Signal recovery from a few linear measurements of its high-order spectra
Signal recovery from a few linear measurements of its high-order spectra
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从高阶光谱的一些线性测量中恢复信号
DOI：
10.1016/j.acha.2021.10.003
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发表时间：
2022
影响因子：
2.5
通讯作者：
Kreymer, Shay
中科院分区：
文献类型：
--
作者：
Bendory, Tamir;Edidin, Dan;Kreymer, Shay
q阶谱是以信号x∈ C N为中心的q次多项式，它在信号的循环移位下是不变的。当q≥ 3时，这个多项式唯一地确定信号，直到循环移位，并且被称为高阶谱。高阶谱，特别是双谱（q= 3）和三谱（q= 4），在各种统计信号处理和成像应用中起着重要作用，如相位恢复和单粒子重建。然而，q阶谱的维数是N q− 1，远远超过x的维数，导致计算负载和存储需求增加。在这项工作中，我们表明没有必要存储和处理完整的高阶光谱：仅通过其高阶光谱的N+ 1个线性测量，就可以唯一地表征信号的对称性。证明依赖于代数几何的工具，并通过数值实验得到证实。
The q-th order spectrum is a polynomial of degree q in the entries of a signal x∈ C N, which is invariant under circular shifts of the signal. For q≥ 3, this polynomial determines the signal uniquely, up to a circular shift, and is called a high-order spectrum. The high-order spectra, and in particular the bispectrum (q= 3) and the trispectrum (q= 4), play a prominent role in various statistical signal processing and imaging applications, such as phase retrieval and single-particle reconstruction. However, the dimension of the q-th order spectrum is N q− 1, far exceeding the dimension of x, leading to increased computational load and storage requirements. In this work, we show that it is unnecessary to store and process the full high-order spectra: a signal can be uniquely characterized up to symmetries, from only N+ 1 linear measurements of its high-order spectra. The proof relies on tools from algebraic geometry and is corroborated by numerical experiments.
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影响因子：
8.6
作者：
Kurta RP;Donatelli JJ;Yoon CH;Berntsen P;Bielecki J;Daurer BJ;DeMirci H;Fromme P;Hantke MF;Maia FRNC;Munke A;Nettelblad C;Pande K;Reddy HKN;Sellberg JA;Sierra RG;Svenda M;van der Schot G;Vartanyants IA;Williams GJ;Xavier PL;Aquila A;Zwart PH;Mancuso AP
通讯作者：
Mancuso AP
影响因子：
2.5
作者：
Tamir Bendory;D. Edidin;W. Leeb;N. Sharon
通讯作者：
Tamir Bendory;D. Edidin;W. Leeb;N. Sharon
影响因子：
9.8
作者：
Maia FR;Hajdu J
通讯作者：
Hajdu J
影响因子：
2.1
作者：
N. Sharon;J. Kileel;Y. Khoo;Boris Landa;A. Singer
通讯作者：
N. Sharon;J. Kileel;Y. Khoo;Boris Landa;A. Singer
DOI：
10.1086/187367
发表时间：
1993
期刊：
The Astrophysical Journal
影响因子：
--
作者：
Xiaochun Luo
通讯作者：
Xiaochun Luo