Signal and Acosutics

In this paper, a signal-filtering method based on empirical mode decomposition is proposed. The filtering method is a fully data-driven approach. A noisy signal is adaptively decomposed into intrinsic oscillatory components called intrinsic mode functions (IMFs) by means of an algorithm referred to as a sifting process. The basic principle of the method is to make use of partial reconstructions of the signal, with the relevant IMFs corresponding to the most important structures of the signal (low-frequency components). A criterion is proposed to determine the IMF, after which, the energy distribution of the important structures of the signal overcomes that of the noise and that of the high-frequency components of the signal. The method is illustrated on simulated and real data, and the results are compared to well-known filtering methods. The study is limited to signals that were corrupted by additive white Gaussian noise and is conducted on the basis of extended numerical experiments.

The aim of this work is the characterization of seafloor using a bathymetric image segmentation approach. Bathymetric image can be viewed as a set of bathymetric profiles. Seafloor is a superposition of fast oscillations superimposed to slow oscillations and their separation is an important step in geophysical and geological exploration. To separate these oscillations a multiresolution approach based on a recent technique referred to as Empirical mode decomposition (EMD) [1] is proposed. This method considers profiles, generated by Multibeam echosounder (ME), at the scale of their local oscillations. Each profile is decomposed into oscillations called Intrinsic mode functions (IMFs). The EMD is applied separately to each profile and Empirical images (EIs) are constructed IMF-per-IMF. For each EI instantaneous frequency and instantaneous amplitude are estimated using a demodulation algorithm [2]. The method is tested on real sonar images.

In this paper a new similarity measure, noted SimilB, for dynamic analysis of a sequence of scintigraphic cardiac images taken throughout the cardiac cycle is presented. This measure is based on the cross-Ψ B-energy operator [1] a nonlinear similarity function which measures the interaction between two time-signals including their first and the second derivatives. Similarity measure, using SimilB, between the Time activity curve (TAC) of each pixel and the mean value of the TACs of a reference region of the scintigraphic image series is calculated. The resulting SimilB map is a functional image representing regions with different temporal dynamics. This analysis allows visualization of the ventricular emptying pattern, which may be useful in studying motion or conduction abnormalities. The proposed method is tested in a normal patient and in two patients with abnormal ventricular contraction patterns.

Sous certaines hypothèses la méthode MUSIC (MUltiple SIgnal Classifcation) donne des résultats de localisation de sources acoustiques satisfaisants. Parmi les hypohèses fortes utilisées dans les developpements de MUSIC il y a la planéité du front d'onde et l'antenne rectiligne ce qui ne sont pas toujours vérifiées. En effet, la non distorsion des fronts d'onde est difficile à garantir du fait que les capteurs se déplacent par rapport à leurs positions d'origine durant l'expérimentation (cas d'antenne souple). La distorsion est due aussi à la non homogènéité du milieu de propagation. La correction des erreurs de phases introduites par la distorsion des fronts d'onde est nécessaire pour pouvoir améliorer le pouvoir séparateur des méthodes de localisation de sources acoustiques. Le but de ce travail est d'estimer à la fois les directions d'arrivée et les erreurs de phase. L'estimation des déphasages est étudiée en utilisant la propriété d'orthogonalité entre les sous espaces signal et bruit. Cette estimation est vue comme un problème de minimisation d'une fonctionnelle, qui en pratique, est Lipschitzienne. Pour ce faire l'algorithme DIRECT (DIviding RECTangles) est utilisé pour la recherche du minimum global de cette fonctionnelle. La méthode proposée est testée sur des données simulées.

Dans cet article, un schémas multirésolution perceptuel basé sur le système visuel humain est proposé. L'idée principale est la détection des structures les plus pertinentes de l'imageà chaqueéchelle de la pyramide Gaussienne en utilisant comme critère le seuil de détection en contraste, JNC (pour Just noticeable contrast) et la notion d'adaptation de luminance. Nous appliquons le filtrage perceptuelà des images de niveaux de gris.

We describe a new segmentation method of dynamic nuclear medicine images based on the cross-« B-energy operator. « B is a nonlinear measure which quantifies the interaction between two time-signals including their first and second derivatives. Similarity measure, noted SimilB, between the time activity curve (TAC) of each pixel and the mean value of the TACs of a reference region of the scintigraphic image series is calculated. The resulting SimilB map is a functional image representing regions with different temporal dynamics. Some new properties of « B are presented. Particularly, we show that « B as a similarity measure is robust to both scale and time shift. The proposed method is applied to nuclear cardiac sequences for visualization and analysis of the ventricular emptying pattern, which may be useful in studying motion or conduction abnormalities. Results of a normal subject and four patients with abnormal ventricular contraction patterns are presented to highlight the suitability of this operator for studying non-stationary TAC series.

