Sparsity-Aware Adaptive Proximal Forward-Backward Splitting Under The Principle Of Minimal Disturbance
Sparsity-Aware Adaptive Proximal Forward-Backward Splitting Under The Principle Of Minimal Disturbance
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DOI：
10.1109/ssp.2018.8450738
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发表时间：
2018-06
期刊：
影响因子：
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通讯作者：
M. Yamagishi;I. Yamada
中科院分区：
文献类型：
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作者：
M. Yamagishi;I. Yamada
最小干扰原则是成功的自适应滤波器所共有的基本规则。同时，利用学习算法的稀疏性是实现最新先进自适应滤波器优异性能的关键。观察到稀疏性感知自适应滤波器不一定符合最小干扰原则，我们提出了一种新颖的自适应滤波器，可以从稀疏性促进和最小干扰原则中受益匪浅。所提出的自适应滤波器源自自适应近端前向-后向分裂，应用于最小化平滑项和非平滑项之和的时变成本函数，其中我们引入了一个新设计的非平滑项，它是加权 $\ell _{1}$ 范数和广义 Tikhonov 正则化的总和，而利用稀疏性的典型选择只是加权 $\ell _{1}$ 范数。数值例子证明了所提出算法的有效性。
The principle of minimal disturbance is an underlying rule shared by successful adaptive filters. Meanwhile, exploiting the sparsity in learning algorithms is a key to achieve excellent performances of recent advanced adaptive filters. Observing that sparsity-aware adaptive filters are not necessarily consistent with the minimal disturbance principle, we propose a novel adaptive filter to benefit tremendously from both the sparsity promoting and the minimal disturbance principle. The proposed adaptive filter is derived from the adaptive proximal forward-backward splitting applied to minimize a time-varying cost function of the sum of the smooth and nonsmooth terms, where we introduce a newly designed nonsmooth term which is the sum of a weighted $\ell _{1}$ norm and a generalized Tikhonov regularization, while a typical choice to exploit the sparsity is the weighted $\ell _{1}$ norm only. A numerical example demonstrates the efficacy of the proposed algorithm.