Multi-penalty regularization with a component-wise penalization
Multi-penalty regularization with a component-wise penalization
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DOI：
10.1088/0266-5611/29/7/075002
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发表时间：
2013-07-01
期刊：
影响因子：
2.1
通讯作者：
Pereverzyev, S. V.
中科院分区：
文献类型：
--
作者：
Naumova, V.;Pereverzyev, S. V.
我们讨论了一种新的正则化方案，用于在Hilbert空间中从给定的噪声数据中重建线性不适定算子方程的解。在这个新方案中，正则化近似被分解成几个分量，这些分量通过最小化多罚泛函来定义。我们从理论和数值上证明了在适当选择正则化参数的情况下，正则化逼近具有所谓的补偿性，即在相同的惩罚算子下，正则化逼近表现出与单惩罚正则化的最佳性能相似的性质。
We discuss a new regularization scheme for reconstructing the solution of a linear ill-posed operator equation from given noisy data in the Hilbert space setting. In this new scheme, the regularized approximation is decomposed into several components, which are defined by minimizing a multi-penalty functional. We show theoretically and numerically that under a proper choice of the regularization parameters, the regularized approximation exhibits the so-called compensatory property, in the sense that it performs similar to the best of the single-penalty regularization with the same penalizing operator.