This talk will rapidly introduce newly developed multiscale systems like curvelets and ridgelets which are very different from wavelet-like systems. Curvelets and ridgelets take the the form of basis elements which exhibit very high directional sensitivity and are highly anisotropic.

I will then describe high accurate digital implementations of those ideas and present some numerical experiments in image processing (detection, denoising, compression, etc). A fair fraction of the talk will be dedicated to discuss new ideas and algorithms for image reconstruction based upon minimum complexity synthesis rules and upon combining several transforms. I hope to present work in progress as well as outline future areas of research.

Collaborators: David Donoho, Franck Guo, Jean-Luc Starck