正交匹配追踪算法的改进RIP分析
Improved RIP Analysis of Orthogonal Matching Pursuit
摘要：
正交匹配追踪（OMP）一直被认为是一个强大的启发式攻击压缩感知问题，然而，它的理论发展，不幸的是，有些缺乏。本文提出了一种改进的约束等距属性（RIP）的T稀疏信号重建的性能保证，渐近接近Davenport等人给出的约束下界。我们还进一步扩展了最先进的推导重建误差界的情况下，一般的非稀疏信号的测量噪声。然后，我们推广我们的结果的情况下，K倍正交匹配追踪（KOMP）。最后，我们提出了一个实证分析表明，OMP和KOMP优于其他压缩感知算法在平均情况下的场景。这是非常令人惊讶的，因为RIP分析（即最坏情况）表明，这些匹配追踪的性能应该比凸优化、CoSAMP和迭代保持差大约T^0.5倍。
英文摘要：
Orthogonal Matching Pursuit (OMP) has long been considered a powerful heuristic for attacking compressive sensing problems; however, its theoretical development is, unfortunately, somewhat lacking. This paper presents an improved Restricted Isometry Property (RIP) based performance guarantee for T-sparse signal reconstruction that asymptotically approaches the conjectured lower bound given in Davenport et al. We also further extend the state-of-the-art by deriving reconstruction error bounds for the case of general non-sparse signals subjected to measurement noise. We then generalize our results to the case of K-fold Orthogonal Matching Pursuit (KOMP). We finish by presenting an empirical analysis suggesting that OMP and KOMP outperform other compressive sensing algorithms in average case scenarios. This turns out to be quite surprising since RIP analysis (i.e. worst case scenario) suggests that these matching pursuits should perform roughly T^0.5 times worse than convex optimization, CoSAMP, and Iterative Thresholding.
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