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• W2897664897 abstract "Measuring the error by an l^1-norm, we analyze under sparsity assumptions an l^0-regularization approach, where the penalty in the Tikhonov functional is complemented by a general stabilizing convex functional. In this context, ill-posed operator equations Ax = y with an injective and bounded linear operator A mapping between l^2 and a Banach space Y are regularized. For sparse solutions, error estimates as well as linear and sublinear convergence rates are derived based on a variational inequality approach, where the regularization parameter can be chosen either a priori in an appropriate way or a posteriori by the sequential discrepancy principle. To further illustrate the balance between the l^0-term and the complementing convex penalty, the important special case of the l^2-norm square penalty is investigated showing explicit dependence between both terms. Finally, some numerical experiments verify and illustrate the sparsity promoting properties of corresponding regularized solutions." @default.
• W2897664897 created "2018-10-26" @default.
• W2897664897 creator A5006439118 @default.
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• W2897664897 creator A5046597133 @default.
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• W2897664897 date "2018-10-20" @default.
• W2897664897 modified "2023-09-23" @default.
• W2897664897 title "Tikhonov regularization with l^0-term complementing a convex penalty: l^1 convergence under sparsity constraints" @default.
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• W2897664897 doi "https://doi.org/10.48550/arxiv.1810.08775" @default.
• W2897664897 hasPublicationYear "2018" @default.
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