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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.

Diop E.H.S.,ENSTA Bretagne | Alexandre R.,IRENav | Boudraa A.O.,ENSTA Bretagne
IEEE Signal Processing Letters | Year: 2010

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. © 2006 IEEE.

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.

Bouchikhi A.,IRENav | Bouchikhi A.,CNRS Communication and Information Sciences Laboratories | Boudraa A.-O.,IRENav
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.

Khaled R.,French Research Institute for Exploitation of the Sea | Priour D.,French Research Institute for Exploitation of the Sea | Billard J.-Y.,IRENAV
Ocean Engineering | Year: 2013

A numerical method for optimization of the cable lengths in trawls with respect to the ratio between the estimated trawl drag and the predicted catch efficiency is developed and applied. The trawl cables of interest are warps, bridles, headline and footrope. The optimization algorithm applies an ordered sequential process changing one cable length at the time. It is assumed in the predictions that the catch efficiency of the trawl is proportional with the trawl mouth area. In a case study optimizing a bottom trawl used on a research vessel by applying the new method it is predicted that it would be possible to reduce the ratio between trawl drag and catch efficiency by up to 46% by optimizing the cable lengths. Thus this would enable a considerable reduction in fuel consumption to catch a specific amount offish. Moreover, we predict an increase in the value of the trawl mouth area leading to better catching efficiency without increase in otter door drag. © 2012 Elsevier Ltd. All rights reserved.

Delacroix S.,French Research Institute for Exploitation of the Sea | Germain G.,French Research Institute for Exploitation of the Sea | Gaurier B.,French Research Institute for Exploitation of the Sea | Billard J.-Y.,IRENAV
Ocean Engineering | Year: 2016

Bubble sweep-down is a significant issue for the oceanographic vessels, which affect the acoustic surveys. Experimental trials, carried out in the Ifremer wave and current circulating tank on a 1/30 model of the Pourquoi pas?, are presented. The results demonstrate that this kind of experimental facility is well suited to study the phenomenon of bubble sweep-down encountered around the bow of a ship under specific conditions. From these results, two kinds of bubble clouds formation have been observed and analysed: bubble clouds generated by vortex shedding and breaking waves. The vortex shedding bubble clouds appear randomly in all the configurations tested, even without waves or motions. This phenomenon is due to the interaction between the turbulent flow and the specific bow shape of the Pourquoi pas?. On the other hand, the breaking wave clouds appear in the presence of relative motions between the free surface and the bow ship and more significantly under wave sollicitations. A complementary paper presents a parametric study carried out to quantify the influence of the test conditions. © 2016 Elsevier Ltd.

Khaled R.,French Research Institute for Exploitation of the Sea | Priour D.,French Research Institute for Exploitation of the Sea | Billard J.-Y.,IRENAV
Ocean Engineering | Year: 2012

This study reports on energy efficiency optimization regarding bottom trawls. Efficient fishing gear uses up only a small amount of energy per fish caught. Drag and mouth area during trawling operations affect energy efficiency. Drag causes the energy consumption and the trawl mouth area impacts the quantity of fish caught, hence an energy efficient gear has a low ratio drag on the mouth area. A novel numerical optimization technique using spatial fish distribution is presented in this work. The tool is based on a FEM mechanical model for trawls which consist mostly of netting panels sewn together. This tool is adapted to minimize an objective function namely the drag-to-mouth area ratio. This technique consists in modifying the design of all the panels of the trawl. In this paper the modifications are constant and quantified in terms of mesh number. Moreover the trawl mouth area takes into account the presence of fish within a given depth with respect to sea bottom and the value of the depth is adapted to the fish species of interest. Trawl design optimization with two uniform fish distributions at a given depth (6 m and 3 m above the sea bed) and one linear distribution at 6 m above the sea bed are compared. The application of this tool when designing a bottom trawl for research vessels leads to an energy economy ranging from 16% to 52% under certain assumptions. © 2012 Elsevier Ltd.

Delacroix S.,French Research Institute for Exploitation of the Sea | Germain G.,French Research Institute for Exploitation of the Sea | Berger L.,French Research Institute for Exploitation of the Sea | Billard J.-Y.,IRENAV
Ocean Engineering | Year: 2016

Bubble sweep-down on oceanographic vessels generates acoustic perturbations. We propose in this work to characterize the sub-surface bubbles occurrence conditions from acoustic data analysis acquired during surveys in relatively shallow water with the IFREMER research vessels Thalassa and Pourquoi Pas?. The methodology of data analysis used in this work allows us to characterize the sailing conditions influence on bubble sweep-down occurrence. The correlation between sailing conditions and acoustic perturbations tends to demonstrate that the presence of bubbles under the hull is clearly related to the wind speed and natural aeration, and that surface bubbles are advected differently in the water column by the two vessels. © 2015 Elsevier Ltd.

Boudraa A.-Q.,IRENav
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 | Dare D.,IRENav
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.

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