Publications

2005

• Image decomposition into a bounded variation component and an oscillating component
  
  • Aujol Jean-François
  • Aubert Gilles
  • Blanc-Féraud Laure
  • Chambolle Antonin
  Journal of Mathematical Imaging and Vision, Springer Verlag, 2005, 22 (1), pp.pages 71-88. We construct an algorithm to split an image into a sum $u+v$ of a bounded variation component and a component containing the textures and the noise. This decomposition is inspired from a recent work of Y. Meyer. We find this decomposition by minimizing a convex functional which depends on the two variables u and v, alternately in each variable. Each minimization is based on a projection algorithm to minimize the total variation. We carry out the mathematical study of our method. We present some numerical results. In particular, we show how the u component can be used in nontextured SAR image restoration.
• Concentration for independent random variables with heavy tails
  
  • Barthe Franck
  • Cattiaux Patrick
  • Roberto Cyril
  AMRX Appl.Math.Res.Express, 2005 (2), pp.39-60. If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish concentration inequalities for finite sequences of $n$ independent copies, with good dependence in $n$.
• Generalized Impedance Impedance Boundary Conditions For Scattering by Strongly Absorbing Obstacles: The Scalar Case
  
  • Haddar Houssem
  • Joly Patrick
  • Nguyen Hoai-Minh
  Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2005, 15 (08), pp.1273-1300. (10.1142/S021820250500073X)
  DOI : 10.1142/S021820250500073X
• 3D piezoelectric surface green's function
  
  • Laude Vincent
  • Jerez-Hanckes Carlos F.
  • Ballandras Sylvain
  , 2005, pp.687-690.