Geodesic
Regularization properties of Tikhonov regularization with sparsity constraints
Electronic transactions on numerical analysis, Tome 30 (2008), pp. 54-74
In this paper, we investigate the regularization properties of Tikhonov regularization with a sparsity (or Besov) penalty for the inversion of nonlinear operator equations. We propose an a posteriori parameter choice rule that ensures convergence in the used norm as the data error goes to zero. We show that the method of surrogate functionals will at least reconstruct a critical point of the Tikhonov functional. Finally, we present some numerical results for a nonlinear Hammerstein equation.
Classification : 65J15, 65J20, 65J22
Keywords: inverse problems, sparsity 
@article{ETNA_2008__30__a21,
     author = {Ramlau,  Ronny},
     title = {Regularization properties of {Tikhonov} regularization with sparsity constraints},
     journal = {Electronic transactions on numerical analysis},
     pages = {54--74},
     year = {2008},
     volume = {30},
     zbl = {1171.65042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__30__a21/}
}
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%A Ramlau,  Ronny
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%J Electronic transactions on numerical analysis
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Ramlau,  Ronny. Regularization properties of Tikhonov regularization with sparsity constraints. Electronic transactions on numerical analysis, Tome 30 (2008), pp. 54-74. http://geodesic.mathdoc.fr/item/ETNA_2008__30__a21/