Diop E.H.S.,Telecom Bretagne |
Diop E.H.S.,MINES ParisTech |
Alexandre R.,IRENav |
Alexandre R.,Shanghai University |
Moisan L.,University of Paris Descartes
Computer Vision and Image Understanding | Year: 2012
Many works have been achieved for analyzing images with a multiscale approach. In this paper, an intrinsic and nonlinear multiscale image decomposition is proposed, based on partial differential equations (PDEs) and the image frequency contents. Our model is inspired from the 2D empirical mode decomposition (EMD) for which a theoretical study is quite nonexistent, mainly because the algorithm is based on heuristic and ad hoc elements making its mathematical study hard. This work has three main advantages. Firstly, we prove that the 2D sifting process iterations are consistent with the resolution of a nonlinear PDE, by considering continuous morphological operators to build local upper and lower envelopes of the image extrema. In addition to the fact that now differential calculus can be performed on envelopes, the introduction of such morphological filters eliminates the interpolation dependency that also terribly suffers the method. Also, contrary to former 2D empirical modes, precise mathematical definition for a class of functions are now introduced thanks to the nonlinear PDE derived from the consistency result, and their characterization on the basis of Meyer spaces. Secondly, an intrinsic multiscale image decomposition is introduced based on the image frequency contents; the proposed approach almost captures the essence and philosophy of the 2D EMD and is linked to the well known Absolutely Minimizing Lipschitz Extension model. Lastly, the proposed multiscale decomposition allows a reconstruction of images. The filterbank capability of the new multiscale decomposition algorithm is shown both on synthetic and real images, and results show that our proposed approach improves a lot on the 2D EMD. Moreover, the complexity of the proposed multiscale decomposition is very reduced compared to the 2D EMD by avoiding the surface interpolation approach, which is the core of all 2D EMD algorithms and is very time consuming. For that purpose also, our work will then be a great benefit; especially, in higher dimension spaces. © 2011 Elsevier Inc. All rights reserved.
IEEE Signal Processing Letters | Year: 2010
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 (cross-ambiguity 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 nonstationary 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. © 2010 IEEE.
Komaty A.,IRENav |
Boudraa A.O.,IRENav |
Nolan J.P.,American University of Washington |
IEEE Signal Processing Letters | Year: 2014
Empirical Mode Decomposition (EMD) and its extended versions such as Multivariate EMD (MEMD) are data-driven techniques that represent nonlinear and non-stationary data as a sum of a finite zero-mean AM-FM components referred to as Intrinsic Mode Functions (IMFs). The aim of this work is to analyze the behavior of EMD and MEMD in stochastic situations involving non-Gaussian noise, more precisely, we examine the case of Symmetric α-Stable S α S noise. We report numerical experiments supporting the claim that both EMD and MEMD act, essentially, as filter banks on each channel of the input signal in the case of S α S noise. Reported results show that, unlike EMD, MEMD has the ability to align common frequency modes across multiple channels in same index IMFs. Further, simulations show that, contrary to EMD, for MEMD the stability property is well satisfied for the modes of lower indices and this result is exploited for the estimation of the stability index of the α S input signal. © 2014 IEEE.
Bouchikhi A.,IRENav |
Bouchikhi A.,CNRS Communication and Information Sciences Laboratories |
Signal Processing | Year: 2012
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. © 2012 Elsevier B.V. All rights reserved.
Boudraa A.-O.,IRENav |
Chonavel T.,Telecom Bretagne |
Cexus J.-C.,ENSTA Bretagne
Signal Processing | Year: 2014
In this paper we consider the hermitian extension of the cross- ΨB-energy operator that we will denote by ΨH. In addition, cross energy terms are formalized through multivariate signals representation. We investigate the connection between the interaction energy function of ΨH 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 ΨH as a similarity between a pair of signals in frequency domain on synthetic and real data. © 2013 Elsevier B.V.