Beyond convergence rates: Exact inversion with Tikhonov regularization with sparsity constraints. (arXiv:1001.3276v1 [math.FA])

The Tikhonov functional with the $ell^1$ penalty yields a regularization
method that generates a sparse approximate solution--the so-called Tikhonov
regularization with sparsity constraints. Recently, it has been shown that this
functional together with a certain a priori parameter rule and a certain source
condition converges linearly to the minimum-$ell^1$ solution. In this paper we
go beyond the question of convergence rates by presenting an a priori parameter
rule which ensures exact recovery of the unknown support. The presented results
are a generalization of exact recovery conditions from sparse approximation
theory.

With an imaging example from digital holography we show that our results lead
to practically relevant estimates, such that one may check a priori if the
experimental setup guarantees exact inversion with Tikhonov regularization with
sparsity constraints.

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Original source : http://arxiv.org/abs/1001.3276...