A Novel Regularization Based on the Error Function for Sparse Recovery
A Novel Regularization Based on the Error Function for Sparse Recovery
复制标题
一种基于误差函数的新颖正则化稀疏恢复方法
DOI：
10.1007/s10915-021-01443-w
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发表时间：
2021
影响因子：
2.5
通讯作者：
Yan, Ming
中科院分区：
文献类型：
--
作者：
Guo, Weihong;Lou, Yifei;Qin, Jing;Yan, Ming
正则化通过添加关于期望解的额外信息（如稀疏性），在解决病态问题中起着重要作用。许多正则化项通常涉及一些向量范数。本文提出了一种利用误差函数近似单位阶跃函数的正则化框架。它可以被看作是norm的代理函数。误差函数对其固有参数的渐近行为表明，所提出的正则化方法可以分别在参数趋近于0和时逼近标准、范数。从统计上讲，它也比方法更少偏见。结合误差函数，我们考虑有约束和无约束两种形式来从欠定线性系统重构稀疏信号。在计算上，这两个问题都可以通过保证收敛的迭代重加权（IRL1）算法来解决。大量实验结果表明，该方法在各种稀疏恢复场景下优于现有方法。
Regularization plays an important role in solving ill-posed problems by adding extra information about the desired solution, such as sparsity. Many regularization terms usually involve some vector norms. This paper proposes a novel regularization framework that uses the error function to approximate the unit step function. It can be considered as a surrogate function for thenorm. The asymptotic behavior of the error function with respect to its intrinsic parameter indicates that the proposed regularization can approximate the standard,norms as the parameter approaches to 0 andrespectively. Statistically, it is also less biased than theapproach. Incorporating the error function, we consider both constrained and unconstrained formulations to reconstruct a sparse signal from an under-determined linear system. Computationally, both problems can be solved via an iterative reweighted(IRL1) algorithm with guaranteed convergence. A large number of experimental results demonstrate that the proposed approach outperforms the state-of-the-art methods in various sparse recovery scenarios.
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影响因子：
5.4
作者：
Wang, Chao;Yan, Ming;Lou, Yifei
通讯作者：
Lou, Yifei
影响因子：
2.3
作者：
A. Papoulis;C. Chamzas
通讯作者：
C. Chamzas
影响因子：
1.2
作者：
Candes, Emmanuel J.;Wakin, Michael B.;Boyd, Stephen P.
通讯作者：
Boyd, Stephen P.
DOI：
10.1364/josa.73.001476
发表时间：
1983
期刊：
Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints
影响因子：
--
作者：
R. Mammone
通讯作者：
R. Mammone