Sparse Representation Based on the Analysis Model With Optimization on the Stiefel Manifold
Sparse Representation Based on the Analysis Model With Optimization on the Stiefel Manifold
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基于Stiefel流形优化分析模型的稀疏表示
DOI：
10.1109/access.2018.2890299
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发表时间：
2019
期刊：
影响因子：
3.9
通讯作者：
Zhenni Li
中科院分区：
文献类型：
--
作者：
Yujie Li;Shuxue Ding;Benying Tan;Haoli Zhao;Zhenni Li
分析模型的稀疏表示成为一项具有挑战性的任务，因为优化问题涉及对分析字典的附加约束。我们提出了通过具有正交性约束的优化函数来学习分析字典的问题，该问题通常可以通过交替实施分析字典更新和稀疏编码步骤来解决。在字典更新步骤中，用于更新具有正交约束的分析字典的传统方法是首先在不考虑约束的情况下在欧几里德空间中执行更新，然后将解投影到满足正交约束的流形上。然而，这种投影方法是近似的，并且通过投影获得的学习字典可能不体现原始字典的固有结构。因此，我们开发了一个新的框架无缝学习的分析字典沿着的流形。该方法可以提供更准确、更有效的分析词典。在稀疏编码问题中，为了避免调整公式的参数，我们引入了一个指示函数作为代价函数优化的惩罚函数。因此，我们将两个参数减少到一个，这更容易优化。然后，我们采用一个Douglas-Rachford型方案来解决这个问题。从数值实验的结果进行评估的分析字典的恢复率，我们可以直观地看到所提出的算法的性能。此外，所提出的算法表现出良好的性能，在图像去噪的实际应用。
Sparse representation with an analysis model becomes a challenging task because the optimization problem involves additional constraints on the analysis dictionary. We present the problem of learning the analysis dictionary through an optimization function with an orthogonality constraint, which can be generally solved by alternately implementing the analysis dictionary update and the sparse coding steps. In the dictionary update step, the traditional method for updating the analysis dictionary with the orthogonality constraint is to first perform the update in Euclidean space without taking the constraint into consideration and then project the solution onto a manifold where the orthogonality constraint is satisfied. However, this projection method is approximate, and the learned dictionary obtained by projection may not embody the inherent structure of the original dictionary. Thus, we develop a novel framework for seamlessly learning the analysis dictionary along with the manifold. This method can provide a more accurate and effective analysis dictionary. In the sparse coding problem, to avoid adjustment of the parameters of the formulation, we introduce an indicator function as the penalty function for optimization of the cost function. Thus, we reduce two parameters to one, which is easier to optimize. Then, we adopt a Douglas–Rachford-like scheme to solve the problem. From the results of the numerical experiments conducted to evaluate the recovery rate of the analysis dictionary, we can intuitively see the performance of the proposed algorithms. Furthermore, the proposed algorithms show good performance in image denoising for realistic applications.
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DOI：
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发表时间：
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期刊：
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影响因子：
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