Abstract：
The characteristics of biomedical signals are not captured by conventional measures like the average amplitude of the signal. The methodologies derived from fractal geometry have been a very useful approach to study the degree of irregularity of a signal. The monofractal analysis of a signal is defined by a single power-law exponent in assuming a scale invariance in time and space. However, temporal and spatial variation in the scale-invariant structure of the biomedical signal often appears. In this case, multifractal analysis is well-suited because it is defined by a multifractal spectrum of power-law exponents. There are several approaches to the implementation of this analysis, and there are numerous ways to present these.In this chapter, we review the use of multifractal analysis for the purpose of characterizing signals in neuroimaging. After describing the tenets of multifractal analysis, we present several approaches to estimating the multifractal spectrum. Finally, we describe the applications of this spectrum on biomedical signals in the characterization of several diseases in neurosciences.
摘要：
生物医学信号的特征不能通过常规测量(如信号的平均幅度)来捕获。从分形几何中得出的方法一直是研究信号不规则程度的非常有用的方法。在假设时间和空间上的尺度不变性时，信号的单分形分析由单个幂律指数定义。然而,生物医学信号的尺度不变结构的时空变化经常出现。在这种情况下,多重分形分析非常适合，因为它是由幂律指数的多重分形谱定义的。有几种方法可以实现这种分析，有很多方法来呈现这些。在这一章中,我们回顾了多重分形分析在神经影像学中表征信号的应用。在描述了多重分形分析的原理之后，我们提出了几种估计多重分形谱的方法。最后,我们描述了该光谱在生物医学信号中在神经科学中几种疾病表征中的应用。
