Grouped L0 least squares penalised Magnetoencephalography

The distributed source inverse problem for Magnetoencephalography (MEG) requires regularisation in order to calculate a stable and accurate solution. Recently there has been interest in source reconstruction via the l₁ penalised least squares problem. Although this gives some sparseness the ideal measure for sparsity is the l₀ norm. Here we develop a cyclic descent algorithm to solve the grouped-variable l₀ penalised least squares problem for an underdetermined linear system. We demonstrate the utility of this method on real MEG data and show an increase in sparsity achieved using the l₀ instead of the l₁ penalty.