Fractal Analysis on Artificial Profiles and Electroencephalography Signals by Roughness Scaling Extraction Algorithm

Abstract

Electroencephalography (EEG) was widely investigated in brain status detection and disease diagnosis, in which the fractal analysis played an important role. In this paper, the roughness scaling extraction (RSE) algorithm proposed in our previous study on surface morphologies was applied to calculate the fractal dimensions (FDs) of artificial profiles and EEG signals. Fractal profiles with ideal FDs ranging from 1.01 to 1.99 were generated through the Weierstrass-Mandelbrot function. The RSE algorithm and the traditional algorithms, including the Higuchi algorithm, the Katz algorithm, and the box counting algorithm, were compared by analyzing the artificial profiles. Based on the mean relative errors and mean square errors, it was found that the RSE algorithm was more accurate than the traditional algorithms. To investigate the influence of noise on FD calculation, noise with different levels was added to the fractal profiles. The RSE and Higuchi algorithms were found reliable at signal-to-noise ratios of 50 and 40 dB, while the accuracy of RSE was also superior to that of the Higuchi. The RSE, Higuchi, and Katz algorithms were utilized to analyze the EEG signals of epilepsy events. The significant FD increasing, which corresponded to the seizure onset, could be detected, and the overlapping between the seizure and non-seizure statuses was small by using the RSE algorithm, indicating its feasibility for the EEG fractal analysis.

Variation Trends of Fractal Dimension in Epileptic EEG Signals

“…The denoising process for EEG signals was essential and there were lots of noise reduction methods, such as wavelet decomposition [28,29] and empirical mode decomposition (EMD) [30,31]. To be consistent with previous research, the denoising process in this study was wavelet decomposition with passband filtering and had been widely used to alleviate the noise influences [22,23,28,29]. The reason for the abovementioned difference of D variations were analyzed and it was found that the denoising operation had an important influence on D variation trend.…”

“…An important basis for using the fractal algorithms to detect epileptic seizures was the D variation during seizure status compared with normal status. However, it was found that some publications reported that D in the seizure status had a downward trend [21,24,25], while other literature reported an upward trend of D variation [20,22,23,26,27], and such a significant divergence and its cause had not been studied in the available literature. Such a significant difference seriously undermined the feasibility and even the reliability of fractal algorithms in epileptic detection.…”

“…Currently, there were many commonly used fractal algorithms, among which the Higuchi algorithm was highly recommended because of its accuracy and high speed [20,21]. In our previous studies, roughness scaling extraction (RSE) algorithm was proposed to detect epileptic seizures, which could be more accurate to calculate fractal dimension (D) relative to the traditional algorithms including Higuchi algorithm [22,23].…”

A Novel Self-Adaptive Wind Speed Prediction Model Considering Atmospheric Motion and Fractal Feature

“…Box-counting dimension algorithm is a classical method to calculate fractal dimension [44]. The Hurst index H is an important parameter in box-counting dimension method.…”

Evaluation of performance fatigability through surface EMG in health and muscle disease: state of the art

“…In addition, Wang et al (2019) introduced a new algorithm named 'roughness scaling extraction' (RSE) to evaluate FD based on a single morphological image. It was found that RSE algorithm was much more accurate than the traditional algorithms.…”