A unified approach to convergence rates for l(1)-regularization and lacking sparsity

作者：Flemming Jens^*; Hofmann Bernd; Veselic Ivan

来源：Journal of Inverse and Ill-Posed Problems, 2016, 24(2): 139-148.

DOI：10.1515/jiip-2015-0058

• Linear ill-posed problems
• Tikhonov-type regularization
• sparsity constraints
• convergence rates
• variational inequalities
• restricted isometry property

In l(1)-regularization, which is an important tool in signal and image processing, one usually is concerned with signals and images having a sparse representation in some suitable basis, e.g., in awavelet basis. Many results on convergence and convergence rates of sparse approximate solutions to linear ill-posed problems are known, but rate results for the l(1)-regularization in case of lacking sparsity had not been published until 2013. In the last two years, however, two articles appeared providing sufficient conditions for convergence rates in case of non-sparse but almost sparse solutions. In the present paper, we suggest a third sufficient condition, which unifies the existing two and, by the way, also incorporates the well-known restricted isometry property.

• 出版日期2016-4