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Well-posedness and convergence rates for sparse regularization with sublinear $l^q$ penalty term

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  • This paper deals with the application of non-convex, sublinear penalty terms to the regularization of possibly non-linear inverse problems the solutions of which are assumed to have a sparse expansion with respect to some given basis or frame. It is shown that this type of regularization is well-posed and yields sparse results. Moreover, linear convergence rates are derived under the additional assumption of a certain range condition.
    Mathematics Subject Classification: Primary: 65J20; Secondary: 65J22, 49N45.


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