用图像先验突破相位恢复的采样极限，实现超低测量下的精准重建
Breaking the Weak Recovery Limit in Random Phase Retrieval with Learned Regularizers
- 引入多种图像先验，结合物理真实的随机测量模型
- 在远低于理论弱恢复限的采样率下仍能准确重构信号
- 为低采样场景下的信号恢复提供新思路，适合压缩感知与成像研究者
我们旨在从仅含幅度的非线性测量中恢复未知信号，这是一个具有挑战性的反问题。尽管理想化的随机测量已有较强的理论保证，定义了信号恢复所需的采样比，但这些结果忽略了信号先验，而先验可能从根本上改变恢复极限，从而实现更少测量和更简单模型下的重建。本文在严重欠采样的条件下，评估了多种图像先验在物理基础随机测量模型中的表现。结果表明，这些先验可使信号在远低于弱恢复极限（即优于随机猜测的理论阈值）的条件下实现高精度恢复。
原文摘要 · Abstract (English)
We seek to recover an unknown signal from nonlinear amplitude-only measurements, a challenging inverse problem. Strong theoretical guarantees have been established for idealized random measurements, defining the sampling ratio required for signal recovery. However, these results neglect signal priors, which can fundamentally shift these limits, potentially enabling reconstruction with far fewer measurements and simpler models. We evaluate a variety of image priors in the context of severe undersampling with physically-grounded random measurement models. Our results show that these priors enable accurate recovery well below the weak recovery limit, the theoretical threshold required for recovery better than a random guess.
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