Multifractal Analysis in Neuroimaging

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.