Doctorant sous la direction de A. Renaux

Lucien Bacharach
Ph.D Student
University Paris-Sud, Orsay
Laboratory of Signals and Systems (L2S), Gif-sur-Yvette
Signals and Statistics Group – Modelisation and Estimation Team

Room C4.03B L2S/CentraleSupelec
lucien (dot) bacharach (at) l2s (dot) centralesupelec (dot) fr

Thesis Director: Alexandre Renaux

Co-supervisor: Mohammed Nabil El Korso

Thesis title: Bayesian Bounds for Change-Point Estimation

Started in October 2015.

Thesis abstract: A change-point can be defined as an abrupt change in a signal properties. More precisely, for a random signal, this can be modelled by a change in the parameters of the probability density function describing this signal (e.g., mean and/or variance change). Those change-points arise in numerous signal processing applications, like fault detection (in industrial production processes or navigation systems), speech signal or astronomical data segmentation, seismic data processing, or maneuvering targets tracking. Depending on the purpose, several formulations of this problem can be made: online/offline detection of a change, offline estimation of a change. We first investigate the latter one. As far as we know, quite few results have been given about the changepoints estimators performances in terms of consistency, bias and mean square error (MSE), at least. Regarding MSE, this can be explained by the difficulty of deriving the Cramér-Rao bound associated to the formulation of the problem. In our study, we then use a Bayesian point of view in combination with tools well adapted to this context (e.g., the Weiss-Weinstein or the Ziv-Zakai bounds), in order to obtain as precise error bounds as possible.

Keywords: Estimation theory, performance bound analysis, Bayesian lower bound, change-point, mean square error

Short bio: I studied aeronautical engineering at ISAE-ENSICA (Toulouse, France), where I got graduated in 2014. Then I received the Master Research degree in Signal and Image Processing from Paris-Sud University (Orsay, France) in 2015. I am currently pursuing the Ph.D. degree in signal processing with Paris-Sud University, at Laboratory of Signals and Systems (L2S, Gif-sur-Yvette, France). My research interests and activities include estimation and detection theory in statistical signal processing, with an emphasis on performance analysis using tools such as lower bounds on the mean square error.

Publications:

Journal papers

  • L. Bacharach, A. Renaux, M. N. El Korso and E. Chaumette, "Weiss-Weinstein bound on multiple change-points estimation",  IEEE Transactions on Signal Processing, Volume: 65, Issue: 10,  May 2017, pp.  2686-2700 [pdf]

Conference papers

  • L. Bacharach, G. Bibiche, A. Renaux and M. N. El Korso, "Bornes bayésiennes pour la localisation d'un point de rupture : Application à des processus exponentiels", in Proc. of Colloque GRETSI (GRETSI 2017), Juan-les-Pins, France, September 2017 [pdf]
  • L. Bacharach, M. N. El Korso, A. Renaux and J.-Y. Tourneret, "A Bayesian lower bound for parameter estimation of Poisson data including multiple changes", in Proc. of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2017), New Orleans, LA, USA, pp. 4486–4490 [pdf] (extended version with proofs: [pdf]).
  • L. Bacharach, M. N. El Korso and A. Renaux, "Weiss-Weinstein Bound for an unknown abrupt frequency change", in Proc. of the IEEE Workshop on Statistical Signal Processing (SSP 2016), Palma de Mallorca, Spain, June 2016, pp. 420–424 [pdf]
  • L. Bacharach, A. Renaux, M. N. El Korso and E. Chaumette, "Weiss-Weinstein bound for change-point estimation", in Proc. of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2015), Cancun, Mexico, December 2015, pp. 477–480 [pdf]

Teaching (in French):

J'effectue une mission d'enseignement avec l'Université Paris-Sud : je donne des cours (principalement des TD et des TP) dans la formation par apprentissage de Polytech Paris-Sud, pour les élèves de 3e et 4e année.

2016 :

  • Électronique (3A Polytech Paris-Sud, formation par apprentissage) :
    • 16h. Travaux Pratiques : amplification, limitations d'un amplificateur opérationnel.
  • Langage Java (4A Polytech Paris-Sud, formation par apprentissage) :
    • 16h. Travaux Pratiques : introduction à la programmation orientée objet.
  • Architecture des microcontrôleurs (4A Polytech Paris-Sud, formation par apprentissage) :
    • 3h. Cours/Travaux Dirigés : introduction aux microcontrôleurs, entrées/sorties tout ou rien, timers.
    • 16h. Travaux Pratiques : entrées/sorties tout ou rien, timers, convertisseur analogique/numérique, liaison série UART.

2015 :

  • Électronique (3A Polytech Paris-Sud, formation par apprentissage) :
    • 16h. Travaux Pratiques : filtrage analogique.
  • Langage Java (4A Polytech Paris-Sud, formation par apprentissage) :
    • 16h. Travaux Pratiques : introduction à la programmation orientée objet.
  • Mathématiques de spécialité (3A Polytech Paris-Sud, formation par apprentissage) :
    • 4h. Cours/Travaux Dirigés : rappels de mathématiques (développements limités, algèbre linéaire, matrices de rotations), introduction à l'algorithme CORDIC.
    • 8h. Travaux Pratiques : programmation du calcul de fonctions trigonométriques par l'algorithme CORDIC.
  • Projet microcontrôleurs (4A Polytech Paris-Sud, formation par apprentissage) :
    • 28h. Travaux Pratiques : programmation de microcontrôleurs (famille dsPIC30F de Microchip®) pour le fonctionnement de robots hexapodes (entrées/sorties tout ou rien, timers, convertisseur analogique/numérique, liaison série UART, bus CAN).

Administrative responsibility: PhD Students delegate at the L2S Laboratory Council.