Needlets and Applications
joint work with D. Picard, G. Kerkyacharian, E. Trélat, M. Bergounioux and E. Gautier
Capitalizing on the beautiful needlet representation construction of P. Petrushev and his coauthors, we have proposed, with G. Kerkyacharian and D. Picard, a needlet thresholding strategy to inverse the fanbeam tomography operator, which is a case of Radon type transform, in the white noise model. The resulting estimator is proved to be adaptive and almost minimax for a large range of Besov spaces. Numerical experiments confirm this good behavior. A similar construction and analysis has been conducted with M. Bergounioux and E. Trélat for an axisymmetric objet. We have obtained oracle type inequalities in this setting. With E. Gautier, we tackle a classical economotric model, the binary choice model, whose geometry corresponds to a half hypersphere, using adapted needlet construction as well as adapted thresholds.