Abdel-Ouahab Boudraa

EMD-Based Filtering Using Similarity Measure Between Probability Density Functions of IMFs

This paper introduces a new signal-filtering, which combines the empirical mode decomposition (EMD) and a similarity measure. A noisy signal is adaptively broken down into oscillatory components called intrinsic mode functions by EMD followed by an estimation of the probability density function (pdf) of each extracted mode. The key idea of this paper is to make use of partial reconstruction, the relevant modes being selected on the basis of a striking similarity between the pdf of the input signal and that of each mode. Different similarity measures are investigated and compared. The obtained results, on simulated and real signals, show the effectiveness of the pdf-based filtering strategy for removing both white Gaussian and colored noises and demonstrate its superior performance over partial reconstruction approaches reported in the literature.

Audio Watermarking Via EMD

In this paper a new adaptive audio watermarking algorithm based on Empirical Mode Decomposition (EMD) is introduced. The audio signal is divided into frames and each one is decomposed adaptively, by EMD, into intrinsic oscillatory components called Intrinsic Mode Functions (IMFs). The watermark and the synchronization codes are embedded into the extrema of the last IMF, a low frequency mode stable under different attacks and preserving audio perceptual quality of the host signal. The data embedding rate of the proposed algorithm is 46.9-50.3 b/s. Relying on exhaustive simulations, we show the robustness of the hidden watermark for additive noise, MP3 compression, re-quantization, filtering, cropping and resampling. The comparison analysis shows that our method has better performance than watermarking schemes reported recently.

IF estimation using empirical mode decomposition and nonlinear Teager energy operator

In this paper, a method based on the empirical mode decomposition (EMD) algorithm and Teager energy operator (TEO) is proposed to estimate the instantaneous frequency (IF) of a signal embedded in noise. IF is used to describe a signals frequency that varies with time. Both EMD and TEO deal with non-stationary signals. The signal is first band pass filtered into subsignals (components) called intrinsic mode functions (IMFs) with well defined IF. Each IMF is a zero-mean AM-FM component. Then TEO tracks the modulation energy of each IMF and estimates the corresponding IF. In order to show the effectiveness of the proposed method, results of IF estimation of noisy AM-FM signals are proposed.

Analysis of Intrinsic Mode Functions: A PDE Approach

The empirical mode decomposition is a powerful tool for signal processing. Because of its original algorithmic, recent works have contributed to its theoretical framework. Following these works, some mathematical contributions on its comprehension and formalism are provided. In this paper, the so called local mean is computed in such a way that it allows the use of differential calculus on envelopes. This new formulation makes us prove that iterations of the sifting process are well approximated by the resolution of partial differential equations (PDE). Intrinsic mode functions are originally defined in a intuitive way. Herein, a mathematical characterization of modes is given with the proposed PDE-based approach.

Unsupervised multisensor data fusion approach

A new iterative approach of multisensor data fusion based on the Dempster-Shafer (1976) formalism is presented. Mass functions, formalized by a Gaussian model, are estimated at each iteration using the output fused image and the source images. The effectiveness of the method is demonstrated on synthetic images.

Multicomponent AM-FM signals analysis based on EMD-B-splines ESA

In this paper a signal analysis framework for estimating time-varying amplitude and frequency functions of multicomponent amplitude and frequency modulated (AM-FM) signals is introduced. This framework is based on local and non-linear approaches, namely Energy Separation Algorithm (ESA) and Empirical Mode Decomposition (EMD). Conjunction of Discrete ESA (DESA) and EMD is called EMD-DESA. A new modified version of EMD where smoothing instead of an interpolation to construct the upper and lower envelopes of the signal is introduced. Since extracted IMFs are represented in terms of B-spline (BS) expansions, a closed formula of ESA robust against noise is used. Instantaneous Frequency (IF) and Instantaneous Amplitude (IA) estimates of a multicomponent AM-FM signal, corrupted with additive white Gaussian noise of varying SNRs, are analyzed and results compared to ESA, DESA and Hilbert transform-based algorithms. SNR and MSE are used as figures of merit. Regularized BS version of EMD-ESA performs reasonably better in separating IA and IF components compared to the other methods from low to high SNR. Overall, obtained results illustrate the effectiveness of the proposed approach in terms of accuracy and robustness against noise to track IF and IA features of a multicomponent AM-FM signal.

Analysis of multicomponent LFM signals by Teager Huang-Hough transform

A novel detection approach of linear FM (LFM) signals, with single or multiple components, in the time-frequency plane of Teager-Huang (TH) transform is presented. The detection scheme that combines TH transform and Hough transform is referred to as Teager-Huang-Hough (THH) transform. The input signal is mapped into the time-frequency plane by using TH transform followed by the application of Hough transform to recognize time-frequency components. LFM components are detected and their parameters are estimated from peaks and their locations in the Hough space. Advantages of THH transform over Hough transform of Wigner-Ville distribution (WVD) are: 1) cross-terms free detection and estimation, and 2) good time and frequency resolutions. No assumptions are made about the number of components of the LFM signals and their models. THH transform is illustrated on multicomponent LFM signals in free and noisy environments and the results compared with WVD-Hough and pseudo-WVD-Hough transforms.

Cross ΨB-energy operator-based signal detectiona)

In this paper, two methods for signal detection and time-delay estimation based on the cross Psi(B)-energy operator are proposed. These methods are well suited for mono-component AM-FM signals. The Psi(B) energy operator measures how much one signal is present in another one. The peak of the Psi(B) operator corresponds to the maximum of interaction between the two signals. Compared to the cross-correlation function, the Psi(B) operator includes temporal information and relative changes of the signal which are reflected in its first and second derivatives. The discrete version of the continuous-time form of the Psi(B) operator, which is used in its implementation, is presented. The methods are illustrated on synthetic and real signals and the results compared to those of the matched filter and the cross correlation. The real signals correspond to impulse responses of buried objects obtained by active sonar in iso-speed single path environments.

A new EMD denoising approach dedicated to voiced speech signals

This paper introduces a new voiced speech denoising approach based on the empirical mode decomposition (EMD) associated to an appropriate sifting process. Noisy signal is decomposed adaptively into intrinsic oscillatory components called (IMFs). Since, the energy of a voiced speech signal is distributed over low and medium frequencies, the obtained lower order IMFs (high frequency components) are expected to be highly contaminated by noise. However, the last IMFs (low and medium frequency components) corresponding to the most structures of the signal, contain very low noise levels. Therefore the filtering of the low order IMFs may introduce a signal distortion rather than reducing noise. The principle of the proposed method is then based on filtering only the first IMFs considered very noisy by the adaptive center weighted average (ACWA) filter. A criterion based on the IMFss energies is used to select the very noisy IMFs that must be filtered. The denoising proposed method is applied successfully to voiced speech signal corrupted with additive white Gaussian noise. The reported results obtained for different noise levels, demonstrate the efficiency of the proposed method for reducing noise and its superiority over other denoising methods considered for comparison.

Iterative estimation of Dempster-Shafer’s basic probability assignment: application to multisensor image segmentation

Basic probability assignment (BPA) definition remains a difficult problem to apply Desmpter-Shafer evidence theory to practical applications such as in image processing. A new iterative approach of multisensor data fusion based on the Dempster-Shafer framework is proposed. BPAs, modeled by a Gaussian distribution, are estimated iteratively and in an unsupervised way using the fused image and the source images. Data fusion is performed at the pixel level. Results on synthetic and real images are presented to illustrate the effectiveness of the proposed fusion scheme. Limitations of the method are discussed.