Sparse Stable Outlier-Robust Signal Recovery Under Gaussian Noise
Sparse Stable Outlier-Robust Signal Recovery Under Gaussian Noise
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DOI：
10.1109/tsp.2023.3244082
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发表时间：
2023
影响因子：
5.4
通讯作者：
Kyohei Suzuki;M. Yukawa
中科院分区：
文献类型：
--
作者：
Kyohei Suzuki;M. Yukawa
本文提出了一种新的稀疏鲁棒信号恢复的框架集成稀疏恢复使用的极小极大凹（MC）惩罚和强大的回归称为稀疏离群鲁棒回归（SORR）使用MC损失。虽然所提出的方法对巨大的离群值具有高度鲁棒性，但可以通过考虑稀疏性和鲁棒性之间的权衡来控制估计的稀疏性。为了适应加性高斯噪声和野值的先验信息，引入了一个辅助向量来对噪声进行建模。显著的鲁棒性和稳定性分别来自于使用MC损失和噪声向量的平方$\ell _{2}$惩罚。此外，同时使用MC和平方$\ell _{2}$惩罚系数向量导致一定显着的分组效果。在一定的非空内部假设下，利用线性参与的Moreau增强子空间（LiMES）框架，通过乘积空间公式推导出了代价的光滑部分凸性的充分必要条件.仿真结果表明，该方法的有效性，在其应用程序的语音去噪在高噪声环境下，以及玩具问题。
This paper presents a novel framework for sparse robust signal recovery integrating the sparse recovery using the minimax concave (MC) penalty and robust regression called sparse outlier-robust regression (SORR) using the MC loss. While the proposed approach is highly robust against huge outliers, the sparseness of estimates can be controlled by taking into consideration a tradeoff between sparseness and robustness. To accommodate the prior information about additive Gaussian noise and outliers, an auxiliary vector to model the noise is introduced. The remarkable robustness and stability come from the use of the MC loss and the squared $\ell _{2}$ penalty of the noise vector, respectively. In addition, the simultaneous use of the MC and squared $\ell _{2}$ penalties of the coefficient vector leads to a certain remarkable grouping effect. The necessary and sufficient conditions for convexity of the smooth part of the cost are derived under a certain nonempty-interior assumption via the product space formulation using the linearly-involved Moreau-enhanced-over-subspace (LiMES) framework. The efficacy of the proposed method is demonstrated by simulations in its application to speech denoising under highly noisy environments as well as to toy problems.