Time–frequency localized three-band biorthogonal wavelet filter bank using semidefinite relaxation and nonlinear least squares with epileptic seizure EEG signal classification

Abstract

In this paper, we design time–frequency localized three-band biorthogonal linear phase wavelet filter bank for epileptic seizure electroencephalograph (EEG) signal classification. Time–frequency localized analysis and synthesis low-pass filters (LPF) are designed using convex semidefinite programming (SDP) by transforming a nonconvex problem into a convex SDP using semidefinite relaxation technique. Three-band parameterized lattice biorthogonal linear phase perfect reconstruction filter bank (BOLPPRFB) is chosen and nonlinear least squares algorithm is used to determine its parameters values that generate the designed analysis and synthesis LPF such that the band-pass and high-pass filters are also well localized in time and frequency domain. The designed analysis and synthesis three-band wavelet filter banks are compared with the standard two-band filter banks like Daubechies maximally regular filter banks, Cohen–Daubechies–Feauveau (CDF) biorthogonal filter banks and orthogonal time–frequency localized filter banks. Kruskal–Wallis statistical test is employed to measure the statistical significance of the subband features obtained from the various two and three-band filter banks for epileptic seizure EEG signal classification. The results show that the designed three-band analysis and synthesis filter banks both outperform two-band filter banks in the classification of seizure and seizure-free EEG signals. The designed three-band filter banks and multi-layer perceptron neural network (MLPNN) are further used together to implement a signal classifier that provides classification accuracy better than the recently reported results for epileptic seizure EEG signal classification.