Flemming, JensHegland, Markus2015-03-302015-03-300003-6811http://hdl.handle.net/1885/13076Sparsity 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 weaker assumptions. Two examples illustrate that this set of weaker assumptions indeed covers additional situations which appear in applications.J. Flemming was supported by the German Science Foundation (DFG) under grant FL 832/1-1. M. Hegland was partially supported by the Technische Universität München Institute of Advanced Study, funded by the German Excellence Initiative. Work on this article was partially conducted during a stay of M. Hegland at TU Chemnitz, supported by the German Science Foundation (DFG) under grant HO 1454/8-1.http://www.sherpa.ac.uk/romeo/issn/0003-6811/..."Pre-print or post-print allowed on institutional repository or subject-based repository after either 12 months embargo. On a non-profit server" from SHERPA/RoMEO site (as at 30/03/15)linear ill-posed problemsTikhonov-type regularizationℓ1-regularizationnonsmooth basissparsity constraintsconvergence ratesvariational inequalities2014-02-2610.1080/00036811.2014.8861062015-12-10