Due to the nonsparse representation, the use of compressed sensing (CS) for physiological signals, such as a multichannel electroencephalogram (EEG), has been a challenge. We present a generalized Bayesian CS framework that is capable of handling representations that arise in the spatiotemporal setting. The proposed model utilizes the standard linear Gaussian observation model associated with the hierarchical modeling of data using the matrix-variate Gaussian scale mixture (GSM). It deploys various random and deterministic parameters to incorporate the knowledge of spatial and temporal correlation present in data. By varying distributions over random parameters, a family of generalized hyperbolic matrix variate distributions is derived. For estimation, we rely on variational Bayes (VB) for random parameters and expectation-maximization (EM) for deterministic parameters. Furthermore, the model is compared with recent developments in matrix-variate distribution-based modeling of data, and we briefly discuss its extension to finite mixtures of skewed distributions. Finally, the framework is applied to the steady-state visual evoked potential (SSVEP)-based EEG benchmark data set, and a comparative study is conducted to show its effectiveness for the frequency detection task. One of the crucial features of the proposed model is that it simultaneously processes multichannel signals with low computational cost and time, making it suitable for real-time systems, especially in a resource-constrained environment. IEEE