Convergence rates in ℓ1-regularization when the basis is not smooth enough
Convergence rates in ℓ1-regularization when the basis is not smooth enough
复制标题
当基础不够平滑时 ℓ1-正则化的收敛率
DOI：
10.1080/00036811.2014.886106
复制
发表时间：
2013
影响因子：
1.1
通讯作者：
M. Hegland
中科院分区：
文献类型：
--
作者：
Jens Flemming;M. Hegland
稀疏正则化是信号重构等不适定问题的一种重要方法。理论研究通常基于这样的假设，即未知解相对于固定基具有稀疏表示。我们放弃这个稀疏性假设，并提供非稀疏解决方案的误差估计。在讨论了作者和合著者之一早些时候发表的这个方向的结果后，我们在较弱的假设下证明了类似的误差估计。两个例子表明，这套较弱的假设确实涵盖了应用中出现的其他情况。
Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumption that the unknown solution has a sparse representation with respect to a fixed basis. We drop this sparsity assumption and provide error estimates for nonsparse solutions. After discussing a result in this direction published earlier by one of the authors and co-authors, we prove a similar error estimate under weaker assumptions. Two examples illustrate that this set of weaker assumptions indeed covers additional situations which appear in applications.
Banach 空间中 Tikhonov 正则化的序贯差异原理的正则化性质
影响因子：
1.1
作者：
S. W. Anzengruber;B. Hofmann;P. Mathé
通讯作者：
P. Mathé