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Convergence rates in ℓ¹-regularization when the basis is not smooth enough

Flemming, Jens; Hegland, Markus


Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumption that the unknown solution has a sparse representation with respect to a fixed basis. We drop this sparsity assumption and provide error estimates for nonsparse solutions. After discussing a result in this direction published earlier by one of the authors and co-authors, we prove a similar error estimate under...[Show more]

CollectionsANU Research Publications
Date published: 2014-02-26
Type: Journal article
Source: Applicable Analysis
DOI: 10.1080/00036811.2014.886106


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