Sylvain Meignen

A fast algorithm for bidimensional EMD

In this letter, we describe a new method for bidimensional empirical mode decomposition (EMD). This decomposition is based on Delaunay triangulation and on piecewise cubic polynomial interpolation. Particular attention is devoted to boundary conditions that are crucial for the feasibility of the bidimensional EMD. The study of the behavior of the decomposition on a different kind of image shows its efficiency in terms of computational cost, and the decomposition of Gaussian white noises leads to bidimensional selective filter banks.

Time-Frequency Reassignment and Synchrosqueezing: An Overview

This article provides a general overview of time-frequency (T-F) reassignment and synchrosqueezing techniques applied to multicomponent signals, covering the theoretical background and applications. We explain how synchrosqueezing can be viewed as a special case of reassignment enabling mode reconstruction and place emphasis on the interest of using such T-F distributions throughout with illustrative examples.

A New Algorithm for Multicomponent Signals Analysis Based on SynchroSqueezing: With an Application to Signal Sampling and Denoising

In this paper, we address the problem of the retrieval of the components from a multicomponent signal using ideas from the synchrosqueezing framework. The emphasis is on the wavelet choice and we propose a novel algorithm based first on the detection of components followed by their reconstruction. Simulations illustrate how the proposed procedure compares with the empirical mode decomposition and other related methods in terms of mode-mixing. We conclude the paper by studying the sensitivity of the proposed technique to sampling and an application to signal denoising.

A New Formulation for Empirical Mode Decomposition Based on Constrained Optimization

The empirical mode decomposition (EMD) is an algorithmic construction that aims at decomposing a signal into several modes called intrinsic mode functions. In this letter, we present a new approach for the EMD based on the direct construction of the mean envelope of the signal. The definition of the mean envelope is achieved through the resolution of a quadratic programming problem with equality and inequality constraints. Some numerical experiments conclude this letter, and comparisons are carried out with the classical EMD.

Second-Order Synchrosqueezing Transform or Invertible Reassignment? Towards Ideal Time-Frequency Representations

This paper considers the analysis of multicomponent signals, defined as superpositions of real or complex modulated waves. It introduces two new post-transformations for the short-time Fourier transform that achieve a compact time-frequency representation while allowing for the separation and the reconstruction of the modes. These two new transformations thus benefit from both the synchrosqueezing transform (which allows for reconstruction) and the reassignment method (which achieves a compact time-frequency representation). Numerical experiments on real and synthetic signals demonstrate the efficiency of these new transformations, and illustrate their differences.

An Alternative Formulation for the Empirical Mode Decomposition

The Empirical Mode Decomposition (EMD) is a relatively new adaptive method for multicomponent signal representation which allows for analyzing nonlinear and nonstationary signals. In spite of its lack of mathematical foundations, very few papers are dedicated to defining new decompositions that would preserve the interesting properties of the EMD while improving the mathematical setting. The new decomposition based on direct constrained optimization we introduce in this article is an attempt in that direction.

Synchronization and desynchronization of neural oscillators

We have used continuous and discrete-time versions of a neural oscillator model to analyze how various types of synaptic connections between oscillators affect synchronization and desynchronization phenomena. First, we present a synthesis of the mathematical properties of both neural oscillator versions. Then, we show that the choice of parameters leads to a relationship between the two versions. Finally, we achieve the coupling of two oscillators in order to study how synaptic connections affect the phase lag. With this in mind, we state some of the results for the continuous-time model. The second part of this paper deals with the behavior of neural networks comprising connected oscillators, which involves looking at the conditions for desynchronization of a totally synchronized oscillator net. Such a study has been carried out both for a fully and for a sparsely connected network. This leads to the observation that some architectures enable proper desynchronization when the size of the network is large. While searching for the conditions for desynchronization, we have discovered that a macroscopic description of the network is sometimes possible. To conclude, we discuss the advantages and the limitations of this macroscopic approach.

On the modeling of small sample distributions with generalized Gaussian density in a maximum likelihood framework

The modeling of sample distributions with generalized Gaussian density (GGD) has received a lot of interest. Most papers justify the existence of GGD parameters through the asymptotic behavior of some mathematical expressions (i.e., the sample is supposed to be large). In this paper, we show that the computation of GGD parameters on small samples is not the same as on larger ones. In a maximum likelihood framework, we exhibit a necessary and sufficient condition for the existence of the parameters. We derive an algorithm to compute them and then compare it to some existing methods on random images of different sizes.

Blob Detection With Wavelet Maxima Lines

In this letter, we propose a novel approach to blob detection based on wavelet transform modulus maxima. We use maxima lines in scale-space to build a new blob detector. The algorithm we propose enables automatic blob detection and blob size determination. The robustness to noise of the blob detector we propose is also shown

The fourier-based synchrosqueezing transform

The short-time Fourier transform (STFT) and the continuous wavelet transform (CWT) are extensively used to analyze and process multicomponent signals, i.e. superpositions of modulated waves. The synchrosqueezing is a post-processing method which circumvents the uncertainty relation inherent to these linear transforms, by reassigning the coefficients in scale or frequency. Originally introduced in the setting of the CWT, it provides a sharp, concentrated representation, while remaining invertible. This technique received a renewed interest with the recent publication of an approximation result related to the application of the synchrosqueezing to multi-component signals. In the current paper, we adapt the formulation of the synchrosqueezing to the STFT and state a similar theoretical result to that obtained in the CWT framework. The emphasis is put on the differences with the CWT-based synchrosqueezing with numerical experiments illustrating our statements.