Geodesic
Convergence rates for \(\ell^1\)-regularization without the help of a variational inequality
Electronic transactions on numerical analysis, Tome 46 (2017), pp. 233-244
We show that convergence rates for $\ell^1$-regularization can be obtained in an elementary way without requiring a classical source condition and without the help of a variational inequality. For the specific case of a diagonal operator we improve the convergence rate found in the literature and conduct numerical experiments that illustrate the predicted rate. The idea of the proof is rather generic and might be used in other settings as well.
Classification : 65J20, 47A52
Keywords: $\ell^1$-regularization, Tikhonov regularization, variational inequality, convergence rates 
@article{ETNA_2017__46__a2,
     author = {Gerth,  Daniel},
     title = {Convergence rates for \(\ell^1\)-regularization without the help of a variational inequality},
     journal = {Electronic transactions on numerical analysis},
     pages = {233--244},
     year = {2017},
     volume = {46},
     zbl = {1369.65070},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2017__46__a2/}
}
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%J Electronic transactions on numerical analysis
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Gerth,  Daniel. Convergence rates for \(\ell^1\)-regularization without the help of a variational inequality. Electronic transactions on numerical analysis, Tome 46 (2017), pp. 233-244. http://geodesic.mathdoc.fr/item/ETNA_2017__46__a2/