Journal
INVERSE PROBLEMS
Volume 26, Issue 11, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0266-5611/26/11/115014
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Funding
- Austrian Science Fund (FWF) within the national research network Industrial Geometry [9203-N12]
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We generalize the notion of Bregman distance using concepts from abstract convexity in order to derive convergence rates for Tikhonov regularization with non-convex regularization terms. In particular, we study the non-convex regularization of linear operator equations on Hilbert spaces, showing that the conditions required for the application of the convergence rates results are strongly related to the standard range conditions from the convex case. Moreover, we consider the setting of sparse regularization, where we show that a rate of order delta(1/p) holds, if the regularization term has a slightly faster growth at zero than vertical bar t vertical bar(p).
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