论文标题
压缩阶段检索：深层生成先验的最佳样品复杂性
Compressive Phase Retrieval: Optimal Sample Complexity with Deep Generative Priors
论文作者
论文摘要
压缩传感的进步提供了具有最佳样品复杂性的线性测量值的稀疏信号的重建算法，但是这种方法对非线性逆问题的自然扩展已经遇到了潜在的基本样品复杂性瓶颈。特别是，可用于稀疏先验的可压缩阶段检索的可拖动算法无法达到最佳样品复杂性。这已经在压缩阶段检索中造成了一个空旷的问题：在通用的无相相线性测量下，是否有可通过最佳样品复杂性成功的可拖动重建算法？同时，机器学习的进展导致以生成模型的形式开发了新的数据驱动的信号先验，这可以超越稀疏先验，其测量值少得多。在这项工作中，我们解决了压缩阶段检索中的开放问题，并证明生成先验可以通过允许在这个具有挑战性的非线性反问题中通过可拖动算法允许最佳样品复杂性来带来基本进步。我们还提供经验，表明在相位检索中利用生成先验可以显着优于稀疏先验。这些结果为生成先验提供了支持，作为在经验和理论上各种环境中信号恢复的新范式。这种范式的优势在于（1）生成先验可以比稀疏治疗者更简洁地表示某些类别的自然信号，（2）生成的先生允许对自然信号歧管进行直接优化，而自然信号歧管在稀疏率下进行棘手，在稀疏下，这是在稀疏中的差异，而在稀疏中，（3）（3）（3）在产生的不合时宜的问题上，优化的优化既优化了，那么优化的优化范围优化了，优化了优化的范围优化，优化了优化的范围，精心构成了精心构想，精心构成的既定范围均匀构想，这是优化的，优化了精准的范围，这是优化的，它可以构成优化的范围。非线性测量案例。
Advances in compressive sensing provided reconstruction algorithms of sparse signals from linear measurements with optimal sample complexity, but natural extensions of this methodology to nonlinear inverse problems have been met with potentially fundamental sample complexity bottlenecks. In particular, tractable algorithms for compressive phase retrieval with sparsity priors have not been able to achieve optimal sample complexity. This has created an open problem in compressive phase retrieval: under generic, phaseless linear measurements, are there tractable reconstruction algorithms that succeed with optimal sample complexity? Meanwhile, progress in machine learning has led to the development of new data-driven signal priors in the form of generative models, which can outperform sparsity priors with significantly fewer measurements. In this work, we resolve the open problem in compressive phase retrieval and demonstrate that generative priors can lead to a fundamental advance by permitting optimal sample complexity by a tractable algorithm in this challenging nonlinear inverse problem. We additionally provide empirics showing that exploiting generative priors in phase retrieval can significantly outperform sparsity priors. These results provide support for generative priors as a new paradigm for signal recovery in a variety of contexts, both empirically and theoretically. The strengths of this paradigm are that (1) generative priors can represent some classes of natural signals more concisely than sparsity priors, (2) generative priors allow for direct optimization over the natural signal manifold, which is intractable under sparsity priors, and (3) the resulting non-convex optimization problems with generative priors can admit benign optimization landscapes at optimal sample complexity, perhaps surprisingly, even in cases of nonlinear measurements.
