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arXiv · 1701.03460

Injectivity and weak*-to-weak continuity suffice for convergence rates in $\ell^1$-regularization

Jens Flemming·Daniel Gerth
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Abstract

We show that the convergence rate of $\ell^1$-regularization for linear ill-posed equations is always $O(\delta)$ if the exact solution is sparse and if the considered operator is injective and weak*-to-weak continuous. Under the same assumptions convergence rates in case of non-sparse solutions are proven. The results base on the fact that certain source-type conditions used in the literature for proving convergence rates are automatically satisfied.

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Jens Flemming, Daniel Gerth. 2017-01-12. Injectivity and weak*-to-weak continuity suffice for convergence rates in $\ell^1$-regularization. https://arxiv.org/abs/1701.03460

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