Locally Competitive Algorithms for Sparse Approximation
Locally Competitive Algorithms for Sparse Approximation
复制标题
稀疏逼近的局部竞争算法
DOI：
10.1109/icip.2007.4379981
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
B. Olshausen
中科院分区：
文献类型：
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作者：
C. Rozell;Don H. Johnson;Richard Baraniuk;B. Olshausen
实用的稀疏逼近算法（特别是贪婪算法）有两个明显的缺点：它们难以在硬件中实现，并且它们对于时变刺激（例如视频）效率低下，因为它们产生不稳定的时间系数序列。我们提出了一类局部竞争算法（lca），它对应于一组稀疏逼近原则，最小化重构MSE和系数成本函数的加权组合。这些系统使用阈值函数来诱导动力系统中的局部非线性竞争。简单的模拟硬件可以实现所需的非线性和竞争。我们证明我们的lca在正常操作条件下是稳定的，并且可以产生与现有方法相当的稀疏度水平。此外，这些lca可以为视频序列产生比贪婪算法产生的系数更规则（即更平滑和更可预测）的系数。
Practical sparse approximation algorithms (particularly greedy algorithms) suffer two significant drawbacks: they are difficult to implement in hardware, and they are inefficient for time-varying stimuli (e.g., video) because they produce erratic temporal coefficient sequences. We present a class of locally competitive algorithms (LCAs) that correspond to a collection of sparse approximation principles minimizing a weighted combination of reconstruction MSE and a coefficient cost function. These systems use thresholding functions to induce local nonlinear competitions in a dynamical system. Simple analog hardware can implement the required nonlinearities and competitions. We show that our LCAs are stable under normal operating conditions and can produce sparsity levels comparable to existing methods. Additionally, these LCAs can produce coefficients for video sequences that are more regular (i.e., smoother and more predictable) than the coefficients produced by greedy algorithms.