基于流形的压缩测量信号恢复与参数估计
Manifold-Based Signal Recovery and Parameter Estimation from Compressive Measurements
摘要：
最近出现了一个被称为压缩感知（CS）的领域，以帮助解决捕获和处理高维信号和数据集的日益增长的挑战。CS利用了令人惊讶的事实，即稀疏信号中包含的信息可以保留在该信号的少量压缩（或随机）线性测量中。已经建立了强有力的理论保证的精度，稀疏或近稀疏的信号可以从嘈杂的压缩测量恢复。在本文中，我们解决类似的问题，在不同的建模框架的上下文中。而不是稀疏模型，我们专注于广泛的类流形模型，这可能会出现在参数和非参数信号的家庭。最近的结果有关的测量空间内的流形的稳定嵌入的基础上，我们建立了确定性和概率的$\ell_2$基于流形的信号恢复和参数估计从噪声压缩测量的实例最优边界。与基于稀疏性的CS的类似结果一致，我们得出结论，在概率环境中可能有更强的界限。我们的工作支持了越来越多的经验证据，即基于流形的模型可以在压缩信号处理中以高精度使用。
英文摘要：
A field known as Compressive Sensing (CS) has recently emerged to help address the growing challenges of capturing and processing high-dimensional signals and data sets. CS exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive (or random) linear measurements of that signal. Strong theoretical guarantees have been established on the accuracy to which sparse or near-sparse signals can be recovered from noisy compressive measurements. In this paper, we address similar questions in the context of a different modeling framework. Instead of sparse models, we focus on the broad class of manifold models, which can arise in both parametric and non-parametric signal families. Building upon recent results concerning the stable embeddings of manifolds within the measurement space, we establish both deterministic and probabilistic instance-optimal bounds in $\ell_2$ for manifold-based signal recovery and parameter estimation from noisy compressive measurements. In line with analogous results for sparsity-based CS, we conclude that much stronger bounds are possible in the probabilistic setting. Our work supports the growing empirical evidence that manifold-based models can be used with high accuracy in compressive signal processing.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
