Time-frequency Analysis Based On Multichannel Matching Pursuit And Application To EEG

ObjectiveMost of biomedical signals are time-varying and non-stationary signals, time-frequency analysis methods are usually used to analysis such signals. Because the time-frequency resolution of the short time Fourier transform is too low and there is cross-term interference in the Wigner-Ville distribution, this paper studies the time-frequency method based on matching pursuit algorithm. By contrast with the short time Fourier transform and Wigner-Ville distribution to verify the performance of the matching pursuit algorithm in terms of time-frequency representation. On this basis, to study the multi-channel matching pursuit algorithm, by studying the impact of different optimal atomic selection criteria for the algorithm to calculate the accuracy and computational time, then a practical optimal atomic selection criteria can be selected, and used multi-channel matching pursuit to do time-frequency representation of EEG.Methods1. Simulation and experimental studies of time-frequency method based on matching pursuitSimulation comparison is done via short time Fourier transform, Wigner-Ville distribution, smoothed pseudo Wigner-Ville distribution and mono-channel matching pursuit. To illustrate the cross-term interference in the Wigner-Ville distribution and the sensitivity of the above methods to noise, the simulation signal is the superposition of two different frequencies (6Hz and8Hz) sinusoidal signals, Gaussian white noisewere added in the signal, the SNR of the simulated signal is respectively5dB,-0.5dB, and5dB. Then these methods were used to analysis the simulation signals.On the basis of the simulation study, short time Fourier transform, Wigner-Ville distribution, smoothed pseudo Wigner-Ville distribution and mono-channel matching pursuit were used to do time-frequency representation of the EEG. The EEG data includes10cases of normal EEG and10cases of epileptic EEG.2. The study of the optimal atomic selection criteria of the multi-channel matching pursuit based on the absolute of signalThe optimal atomic selection criterion of the iterative process is one of the important research directions in the multi-channel matching pursuit algorithm. There are two optimal atomic selection criteria have been applied:based on the signal energy of the selection criteria and selection criteria based on the signal mean. While calculation accuracy of atomic selection criteria based on signal energy is high, but it has long computation time; the selection criteria based on the signal mean atomic has shorter time, but its calculation accuracy is too low. This article takes the optimal atomic selection criteria based on the signal absolute value, and compared to the first two selection criteria with simulation experiments. In the comparative experiment, the number of iterations in turn is set to10,20,50,100,200,300,400,500,600,700,800,900,1000. And can observe the impact of the three optimal atomic selection criteria in different number of iterations.Using the multi-channel matching pursuit with the optimal atomic selection criteria based on the signal absolute value to do time-frequency of EEG. The EEG data includes10cases of normal EEG and10cases of abnormal EEG.Results1. The time-frequency representation of simulation show that methods based on matching pursuit can eliminate the cross-term interference in the wigner-ville distribution; it also has good concentration of time-frequency representation and anti-jamming ability to noise. The matching pursuit time-frequency analysis also has excellent performance in the actual processing of the EEG.2. Through experiment on the optimal atomic selection criteria, the selection criteria based on signal energy has the highest calculation accuracy, but it need the longest time; the optimal atomic selection criteria based on the signal mean has the least calculation accuracy; however it need the shortest time; In this paper, we use the criteria based on the signal absolute value, the accuracy has no difference with the selection criteria based on signal energy optimal atomic on the statistical significance, but the computing time have been reduced.3. Applying the multi-channel matching pursuit to do time-frequency analysis of EEG is able to represent each lead of the EEG’information in the same plane. At a given moment, you can also observe the time-frequency information of the different leads.ConclusionsMatching pursuit can represent the signal in parameters, not only eliminates the interference in the Wigner-Ville distribution, and can obtain higher time-frequency resolution. Multi-channel matching pursuit with different optimal atomic selection criteria and the number of iterations can result in different calculation accuracy and computation time in the signal decomposition and reconstruction. Time-frequency representation based on this algorithm takes the matrix model to express the signal time-frequency information, thus can observe the difference time-frequency information between the leads at a given moment. There is a problem in this method, if two adjacent moments both exists strong time-frequency information, it may lead to the matrix overlay, and thus it may be difficult to understand the results. So time-frequency representation based on multi-channel matching pursuit needs further work.