论文标题
子空间阶段检索
Subspace Phase Retrieval
论文作者
论文摘要
近年来，阶段检索在统计，应用数学和光学工程方面受到了很多关注。在本文中，我们提出了一种有效的算法，称为子空间阶段检索（SPR），它可以准确地恢复$ n $二维的$ k $ k $ -sparse complect-complect-complect-complect-valued Signal $ \ x $，给定其$ω（k^2 \ log n）$ ofer lassimuty-lyly高斯样本，如果最低的高斯noverimim nokimim nokimim nokimim nimum nimim unsuse $ $ $ \ x $ \ x $ \ x x =ω（\ | \ x \ |/\ sqrt {k}）$。 Furthermore, if the energy sum of the most significant $\sqrt{k}$ elements in $\x$ is comparable to $\|\x\|^2$, the SPR algorithm can exactly recover $\x$ with $Ω(k \log n)$ magnitude-only samples, which attains the information-theoretic sampling complexity for sparse phase retrieval.数值实验表明，与现有的实验相比，所提出的算法实现了最新的重建性能。
In recent years, phase retrieval has received much attention in statistics, applied mathematics and optical engineering. In this paper, we propose an efficient algorithm, termed Subspace Phase Retrieval (SPR), which can accurately recover an $n$-dimensional $k$-sparse complex-valued signal $\x$ given its $Ω(k^2\log n)$ magnitude-only Gaussian samples if the minimum nonzero entry of $\x$ satisfies $|x_{\min}| = Ω(\|\x\|/\sqrt{k})$. Furthermore, if the energy sum of the most significant $\sqrt{k}$ elements in $\x$ is comparable to $\|\x\|^2$, the SPR algorithm can exactly recover $\x$ with $Ω(k \log n)$ magnitude-only samples, which attains the information-theoretic sampling complexity for sparse phase retrieval. Numerical Experiments demonstrate that the proposed algorithm achieves the state-of-the-art reconstruction performance compared to existing ones.
