Abstract #300214

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JSM 2003 Abstract #300214
Activity Number: 469
Type: Contributed
Date/Time: Thursday, August 7, 2003 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #300214
Title: Sharp Adaptive Estimation in Severely Ill-Posed Inverse Problems
Author(s): Cavalier Laurent*+
Companies: University Aix-Marseille 1
Address: CMI, 39 Rue Joliot-Curie, Marseille, , 13453, France
Keywords: inverse problems ; adaptive estimation
Abstract:

We consider the problem of solving linear operator equations from noisy data under the assumption that the singular values of the operator decrease exponentially fast and that the underlying solution is also exponentially smooth in the Fourier domain. We suggest an estimator of the solution based on a running version of block thresholding in the space of Fourier coefficients. This estimator is shown to be sharp adaptive to the unknown smoothness of the solution.


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