An intelligent approach for variable size segmentation of non-stationary signals

Abstract

In numerous signal processing applications, non-stationary signals should be segmented to piece-wise stationary epochs before being further analyzed. In this article, an enhanced segmentation method based on fractal dimension (FD) and evolutionary algorithms (EAs) for non-stationary signals, such as electroencephalogram (EEG), magnetoencephalogram (MEG) and electromyogram (EMG), is proposed. In the proposed approach, discrete wavelet transform (DWT) decomposes the signal into orthonormal time series with different frequency bands. Then, the FD of the decomposed signal is calculated within two sliding windows. The accuracy of the segmentation method depends on these parameters of FD. In this study, four EAs are used to increase the accuracy of segmentation method and choose acceptable parameters of the FD. These include particle swarm optimization (PSO), new PSO (NPSO), PSO with mutation, and bee colony optimization (BCO). The suggested methods are compared with other most popular approaches (improved nonlinear energy operator (INLEO), wavelet generalized likelihood ratio (WGLR), and Varri's method) using synthetic signals, real EEG data, and the difference in the received photons of galactic objects. The results demonstrate the absolute superiority of the suggested approach.

Keywords: Adaptive segmentation; Discrete wavelet transform; Evolutionary algorithm; Fractal dimension; Particle swarm optimization.

Fig. 1

Variation in FD when amplitude or frequency changes.

Fig. 2

Pseudo code of the basic BCO.

Fig. 3

Real photon emission data; (a) the number of received photons as a function of time and (b) the difference between the received photons.

Fig. 4

Results of applying the proposed technique with BCO to (a) original signal, (b) decomposed signal by one-level DWT, (c) output of FD, and (d) G function result. As it can be seen that the boundaries for all seven segments can be accurately detected.

Fig. 5

Results of applying the existing techniques; (a) original signal, (b) output of WGLR method, (c) output of Varri’s method, and (d) output of INLEO method.

Fig. 6

Comparison between the performances of PSO, NPSO, and PSO with mutation.

Fig. 7

Comparison between the performances of PSO with mutation and BCO.

Fig. 8

Results of the suggested methods in comparison with six existing techniques on 50 synthetic datasets; (a) Proposed method with BCO, (b) Proposed method with PSO with mutation, (c) Proposed method with NPSO, (d) Proposed method with PSO, (e) INLEO method , (f) WGLR method , (g) Varri’s method , (h) Proposed method based on the ICA , (i) Proposed method based on the GA , and (j) Proposed method in Anisheh and Hassanpour .

Fig. 9

Segmentation of real EEG data using the proposed method; (a) original signal, (b) decomposed signal after applying five-level DWT, (c) output of FD, and (d) G function result. It can be seen that all five segments can be accurately segmented.

Fig. 10

Segmentation of real EEG using the existing methods; (a) original signal, (b) output of GLR method, (c) output of WGLR method, (d) output of INLEO method, and (e) output of Varri’s method.

Fig. 11

Result of the suggested method with BCO when compared with evolutionary approach based on ICA , INLEO , WGLR and Varri’s methods, when applied to 40 real EEG datasets.

Fig. 12

Segmentation of the difference signal of the real photons arrival rates using the proposed method; (a) original signal, (b) decomposed signal after applying three-level DWT, (c) output of FD, and (d) G function result. It can be seen that all five segments can be accurately detected.

Fig. 13

Segmentation of the difference signal of the real photons’ arrival rates using the existing methods: (a) original signal, (b) output of GLR method, (c) output of WGLR method, (d) output of Varri’s method, and (e) output of INLEO method.