Page web / Webpage : http://cbio.ensmp.fr/~erichard/

Résumé / Summary :
The Gaussian width of the tangent cone and some related objects naturally arise as golden measures of complexity in compressed sensing. We will discuss recent works that have introduced interesting properties of this object, namely the lower bound it provides on the number of iid measurements required for achieving perfect recovery (Chandrasekaran et al. 2012), and also connections with phase transition (Amelunxen et al 2013). Some examples from a recent work on the inference of sparse low-rank matrices will be discussed at the end.

Bibliographie / References :

• The convex geometry of linear inverse problems,
  by Chandrasekaran et al. (2012)
• Living on the edge: a geometric theory of phase transition in convex optimization, by Amelunxen et al. (2013)
• Computational and statistical tradoffs via convex relaxation,
  by Chandrasekaran and Jordan (2012)
• Intersecting singularities for multi-structured estimation,
  by Richard, E. Bach, F. and Vert, J.-P. (2013)