Sparse Autoregressive Modeling via the Least Absolute LP-Norm Penalized Solution

The conventional autoregressive (AR) model has been widely applied in the various electroencephalogram (EEG) analyses such as spectrum estimation, waveform fittings, and in classification tasks. Nevertheless, evoked EEG is usually inevitably contaminated by multiple background activities (ongoing EEG) as well as the strong outliers which may distort the AR estimates of various AR estimation methods including LS, Yule-Walker, and Burg. Moreover, current AR approaches perform well only when the length of the time-series is much larger than the number of brain sites studied, which is exactly the reverse of the situation in neuroimaging whereby relatively short time-series are measured over thousands of voxels thus the need for penalized methods to obtain sparse solutions. In this paper, we introduce a novel ADMM-based AR estimator termed LAPPS (Least Absolute LP (0