Adaptive wavelet Galerkin methods for linear inverse problems
AbstractWe introduce and analyse numerical methods for the treatment of inverse problems, based on an adaptive wavelet Galerkin discretization. These methods combine the theoretical advantages of the wavelet-vaguelette decomposition (WVD) in terms of optimally adapting to the unknown smoothness of the solution, together with the numerical simplicity of Galerkin methods. Two strategies are proposed: the first one simply combines a thresholding algorithm on the data with a Galerkin inversion on a fixed liner space, while the second one performs the inversion through an adaptive procedure in which a smaller space adapted to the solution is iteratively constructed. For both methods, we recover the same minimax rates achieved by WVD for various function classes modeling the solution. --
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Bibliographic InfoPaper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 2002,50.
Date of creation: 2002
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- Anne Vanhems & Jean-Michel Loubes, 2004. "Saturation spaces for regularization methods in inverse problems," Econometric Society 2004 North American Summer Meetings 380, Econometric Society.
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