Dictionary learning with log-regularizer for sparse representation
Dictionary learning with log-regularizer for sparse representation
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DOI：
10.1109/icdsp.2015.7251946
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发表时间：
2015-07
期刊：
影响因子：
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通讯作者：
Zhenni Li;Shuxue Ding;Yujie Li
中科院分区：
文献类型：
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作者：
Zhenni Li;Shuxue Ding;Yujie Li
我们提出了一个快速有效的算法学习过完备字典稀疏表示的信号使用非凸对数正则化稀疏。在最近的稀疏建模研究中，对数正则化子的特殊重要性已被认识到。对数正则化，但是，导致一个非凸和非光滑的优化问题，难以有效地解决。本文提出了一种基于分解方案和交替优化的方法，将整个问题转化为一组单变量函数的次最小化，每个次最小化只依赖于一个字典原子或系数向量。虽然关于系数向量的子问题仍然是非光滑和非凸的，但值得注意的是，通过引入一种新的技术，即对数阈值算子，它变得简单得多，并具有封闭形式的解决方案。该算法的主要优点是，我们的分析和模拟研究表明，它是更有效的比国家的最先进的算法具有不同的稀疏性约束。
We propose a fast and efficient algorithm for learning overcomplete dictionary for sparse representation of signals using the nonconvex log-regularizer for sparsity. The special importance of log-regularizer has been recognized in recent studies on sparse modeling. The log-regularizer, however, leads to a nonconvex and nonsmooth optimization problem that is difficult to solve efficiently. In this paper, We propose a method based on a decomposition scheme and alternating optimization that can turn the whole problem into a set of subminimizations of univariate functions, each of which is dependent on only one dictionary atom or the coefficient vector. Although the subproblem with respects to the coefficient vector is still nonsmooth and nonconvex, remarkably, it becomes much simpler and it has a closed-form solution by introducing a novel technique that is log-thresholding operator. The main advantages of the proposed algorithm is that, as suggested by our analysis and simulation study, it is more efficient than state-of-the-art algorithms with different sparsity constraints.