Convolutional Dictionary Learning with Huber Error and l<sub>1</sub> Regularization Terms
Convolutional Dictionary Learning with Huber Error and l<sub>1</sub> Regularization Terms
复制标题
使用 Huber 误差和 l<sub>1</sub> 正则化项进行卷积字典学习
DOI：
10.1109/ispacs51563.2021.9651025
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Kuroki Yoshimitsu
中科院分区：
文献类型：
--
作者：
Yoda Satoshi;Kawazoe Hironori;Kuroki Yoshimitsu
本文提出了一种鲁棒的卷积字典学习方法。卷积字典学习用字典滤波器和相应系数的和来近似信号，其代价函数由两个项的加权和组成：误差项和正则化项。许多研究分别对前者和后者使用l2和l1范数，并且为了增加鲁棒性，用l1范数代替误差项。对于这类两个凸项之和的优化问题，近似梯度法是一种很好的求解方法，但对于两个l1项不适用，因为这两个l1项的梯度在任意点都不连续。本文尝试将Moreau包络应用于l1误差项，并将l1误差表示为可微且Lipschitz连续的Huber误差函数。实验结果表明，该方法生成的词典比使用l2错误项的词典更鲁棒。
This paper addresses a robust convolutional dictionary learning method against outliers. Convolutional dictionary learning approximates a signal with the sum of dictionary filters and corresponding coefficients, and its cost function consists of the weighted sum of the two terms: error and regularization terms. Many studies employ the l2and the l1norms for the former and the latter respectively, and to increase the robustness, the l1norm is substituted for the error term. For such optimization problems with the sum of the two convex terms, the proximal gradient method is a powerful solver; however, it is not applicable for the two l1terms, of which gradient is not continuous at any point. This paper tries to apply the Moreau envelope for the l1error term, and the l1error is expressed as Huber error function, which is differentiable and Lipschitz continuous. Experimental results show that dictionaries generated with the proposed method are robuster than those with the l2error term.