Nonlinear estimation for linear inverse problems with error in the operator
Hoffmann, Marc ; Reiss, Markus
Ann. Statist., Tome 36 (2008) no. 1, p. 310-336 / Harvested from Project Euclid
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We study two nonlinear methods for statistical linear inverse problems when the operator is not known. The two constructions combine Galerkin regularization and wavelet thresholding. Their performances depend on the underlying structure of the operator, quantified by an index of sparsity. We prove their rate-optimality and adaptivity properties over Besov classes.
Publié le : 2008-02-15
Classification:  Statistical inverse problem,  Galerkin projection method,  wavelet thresholding,  minimax rate,  degree of ill-posedness,  matrix compression,  65J20,  62G07 
@article{1201877303,
     author = {Hoffmann, Marc and Reiss, Markus},
     title = {Nonlinear estimation for linear inverse problems with error in the operator},
     journal = {Ann. Statist.},
     volume = {36},
     number = {1},
     year = {2008},
     pages = { 310-336},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1201877303}
}

Hoffmann, Marc; Reiss, Markus. Nonlinear estimation for linear inverse problems with error in the operator. Ann. Statist., Tome 36 (2008) no. 1, pp.  310-336. http://gdmltest.u-ga.fr/item/1201877303/