Erwan Le Pennec

Needlets and applications

joint work with E. Gautier, G. Kerkyacharian and D. Picard

This work started with acollaboration with G. Kerkyacharian and D. Picard around tomography and an inverse problem linked to the Radon transform.

The geometry of the fan beam tomography is not the one of $\mathbb{R}^2$ but rather the of the projection of an half-sphere. In order to inverse the corresponding Radon operator, we wonstruct a representation that is well localized bothh spectrally and spatially. Obtained by techniques à la Littlewood-Paley, as the Meyer wavelets for the operators diagonal in the Fourier basis, Radon needlets allows to construct thresholding estimators that are optimal, up to a logarithmic factor, for a wide variety of Besov spaces and all norms $L^p$.

With E. Gautier, we study an econometric problem whose geometry is related to the sphere, for which a needlet construction also exists.

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