稀疏三角多项式的随机采样 II - 正交匹配追踪 vs 基追踪
Random Sampling of Sparse Trigonometric Polynomials II - Orthogonal Matching Pursuit versus Basis Pursuit
AI总结：
研究通过基追踪和贪婪算法（如正交匹配追踪和阈值法）从少量随机采样中重建稀疏多元三角多项式的问题，理论分析阈值法和OMP的重建成功概率，数值实验表明基追踪速度明显慢于贪婪算法但重建率相似。
摘要：
我们研究了通过基追踪和贪婪算法（如正交匹配追踪（OMP）和阈值法）从少量随机采样中重建稀疏多元三角多项式的问题。虽然基追踪的重建最近已被多位作者研究，但我们为阈值法和OMP通过连续和离散概率模型进行采样点的重建成功概率提供了理论结果。我们进行了数值实验，结果表明通常基追踪比贪婪算法慢得多，而重建率非常相似。
英文摘要：
We investigate the problem of reconstructing sparse multivariate trigonometric polynomials from few randomly taken samples by Basis Pursuit and greedy algorithms such as Orthogonal Matching Pursuit (OMP) and Thresholding. While recovery by Basis Pursuit has recently been studied by several authors, we provide theoretical results on the success probability of reconstruction via Thresholding and OMP for both a continuous and a discrete probability model for the sampling points. We present numerical experiments, which indicate that usually Basis Pursuit is significantly slower than greedy algorithms, while the recovery rates are very similar.
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