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

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.