发表机构
Oberlin College; University of Wisconsin – Madison（欧柏林学院; 威斯康星大学麦迪逊分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对从有限DFT样本恢复整数信号的问题，采用格算法将其转化为格中找短向量的问题，推导了保证成功恢复的参数估计并分析算法稳定性，数值实验验证了理论与实际恢复阈值的一致性。
AI 中文摘要
我们分析基于格（lattice）的算法，用于从部分离散傅里叶变换（DFT）测量值中恢复整数值信号。这些算法将信号恢复问题转化为在适当构造的格中寻找短向量的问题。我们推导了保证成功恢复的参数估计值，并量化这些估计值如何依赖于信号长度、初始猜测的误差以及采样的DFT系数数量。该分析刻画了反演算法的稳定性，因为格参数与所需测量精度密切相关。数值实验表明，在广泛的问题参数范围内，理论预测与观测到的恢复阈值之间存在密切一致性。
英文摘要
We analyze lattice-based algorithms for recovering integer-valued signals from partial discrete Fourier transform (DFT) measurements. These algorithms formulate signal recovery as the problem of finding short vectors in an appropriately constructed lattice. We derive parameter estimates that predict the regimes required for successful recovery and quantify how these estimates depend on the signal length, the error of an initial guess, and the number of sampled DFT coefficients. The analysis also reveals a close connection between the lattice parameters and the precision of the measured DFT coefficients, providing insight into the numerical stability of the inversion. Numerical experiments demonstrate close agreement between the theoretical predictions and observed recovery thresholds over a broad range of problem parameters.
Comments45 pages, 11 figures, 2 tables
