提出混合采样策略，提升图像压缩感知的重建精度与可靠性。
Partially deterministic sampling for compressed sensing with denoising guarantees
- 结合随机与确定性采样，优化伯努利选择器的行选取方案。
- 在生成模型和稀疏先验下均实现更优重建效果，且样本复杂度更低。
- 提供新理论保证，支持去噪能力分析，适合实际高价值采样场景。
研究当采样向量从酉矩阵的行中选取时的压缩感知问题。现有方法通常随机选取采样向量，这推动了该领域的理论与实证进展。然而实际应用中常存在关键采样向量，此时从业者会偏离理论而采用确定性采样。本文针对伯努利选择器，推导出一种优化采样方案，自然融合随机与确定性行选取，严格决定哪些行应被确定性采样。该方案在生成模型与稀疏先验下的图像压缩感知中，相比有放回与无放回采样均取得显著改进，通过理论分析与数值实验验证。此外，理论保证包含更优的样本复杂度界，并首次在该设置下给出新颖的去噪保证。
原文摘要 · Abstract (English)
We study compressed sensing when the sampling vectors are chosen from the rows of a unitary matrix. In the literature, these sampling vectors are typically chosen randomly; the use of randomness has enabled major empirical and theoretical advances in the field. However, in practice there are often certain crucial sampling vectors, in which case practitioners will depart from the theory and sample such rows deterministically. In this work, we derive an optimized sampling scheme for Bernoulli selectors which naturally combines random and deterministic selection of rows, thus rigorously deciding which rows should be sampled deterministically. This sampling scheme provides measurable improvements in image compressed sensing for both generative and sparse priors when compared to with-replacement and without-replacement sampling schemes, as we show with theoretical results and numerical experiments. Additionally, our theoretical guarantees feature improved sample complexity bounds compared to previous works, and novel denoising guarantees in this setting.
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