Synthesis of EEG signals modeled using non-linear oscillator based on speech data with EKF

Abstract

In the existing literature, one of the major issue in regression technique is the noisy training data. In this research work, the mathematical model for parameter estimation of neurological signals is developed for investigation of Brain dynamics. This proposed model is developed by using non-linear dynamics of oscillator models. It is assumed that state of the brain of a given person is characterized by an unknown parameter vector ‘θ’ that parameterizes a coupled nonlinear oscillator differential equation model which generates a harmonic process serving as a model for the EEG data collected on the brain surface. It is assumed that the EEG data and speech data of the same person are correlated, so that the speech data obeys another differential equation with a parameter ‘ϕ’ that is a fixed function of the EEG a parameter ‘θ’. ‘θ’ and ‘ϕ’ are estimated by an EKF based on training process based on joint the EEG and speech data. This enables us to get accurate estimates of ‘θ’ and ‘ϕ’ for each person. This training process is repeated for ‘N’ persons and accordingly a parameter vector is obtained for each person. This completes the training process. The validation of this model involves choosing a fresh person not belonging to the training set and estimating the EEG parameter vector for this person based only on his speech data. For this, a function ‘ψ’ which correlates the speech parameter ‘ϕ’ with the EEG parameter ‘θ’ as ‘ϕ=ψ(θ̂)’ is estimated by an affine linear relationship which is substituted into the speech model. The EEG model is then used to generate this person’s EEG data and we compare this with the true EEG data of his brain. This validation scheme can also be used to classify the fresh person’s brain by comparing his parameters with those obtained from the training set.