## Convergence rates for l1-regularization without the help of a variational inequality

Daniel Gerth

### Abstract

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.

Full Text (PDF) [289 KB]

### Key words

$\ell^1$-regularization, Tikhonov regularization, variational inequality, convergence rates

65J20, 47A52

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