PMB Intelligence LLC, West Lafayette, Indiana, United States of America.
PLoS One. 2011;6(9):e24331. doi: 10.1371/journal.pone.0024331. Epub 2011 Sep 6.
Chaos and random fractal theories are among the most important for fully characterizing nonlinear dynamics of complicated multiscale biosignals. Chaos analysis requires that signals be relatively noise-free and stationary, while fractal analysis demands signals to be non-rhythmic and scale-free.
METHODOLOGY/PRINCIPAL FINDINGS: To facilitate joint chaos and fractal analysis of biosignals, we present an adaptive algorithm, which: (1) can readily remove nonstationarities from the signal, (2) can more effectively reduce noise in the signals than linear filters, wavelet denoising, and chaos-based noise reduction techniques; (3) can readily decompose a multiscale biosignal into a series of intrinsically bandlimited functions; and (4) offers a new formulation of fractal and multifractal analysis that is better than existing methods when a biosignal contains a strong oscillatory component.
The presented approach is a valuable, versatile tool for the analysis of various types of biological signals. Its effectiveness is demonstrated by offering new important insights into brainwave dynamics and the very high accuracy in automatically detecting epileptic seizures from EEG signals.
混沌和随机分形理论是充分描述复杂多尺度生物信号非线性动力学的最重要理论之一。混沌分析要求信号相对无噪声且稳定，而分形分析则要求信号是非周期性且无标度的。
方法/主要发现：为了便于对生物信号进行联合混沌和分形分析，我们提出了一种自适应算法，该算法：(1)可以轻易地从信号中去除非平稳性，(2)比线性滤波器、小波去噪和基于混沌的降噪技术更有效地降低信号中的噪声；(3)可以轻易地将多尺度生物信号分解为一系列固有带宽限制的函数；(4)提供了一种新的分形和多重分形分析的表述，当生物信号包含强振荡分量时，比现有方法更好。
所提出的方法是一种非常有价值的、通用的生物信号分析工具。它的有效性通过为脑电波动力学提供新的重要见解以及从 EEG 信号中自动检测癫痫发作的非常高的准确性得到了证明。