In white-light interference microscopy, measurement of surface shape generally requires peak extraction of the fringe function envelope. In this paper the Teager-Kaiser energy and higher-order energy operators are proposed for efficient extraction of the fringe envelope. These energy operators are compared in terms of precision, robustness to noise, and subsampling. Flexible energy operators, depending on order and lag parameters, can be obtained. Results show that smoothing and interpolation of envelope approximation using spline model performs better than Gaussian-based approach.

A new similarity measure, called SimilB, for time series analysis, based on the cross-Ψ B-energy operator (2004), is introduced. Ψ B is a nonlinear measure which quantifies the interaction between two time series. Compared to Euclidean distance (ED) or the Pearson correlation coefficient (CC), SimilB includes the temporal information and relative changes of the time series using the first and second derivatives of the time series. SimilB is well suited for both nonstationary and stationary time series and particularly those presenting discontinuities. Some new properties of Ψ B are presented. Particularly, we show that Ψ B as similarity measure is robust to both scale and time shift. SimilB is illustrated with synthetic time series and an artificial dataset and compared to the CC and the ED measures.

ΨB operator is an energy operator that measures the interactions between two complex signals. In this letter, new properties of ΨB operator are presented. Connections between ΨB operator and some time-frequency representations (crossambiguity function, short-time Fourier transform, Zak transform, and Gabor coefficients) are established. Link between ΨB operator of two input signals and their cross-spectrum is also derived. For two equal input signals, we find that Fourier transform of ΨB operator is proportional to the second derivative of the ambiguity function. The established links show the ability of ΨB operator to analyze non stationary signals. A numerical example is provided for illustrating how to estimate the second order moment, of a FM signal, using ΨB operator. We compare the result to the moment given by the Wigner Ville distribution.

In this paper a speech denoising strategy based on time adaptive thresholding of intrinsic modes functions (IMFs) of the signal, extracted by empirical mode decomposition (EMD), is introduced. The denoised signal is reconstructed by the superposition of its adaptive thresholded IMFs. Adaptive thresholds are estimated using the Teager-Kaiser energy operator (TKEO) of signal IMFs. More precisely, TKEO identifies the type of frame by expanding differences between speech and non-speech frames in each IMF. Based on the EMD, the proposed speech denoising scheme is a fully data-driven approach. The method is tested on speech signals with different noise levels and the results are compared to EMD-shrinkage and wavelet transform (WT) coupled with TKEO. Speech enhancement performance is evaluated using output signal to noise ratio (SNR) and perceptual evaluation of speech quality (PESQ) measure. Based on the analyzed speech signals, the proposed enhancement scheme performs better than WT-TKEO and EMD-shrinkage approaches in terms of output SNR and PESQ. The noise is greatly reduced using time-adaptive thresholding than universal thresholding. The study is limited to signals corrupted by additive white Gaussian noise.

In this paper, two methods for signal detection and time-delay estimation based on the cross ⌿ B-energy operator are proposed. These methods are well suited for mono-component AM-FM signals. The ⌿ B energy operator measures how much one signal is present in another one. The peak of the ⌿ B operator corresponds to the maximum of interaction between the two signals. Compared to the cross-correlation function, the ⌿ 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 ⌿ 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.

This letter presents an improvement of the image source method (ISM) for geoacoustic inversion. The new algorithm is based on the Teager-Kaiser Energy Operator which amplifies the discontinuities in signals while the soft transitions are reduced. This property is exploited for accurate detection of time arrivals and thus for location of the image sources. The effectiveness of the method is shown on both synthetic and real data and the inversion results are, overall, in good agreement with ground truth and other inversion results with a significant reduction of computation time.

Block truncation coding (BTC) is a well known lossy compression scheme. Due to its low complexity and easy implementation, BTC has gained wide interest in its further development and application for image compression. Based on simple thresholding, BTC retains sharp edges and thus leads to artifacts such as the staircase effect. The second problem encountered in BTC is the splitting of homogeneous regions, which produces false contours. In this work a fuzzy approach of BTC to avoid truncating homogeneous blocks and to preserve smooth edges in two-cluster blocks is proposed. Each image block, viewed as a fuzzy set, is segmented into two clusters using a fuzzy clustering algorithm. The block is then encoded by modified fuzzy weighted means of the two clusters. Initialization strategies of the fuzzy clustering algorithm and a contextual quantization method are proposed. Experimental results show an improvement of visual quality of reconstructed images and peak signal-to-noise ratio when compared to BTC, economical BTC (EBTC), absolute moment BTC (AMBTC), and a minimum mean square error quantizer (MMSEQ). Computation time required by AMBTC, EBTC, and fuzzy BTC methods are reported.

