Elastic-net regularization versus l(1)-regularization for linear inverse problems with quasi-sparse solutions
Publication in refereed journal

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其它資訊
摘要We consider the ill-posed operator equation Ax = y with an injective and bounded linear operator A mapping between l(2) and a Hilbert space Y, possessing the unique solution x={x(k)}(k-1)(infinity). For the cases that sparsity x is an element of l(0) is expected but often slightly violated in practice, we investigate in comparison with the l(1)-regularization the elastic-net regularization, where the penalty is a weighted superposition of the l(1)-norm and the l(2)-norm square, under the assumption that x is an element of l(1). There occur two positive parameters in this approach, the weight parameter. and the regularization parameter as the multiplier of the whole penalty in the Tikhonov functional, whereas only one regularization parameter arises in l(1)-regularization. Based on the variational inequality approach for the description of the solution smoothness with respect to the forward operator A and exploiting the method of approximate source conditions, we present some results to estimate the rate of convergence for the elastic-net regularization. The occurring rate function contains the rate of the decay x(k) -> 0 for k -> infinity and the classical smoothness properties of x as an element in l(2).
出版社接受日期21.11.2016
著者De-Han Chen, Bernd Hofmann, Jun Zou
期刊名稱Inverse Problems
出版年份2017
月份1
卷號33
期次1
出版社IOP PUBLISHING LTD
頁次015004
國際標準期刊號0266-5611
電子國際標準期刊號1361-6420
語言英式英語
關鍵詞linear ill-posed problems,sparsity constraints,elastic-net regularization,l(1)-regularization,convergence rates,source conditions
Web of Science 學科類別Mathematics, Applied;Physics, Mathematical;Mathematics;Physics

上次更新時間 2021-28-11 於 23:37