接近oracle性能的信号空间贪心方法分析
Near Oracle Performance and Block Analysis of Signal Space Greedy Methods
AI总结：
本文分析了在存在高斯白噪声下的信号空间CoSaMP方法，证明其在任意字典下具有接近oracle的性能，并探讨了具有块结构支持的信号的块变体方法，扩展到基于模型的压缩感知框架。
摘要：
压缩采样（CoSa）是一种新方法，证明稀疏信号可以从少量线性测量中恢复。贪心算法如CoSaMP为此恢复设计，其变体已适应于稀疏性相对于任意字典而非正交基的情况。本文分析了在存在均值为零的高斯白噪声下的所谓信号空间CoSaMP方法，证明了在某些任意字典下信号的恢复具有接近oracle的性能。此外，我们分析了具有块结构支持的信号的块变体方法，将该方法扩展到基于模型的压缩感知框架。数值实验表明，在这些设置下，块方法显著优于标准方法。
英文摘要：
Compressive sampling (CoSa) is a new methodology which demonstrates that sparse signals can be recovered from a small number of linear measurements. Greedy algorithms like CoSaMP have been designed for this recovery, and variants of these methods have been adapted to the case where sparsity is with respect to some arbitrary dictionary rather than an orthonormal basis. In this work we present an analysis of the so-called Signal Space CoSaMP method when the measurements are corrupted with mean-zero white Gaussian noise. We establish near-oracle performance for recovery of signals sparse in some arbitrary dictionary. In addition, we analyze the block variant of the method for signals whose supports obey a block structure, extending the method into the model-based compressed sensing framework. Numerical experiments confirm that the block method significantly outperforms the standard method in these settings.
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