An expectation-maximization algorithm for space-time sparsity regularization of the MEG inverse problem

We present a framework for “space-time sparsity” (STS) regularization in the MEG inverse problem via maximization of an appropriately penalized likelihood function. STS is based on the physiological perspective that the true brain activity over a given time span is likely to involve a set of spatially and temporally local events. We employ spatial and temporal bases to represent these local events and use a penalty function to favor solutions involving only a few space-time events. Space-time sparse solutions are achieved by penalizing only the largest coefficient associated with each space-time event. We adapt the Expectation Maximization (EM) Algorithm to solve the penalized likelihood problem and illustrate the potential of our method using simulated data.