A dictionary-learning algorithm for the analysis sparse model with a determinant-type of sparsity measure
A dictionary-learning algorithm for the analysis sparse model with a determinant-type of sparsity measure
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DOI：
10.1109/icdsp.2014.6900819
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发表时间：
2014-09
期刊：
影响因子：
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通讯作者：
Yujie Li;Shuxue Ding;Zhenni Li
中科院分区：
文献类型：
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作者：
Yujie Li;Shuxue Ding;Zhenni Li
信号稀疏表示的字典学习已成功地应用于信号处理。现有的方法大多是基于综合模型的，该模型中的词典是过完备的。本文提出了一种基于分析模型的词典学习和稀疏表示。在这个新的模型中，分析字典乘以信号可以得到稀疏的结果。虽然已有文献对其进行了研究，但还没有关于非负信号表征的研究，这应该不是一个微不足道的问题。此外，在本文中，我们还建议使用行列式稀疏度量从信号中学习分析字典。在公式中，我们采用欧几里德距离作为误差度量。在此基础上，提出了一种新的字典学习和稀疏表示算法。对分析词典恢复的数值实验表明了该方法的有效性。
Dictionary learning for sparse representation of signals has been successfully applied in signal processing. Most the existing methods are based on the synthesis model, in which the dictionary is overcomplete. This paper addresses the dictionary learning and sparse representation with the so-called analysis model. In this new model, the analysis dictionary multiplying the signal can lead to a sparse outcome. Though it has been studied in the literature, there is still not an investigation in the context of nonnegative signal representation, which should not be a trivial problem. In this paper, moreover, we propose to learn an analysis dictionary from signals using a determinant-type of sparsity measure. In the formulation, we adopt the Euclidean distance as the error measure. Based on these, we present a new algorithm for the dictionary learning and sparse representation. Numerical experiments on recovery of analysis dictionary show the effectiveness of the proposed method.