在每通道采样数固定条件下，优化二维傅里叶压缩感知的采样模式。
Two-dimensional Fourier compressed sensing under a fixed readout budget per channel
- 针对每通道固定采样数约束，推导压缩感知矩阵互相关下界。
- 新下界高于经典Welch界，体现采样受限的影响。
- 构造确定性采样模式并验证优于随机采样，适用于成像与雷达领域。
从子采样的傅里叶表示中恢复稀疏信号是通信、雷达和成像中的重要问题。本文关注在每通道（如傅里叶域中的行或列）仅允许固定数量采样点的约束下，重构稀疏二维信号（矩阵）。对于给定的每通道采样预算，我们推导了相应压缩感知矩阵互相关性的下界。结果表明，由于采样预算受限，该下界高于经典Welch界。同时，我们构造了在一类矩阵维度和采样预算下达到该下界的确定性子采样模式，并通过仿真将其与随机采样进行对比评估。
原文摘要 · Abstract (English)
Recovering sparse signals from their subsampled Fourier representation is an important problem in communications, radar, and imaging. In this letter, we focus on reconstructing sparse 2D signals (matrices) under the constraint that only a fixed number of entries can be sampled from each channel, e.g., a row or a column in the Fourier domain. For a specified per-channel readout budget, we derive a lower bound on the mutual coherence of the corresponding compressed sensing matrix. We show that our bound is larger than the classical Welch bound, due to a limited readout budget. We also construct deterministic subsampling patterns that attain this bound for a class of matrix dimensions and readout budgets, and benchmark them against random subsampling through simulations.
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