (IMFs), which are approximately orthogonal to each other with respect to the $\ell_2$ inner product. In this paper, a novel optimization problem is designed to achieve this decomposition which takes into account important features desired of the BEMD. Specifically, we propose a data-adapted iterative method which we call Opt-BEMD which minimizes in each iteration a smoothness functional subject to inequality constraints involving the strictly local extrema of the image. In this way, the method constructs a sparse data-adapted basis for the input function as well as an envelope in a mathematically stringent sense. Moreover, we propose an ensemble version of Opt-BEMD to strengthen its performance when applied to noise-contaminated images or images with only few extrema

Using EMD-FrFT filtering to mitigate high power interference in chirp tracking radars

This letter presents a new signal processing subsystem for conventional monopulse tracking radars that offers an improved solution to the problem of dealing with manmade high power interference (jamming). It is based on the hybrid use of empirical mode decomposition (EMD) and fractional Fourier transform (FrFT). EMD-FrFT filtering is carried out for complex noisy radar chirp signals to decrease the signal's noisy components. An improvement in the signal-to-noise ratio (SNR) of up to 18 dB for different target SNRs is achieved using the proposed EMD-FrFT algorithm

Enhanced monopulse radar tracking using empirical mode decomposition

Monopulse radar processors are used to track targets that appear in the look direction beamwidth. The target tracking information (range, azimuth angle, and elevation angle) are affected when manmade high power interference (jamming) is introduced to the radar processor through the radar antenna main lobe (main lobe interference) or antenna side lobe (side lobe interference). This interference changes the values of the error voltage which is responsible for directing the radar antenna towards the target. A monopulse radar structure that uses filtering in the empirical mode decomposition (EMD) domain is presented in this paper. EMD is carried out for the complex radar chirp signal with subsequent denoising and thresholding processes used to decrease the noise level in the radar processed data. The performance enhancement of the monopulse radar tracking system with EMD based filtering is included using the standard deviation angle estimation error (STDAE)

Data-driven multivariate and multiscale methods for brain computer interface

This thesis focuses on the development of data-driven multivariate and multiscale methods for brain computer interface (BCI) systems. The electroencephalogram (EEG), the most convenient means to measure neurophysiological activity due to its noninvasive nature, is mainly considered. The nonlinearity and nonstationarity inherent in EEG and its multichannel recording nature require a new set of data-driven multivariate techniques to estimate more accurately features for enhanced BCI operation. Also, a long term goal is to enable an alternative EEG recording strategy for achieving long-term and portable monitoring. Empirical mode decomposition (EMD) and local mean decomposition (LMD), fully data-driven adaptive tools, are considered to decompose the nonlinear and nonstationary EEG signal into a set of components which are highly localised in time and frequency. It is shown that the complex and multivariate extensions of EMD, which can exploit common oscillatory modes within multivariate (multichannel) data, can be used to accurately estimate and compare the amplitude and phase information among multiple sources, a key for the feature extraction of BCI system. A complex extension of local mean decomposition is also introduced and its operation is illustrated on two channel neuronal spike streams. Common spatial pattern (CSP), a standard feature extraction technique for BCI application, is also extended to complex domain using the augmented complex statistics. Depending on the circularity/noncircularity of a complex signal, one of the complex CSP algorithms can be chosen to produce the best classification performance between two different EEG classes. Using these complex and multivariate algorithms, two cognitive brain studies are investigated for more natural and intuitive design of advanced BCI systems. Firstly, a Yarbus-style auditory selective attention experiment is introduced to measure the user attention to a sound source among a mixture of sound stimuli, which is aimed at improving the usefulness of hearing instruments such as hearing aid. Secondly, emotion experiments elicited by taste and taste recall are examined to determine the pleasure and displeasure of a food for the implementation of affective computing. The separation between two emotional responses is examined using real and complex-valued common spatial pattern methods. Finally, we introduce a novel approach to brain monitoring based on EEG recordings from within the ear canal, embedded on a custom made hearing aid earplug. The new platform promises the possibility of both short- and long-term continuous use for standard brain monitoring and interfacing applications

FPGA based real-time implementation of Bivariate Empirical Mode Decomposition

A field programmable gate array (FPGA)-based parallel architecture for the real-time and online implementation of the bivariate extension of the empirical mode decomposition (EMD) algorithm is presented. Multivariate extensions of EMD have attracted significant attention in recent years owing to their scope in applications involving multichannel and multidimensional data processing, e.g. biomedical engineering, condition monitoring, image fusion. However, these algorithms are computationally expensive due to the empirical and data-driven nature of these methods. That has hindered the utilisation of EMD, and particularly its bivariate and multivariate extensions, in real-time applications. The proposed parallel architecture is aimed at bridging this gap through real-time computation of the bivariate EMD algorithm. The crux of the architecture is the simultaneous computation of multiple signal projections, locating their local extrema and finally the calculation of their associated complex-valued envelopes for the estimation of local mean. The architecture is implemented on a Xilinx Kintex 7 FPGA and offers significant computational improvements over the existing software-based sequential implementations of bivariate EMD