An extension of the 2-D discrete Teager-Kaiser energy operator and the 1-D higher-order energy operators to the 2-D continuous case is proposed. These 2-D continuous operators are flexible enough to apply a large class of image gradient filters, and consequently different discrete energy operators are derived. Particularly, the proposed model takes into account the diagonal directions, through the partial derivatives. The obtained operators are computationally very simple, like the classical 2D Teager-Kaiser operator, and are well suited for imageprocessing applications such as image demodulation or image contrast enhancement. Results of demodulation of synthetic and real images, to estimate envelope information, are presented to show the feasibility of the proposed operators.

In this paper we consider the hermitian extension of the cross-Ψ B-energy operator that we will denote by Ψ H. In addition, cross energy terms are formalized through multivariate signals representation. We investigate the connection between the interaction energy function of Ψ H and the cross-power spectral density (CPSD) of two complex valued signals. In particular, this link permits to use this operator for estimating the CPSD. We illustrate the interest of Ψ H as a similarity between a pair of signals in frequency domain on synthetic and real data.

This paper introduces a new multi-dimensional higher order operator derived from the Teager-Kaiser energy-tracking function. A mathematical model which integrates different existing non-linear operators at any orders is constructed. The proposed non-linear continuous filter is computed using tensors provided by the Kronecker products of higher order derivatives of the signal. In particular, the introduced operator takes into account the diagonal directions through the partial derivatives. We prove that there is a recurrence relationship that allows us to deduce all functions at different orders. To show the effectiveness of the proposed operator, demodulation of noisy multi-dimensional amplitude-modulation (AM)-frequency-modulation (FM) signals are presented and results compared to those of some well-known demodulation approaches.

For the first time, a proof of the sifting process (SP) and so the empirical mode decomposition (EMD), is given. For doing this, lower and upper envelopes are modeled in a more convenient way that helps us prove the convergence of the SP towards a solution of a partial differential equation (PDE). We also prove that such a PDE has a unique solution, which ensures the uniqueness of the EMD decomposition. The new formulation of envelopes has another benefit. In fact, it removes interpolation problems and related issues. Not only helps the modelization of envelopes to give a mathematical framework on the EMD, but also, as confirmed by the numerical simulations, the PDE-based EMD improves a lot the classical EMD.

In this paper a new audio coding scheme combining the Hilbert transform and the Empirical Mode Decomposition (EMD) is introduced. Based on the EMD, the coding is fully data-driven approach. Audio signal is first decomposed adaptively, by EMD, into intrinsic oscillatory components called Intrinsic Mode Functions (IMFs). The key idea of this work is to code both instantaneous amplitude (IA) and instantaneous frequency (IF), of the extracted IMFs, calculated using Hilbert transform. Since IA (resp. IF) is strongly correlated, it is encoded via a linear prediction technique. The decoder recovers the original signal by superposition of the demodulated IMFs. The proposed approach is applied to audio signals, and the results are compared to those obtained by AAC (Advanced Audio Coding) and MP3 codecs, and wavelets based compression. Coding performances are evaluated using the bit rate, Objective Difference Grade (ODG) and Noise to Mask Ratio (NMR) measures. Based on the analyzed audio signals, overall, our coding scheme performs better than wavelet compression, AAC and MP3 codecs. Results also show that this new scheme has good coding performances without significant perceptual distortion, resulting in an ODG in range [-1,0] and large negative NMR values.

In this paper, the Cross-Teager-Kaiser Energy Operator (CTKEO) used for interaction measure between two signals is generalized for complex-valued patterns and images. This new operator called 2D-CTKEO and noted Ψ 2B [., .] is useful for some image processing problems. Some properties of 2D-CTKEO showing the interest of such operator for image analysis are provided. Based on Ψ 2B [., .] operator, two similarity functions, called Simil 1 2B and Simil 2 2B , are constructed. The effectiveness of Ψ 2B [., .] operator is demonstrated on noise-free and noisy images. These results show that Ψ 2B [., .] is useful for detection of interest points such as corners and edges and for template matching.

In this paper a noise filtering method using the Empirical Mode Decomposition (EMD) is proposed. The noisy signal is decomposed into oscillatory components called Intrinsic Mode Functions (IMFs) using a process referred to as sifting. The basic idea of the proposed scheme is the partial reconstruction of the signal using the IMFs corresponding to the most important structures of the signal (low frequency modes). A new criterion is proposed to determine the IMF after which the energy distribution of the important structures of the signal overcomes that of the noise and that of the high frequency components of the signal. The method is tested on simulated and real signals.