正交匹配追踪在受限等距性质下的表现
Orthogonal Matching Pursuit under the Restricted Isometry Property
AI总结：
本文研究了正交匹配追踪算法在字典中的性能，证明在受限等距性质条件下，OMP能生成近最优的n项逼近。
摘要：
本文研究了正交匹配追踪算法在字典中的性能，证明在受限等距性质条件下，OMP能生成近最优的n项逼近。
英文摘要：
This paper is concerned with the performance of Orthogonal Matching Pursuit (OMP) algorithms applied to a dictionary $\mathcal{D}$ in a Hilbert space $\mathcal{H}$. Given an element $f\in \mathcal{H}$, OMP generates a sequence of approximations $f_n$, $n=1,2,\dots$, each of which is a linear combination of $n$ dictionary elements chosen by a greedy criterion. It is studied whether the approximations $f_n$ are in some sense comparable to {\em best $n$ term approximation} from the dictionary. One important result related to this question is a theorem of Zhang \cite{TZ} in the context of sparse recovery of finite dimensional signals. This theorem shows that OMP exactly recovers $n$-sparse signal, whenever the dictionary $\mathcal{D}$ satisfies a Restricted Isometry Property (RIP) of order $An$ for some constant $A$, and that the procedure is also stable in $\ell^2$ under measurement noise. The main contribution of the present paper is to give a structurally simpler proof of Zhang's theorem, formulated in the general context of $n$ term approximation from a dictionary in arbitrary Hilbert spaces $\mathcal{H}$. Namely, it is shown that OMP generates near best $n$ term approximations under a similar RIP condition.
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。
