Iterated soft shrinkage with adaptive operator evaluations
Iterated soft shrinkage with adaptive operator evaluations
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DOI：
10.1515/jiip.2009.023
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Thomas Bonesky;Peter Maass
中科院分区：
文献类型：
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作者：
Thomas Bonesky;Peter Maass
摘要本文研究了稀疏约束下Tikhonov泛函最小化的迭代软收缩问题。受偏微分方程参数辨识问题的启发，我们假设只有自适应算子求值[Ax]h是可用的。自适应求精策略导致[A]h在每个迭代步骤中的不同实现，因此，我们不能假设算子范数的逼近误差的界。我们将发展1<；p≤2的线性反问题的基本收敛和正则化结果，这些结果具有自适应算子求值和惩罚项。
Abstract This paper is concerned with iterated soft shrinkage for minimizing Tikhonov functionals with sparsity constraints. Motivated by parameter identification problems for partial differential equations we assume, that only adaptive operator evaluations [Ax] h are available. Adaptive refinement strategies lead to different realizations of [A] h in every iteration step, hence, we cannot assume a bound on the approximation error in the operator norm. We will develop the basic convergence and regularization results for linear inverse problems with adaptive operator evaluations and penalty terms for 1 < p ≤ 2.