Inverse Solution of Steady-State Responses Based on Sparse Bayesian Learning

Abstract

Steady-state responses (SSRs), evoked by various patterns of periodic stimuli, comprise an important category of evoked potentials. To explore the neural generators of SSRs, a unified framework solving the inverse problem for a single subject or integrating multiple subjects is indispensable. Inspired by the phenomenon that the oscillation frequency of an SSR follows that of the periodic stimulus, we consider the problem of source localization for SSRs using the Fourier components at the stimulation frequency instead of directly using the waveform in this paper. The multi-channel electroencephalogram (EEG) Fourier components at the stimulation frequency is shown to equal multiplying the lead field matrix (LFM) by a complex-valued vector that contains the amplitudes and phases of sources in the cortex, contaminated by spontaneous EEG and electrical noise. This complex-valued inverse problem is further solved in the framework of sparse Bayesian learning, where the non-stationarity of spontaneous EEG among epochs is considered, and the joint sparsity of complex-valued source component vectors is modeled and utilized to improve the source localization performance. Expectation-maximization (EM) is employed to give the ultimate SSR source localization algorithm. By the proposed method, not only a single subject's SSR source localization can be achieved, but also the common locations of a certain type of SSR integrating multiple subjects can be given, even when the electrode layout or number of electrodes varies among subjects. The validity and superior performance of the proposed method was verified by simulations compared with other methods. Real SSR stimulation/recording experiments were also performed, where the electric generators of 40-Hz auditory steady-state responses (ASSRs) by various stimulation patterns were investigated.