Convergence rates and source conditions for Tikhonov regularization with sparsity constraints
نویسندگان
چکیده
منابع مشابه
Convergence rates and source conditions for Tikhonov regularization with sparsity constraints
This paper addresses the regularization by sparsity constraints by means of weighted lp penalties for 0 ≤ p ≤ 2. For 1 ≤ p ≤ 2 special attention is payed to convergence rates in norm and to source conditions. As main results it is proven that one gets a convergence rate of √ δ in the 2-norm for 1 < p ≤ 2 and in the 1-norm for p = 1 as soon as the unknown solution is sparse. The case p = 1 needs...
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Tikhonov regularization with p-powers of the weighted `p norms as penalties, with p ∈ (1, 2), have been lately employed in reconstruction of sparse solutions of ill-posed inverse problems. This paper points out convergence rates for such a regularization with respect to the norm of the weighted spaces, by assuming that the solutions satisfy certain smoothness (source) condition. The meaning of ...
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ژورنال
عنوان ژورنال: Journal of Inverse and Ill-posed Problems
سال: 2008
ISSN: 0928-0219,1569-3945
DOI: 10.1515/jiip.2008.025