Optimal Solutions for Non-Convex Minimization Problems Arising in Image Processing and Machine Learning

--------------------------------------------------------------------
Joint CSE and Center for Visual Computing and Image Science Seminar
--------------------------------------------------------------------

Speaker:	Dr. Xavier BRESSON
		Department of Mathematics
		University of California, Los Angeles (UCLA)

Title: 		"Optimal Solutions for Non-Convex Minimization Problems
		 Arising in Image Processing and Machine Learning"

Date:		Monday, 8 March 2010

Time:		11:00am - 12 noon

Venue:		Rm3401 (via lifts 17/18), HKUST


Abstract:

I will present a new approach to compute optimal solutions for fundamental
non-convex problems of optimization in image processing and machine
learning. Unlike most methods published in the literature, our approach
guarantees the existence of optimal solutions. This is an important step
towards more robust and faster algorithms for real-world applications. Our
approach consists in finding a convex relaxation of the original
non-convex optimization problems and thresholding the relaxed solution to
reach the solution of the original problem. This general approach allows
us to solve two highly difficult problems: the multi-phase classification
problem and the Cheeger ratio cut problem, which are known to be NP-hard
problems in combinatorial theory.


****************
Biography:

Xavier Bresson received a M.Sc. in Theoretical Physics from University of
Provence, a M.Sc. in Electrical Engineering from Ecole Superieure
d'Electricite, Paris, and a M.Sc. in Signal Processing from University of
Paris XI. In 2005, he completed a PhD in the field of Computer Vision at
the Swiss Federal Institute of Technology (EPFL). He is currently a
postdoctoral scholar in the Department of Mathematics at University of
California, Los Angeles (UCLA). His main research activities are focused
on computer vision, image processing, medical imaging, machine learning,
energy minimization methods, non-differentiable energy functionals, convex
optimization schemes, parabolic partial differential equations, discrete
geometry.