随机噪声下基于相干性的稀疏向量估计性能保证
Coherence-Based Performance Guarantees for Estimating a Sparse Vector Under Random Noise
摘要：
我们考虑从欠定测量Ax+w估计确定性稀疏向量x的问题，其中w表示高斯白噪声，A是给定的确定性字典。我们分析了三种稀疏估计算法的性能：基追踪去噪（BPDN），正交匹配追踪（OMP）和阈值。这些算法被证明可以以很高的概率实现接近预言机的性能，假设x是足够稀疏的。我们的结果是非渐近的，并且仅基于A的相干性，因此它们适用于任意字典。在高和低信噪比下观察到的性能表明了每种算法的性能保证所需的精确条件的差异。这提供了对凸松弛技术（如BPDN）的优点和缺点的见解，而不是贪婪的方法，如OMP和阈值。
英文摘要：
We consider the problem of estimating a deterministic sparse vector x from underdetermined measurements Ax+w, where w represents white Gaussian noise and A is a given deterministic dictionary. We analyze the performance of three sparse estimation algorithms: basis pursuit denoising (BPDN), orthogonal matching pursuit (OMP), and thresholding. These algorithms are shown to achieve near-oracle performance with high probability, assuming that x is sufficiently sparse. Our results are non-asymptotic and are based only on the coherence of A, so that they are applicable to arbitrary dictionaries. Differences in the precise conditions required for the performance guarantees of each algorithm are manifested in the observed performance at high and low signal-to-noise ratios. This provides insight on the advantages and drawbacks of convex relaxation techniques such as BPDN as opposed to greedy approaches such as OMP and thresholding.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
