Greedy-like algorithms for the cosparse analysis model
Greedy-like algorithms for the cosparse analysis model
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DOI：
10.1016/j.laa.2013.03.004
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发表时间：
2012-07
影响因子：
1.1
通讯作者：
R. Giryes;Sangnam Nam;Michael Elad;R. Gribonval;M. Davies
中科院分区：
文献类型：
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作者：
R. Giryes;Sangnam Nam;Michael Elad;R. Gribonval;M. Davies
cosparse分析模型最近被引入作为一个有趣的替代标准稀疏合成方法。这个新的结构所带来的一个突出问题是分析追踪问题，即需要找到一个属于这个模型的信号，给出一组损坏的测量。在这项工作中，我们进一步追求这个问题，并提出了一个新的家庭的追求算法的cosparse分析模型，模仿贪婪的方法压缩采样匹配追求（CoSaMP），子空间追求（SP），迭代硬阈值（IHT）和硬阈值追求（HTP）。假设一个接近最佳的投影方案，找到最近的cosparse子空间的任何向量的可用性，我们提供这些算法的性能保证。我们的理论研究依赖于一个受限制的等距属性适应上下文的cosparse分析模型。我们通过采用一个简单的阈值投影，经验性地探索这些算法的性能，证明了它们的良好性能。
The cosparse analysis model has been introduced recently as an interesting alternative to the standard sparse synthesis approach. A prominent question brought up by this new construction is the analysis pursuit problem–the need to find a signal belonging to this model, given a set of corrupted measurements of it. Several pursuit methods have already been proposed based on ℓ 1 relaxation and a greedy approach. In this work we pursue this question further, and propose a new family of pursuit algorithms for the cosparse analysis model, mimicking the greedy-like methods–compressive sampling matching pursuit (CoSaMP), subspace pursuit (SP), iterative hard thresholding (IHT) and hard thresholding pursuit (HTP). Assuming the availability of a near optimal projection scheme that finds the nearest cosparse subspace to any vector, we provide performance guarantees for these algorithms. Our theoretical study relies on a restricted isometry property adapted to the context of the cosparse analysis model. We explore empirically the performance of these algorithms by adopting a plain thresholding projection, demonstrating their good performance.