基于Savitzky-Golay滤波与齐次微分器的自动去噪和微分用于微分嵌入吸引子重构

中文摘要 AI 辅助

微分嵌入方法旨在从含噪的测量时间序列中重构动力系统的吸引子，但这需要准确估计信号导数。我们提出了SHADED（基于Savitzky-Golay和齐次微分器的自动去噪与微分）方法，这是一种新颖的去噪及任意阶导数估计方法，能够从含噪时间序列数据中通过微分嵌入实现吸引子重构。齐次微分器（HD）在存在噪声的情况下保证有限时间导数估计，而随后的Savitzky-Golay（SG）滤波则减弱抖振。关键在于，SHADED自动从数据中提取应用HD和SG所需的所有参数，无需可能导致不准确重构的人工调参，并且如果可用，还可以纳入先验知识，从而为含噪信号的基于数据的数值微分提供一个灵活的工具。所获得的微分嵌入可以揭示底层动力学的特征，这些特征可用于例如系统辨识、模式识别以及动态状态之间的区分；后者在生物医学环境中尤为重要，有助于区分不同的生理和病理状态。我们通过在计算神经科学模型、LTspice仿真的混沌电子电路以及光电容积脉搏波和动脉血压实验记录上测试SHADED来证明其有效性：在所有上述案例研究中，SHADED均能产生准确的导数估计，并通过微分嵌入实现准确的吸引子重构（当存在真实值时）或与预期动力学一致的几何上连贯且可复现的重构（在没有真实值的情况下），而无需手动参数调整。

英文摘要

Differential embedding methods aim to reconstruct attractors of dynamical systems from noisy measured time series, but require accurate estimates of signal derivatives. We introduce SHADED (Savitzky-Golay and Homogeneous-differentiator based Automatic DEnoising and Differentiation), a novel methodology for denoising and estimation of derivatives up to an arbitrary order, which enables attractor reconstruction via differential embedding from noisy time series data. Homogeneous Differentiators (HD) guarantee finite-time derivative estimates in the presence of noise, while subsequent Savitzky-Golay (SG) filtering attenuates chattering. Crucially, SHADED extracts all parameters required for application of both HD and SG automatically from the data, without requiring manual tuning that may lead to inaccurate reconstruction, and can also incorporate prior knowledge, if available, thereby yielding a flexible tool for data-driven numerical differentiation of noisy signals. The obtained differential embeddings can reveal features of the underlying dynamics that are useful, e.g., for system identification, pattern recognition and discrimination between dynamic regimes; the latter application is particularly important in biomedical settings, to help distinguish between different physiological and pathological states. We demonstrate the efficacy of SHADED by testing it on computational neuroscience models, LTspice-simulated chaotic electronic circuits, and photoplethysmography and arterial blood pressure experimental recordings: across all these case studies, SHADED produces accurate derivative estimates and accurate attractor reconstructions via differential embedding (whenever a ground truth is available) or geometrically coherent and reproducible reconstructions consistent with the expected dynamics (in the absence of a ground truth), without the need for manual parameter tuning.

发表机构

• University of Trento（特伦托大学）
• Tel Aviv University（特拉维夫大学）

机构由 AI 辅助整理，请以论文原文为准。