Evolutionary coherence on EEG signals for epileptic seizure detection

Electroencephalogram (EEG) signal for epileptic seizure is nonstationary by nature. The onset of epileptic seizure is determined by the increase in synchronicity of firing neurons, and the spreading of epileptic seizure could be traced with investigating on the evolution of synchronicity across channels. However, there are only a few previous studies on utilizing evolutionary coherence in detecting epileptic seizure EEG events. Besides that, these researches also mostly focus on only a few channels for mere simple and quick comparison. There is also a lack of research in comparing coherence analysis from different non-parametric approaches. Therefore, this research aims to analyze the brain connectivity in EEG epileptic seizure using nonstationary coherence by applying specifically SLEX coherence, wavelet coherence and STFT coherence. The algorithm is tested on a real epileptic seizure patient with focal epilepsy seizure at the left temporal lobe. The coherence obtained is further plotted using Circos software package, which is advantageous in mapping complex links and relationships. In conclusion, evolutionary coherence on EEG signals for epileptic seizure detection has been performed using STFT, wavelet and SLEX coherence. It was found that wavelet and SLEX coherence are capable of epileptogenic focus localization and seizure prediction, with wavelet coherence showing slightly better performance

A Statistical Study of Wavelet Coherence for Stationary and Nonstationary Processes

The coherence function measures the correlation between a pair of random processes in the frequency domain. It is a well studied and understood concept, and the distributional properties of conventional coherence estimators for stationary processes have been derived and applied in a number of physical settings. In recent years the wavelet coherence measure has been used to analyse correlations between a pair of processes in the time-scale domain, typically in hypothesis testing scenarios, but it has proven resistant to analytic study with resort to simulations for statistical properties. As part of the null hypothesis being tested, such simulations invariably assume joint stationarity of the series. In this thesis two methods of calculating wavelet coherence have been developed and distributional properties of the wavelet coherence estimators have been fully derived. With the first method, in an analogous framework to multitapering, wavelet coherence is estimated using multiple orthogonal Morse wavelets. The second coherence estimator proposed uses time-domain smoothing and a single Morlet wavelet. Since both sets of wavelets are complex-valued, we consider the case of wavelet coherence calculated from discrete-time complex-valued and stationary time series. Under Gaussianity, the Goodman distribution is shown, for large samples, to be appropriate for wavelet coherence. The true wavelet coherence value is identified in terms of its frequency domain equivalent and degrees of freedom can be readily derived. The theoretical results are verified via simulations. The notion of a spectral function is considered for the nonstationary case. Particular focus is given to Priestley’s evolutionary process and a Wold-Cramér nonstationary representation where time-varying spectral functions can be clearly defined. Methods of estimating these spectra are discussed, including the continuous wavelet transform, which when performed with a Morlet wavelet and temporal smoothing is shown to bear close resemblance to Priestley’s own estimation procedure. The concept of coherence for bivariate evolutionary nonstationary processes is discussed in detail. In such situations it can be shown that the coherence function, as in the stationary case, is invariant of time. It is shown that for spectra that vary slowly in time the derived statistics of the temporally smoothed wavelet coherence estimator are appropriate. Further to this the similarities with Priestleys spectral estimator are exploited to derive distributional properties of the corresponding Priestley coherence estimator. A well known class of the evolutionary and Wold-Cramér nonstationary processes are the modulated stationary processes. Using these it is shown that bivariate processes can be constructed that exhibit coherence variation with time, frequency, and time-and-frequency. The temporally smoothed Morlet wavelet coherence estimator is applied to these processes. It is shown that accurate coherence estimates can be achieved for each type of coherence, and that the distributional properties derived under stationarity are applicable

Spectral analysis for nonstationary audio

A new approach for the analysis of nonstationary signals is proposed, with a focus on audio applications. Following earlier contributions, nonstationarity is modeled via stationarity-breaking operators acting on Gaussian stationary random signals. The focus is on time warping and amplitude modulation, and an approximate maximum-likelihood approach based on suitable approximations in the wavelet transform domain is developed. This paper provides theoretical analysis of the approximations, and introduces JEFAS, a corresponding estimation algorithm. The latter is tested and validated on synthetic as well as real audio signal.Comment: IEEE/ACM Transactions on Audio, Speech and Language Processing, Institute of Electrical and Electronics Engineers, In pres