Non-convex sparse regularisation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:365

Article

Grasmair, Markus

关键词: Tikhonov regularisation;    Sparsity;    Convergence rates;   

DOI  :  10.1016/j.jmaa.2009.09.055

来源: Elsevier

【 摘 要 】

We study the regularising properties of Tikhonov regularisation on the sequence space l(2) with weighted, non-quadratic penalty term acting separately on the coefficients of a given sequence. We derive sufficient conditions for the penalty term that guarantee the well-posedness of the method, and investigate to which extent the same conditions are also necessary. A particular interest of this paper is the application to the solution of operator equations with sparsity constraints. Assuming a linear growth of the penalty term at zero, we prove the sparsity of all regularised solutions. Moreover, we derive a linear convergence rate under the assumptions of even faster growth at zero and a certain injectivity of the operator to be inverted. These results in particular cover non-convex l(P) regularisation with 0 < p < 1. (c) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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