L0-regularized time-varying sparse inverse covariance estimation for tracking dynamic fMRI brain networks

Exploration of time-varying functional brain connectivity based on functional Magnetic Resonance Imaging (fMRI) data is important for understanding dynamic brain mechanisms. l₁-penalized inverse covariance is a common measure for the inference of sparse structure of functional brain networks, and it has been recently extended to estimate time-varying sparse brain networks by using a sliding window and incorporating a smoothing constraint on temporal variation. However, l₁ penalty cannot induce maximum sparsity, as compared with l₀ penalty, so l₀ penalty is supposed to have superior quality on inverse covariance estimation. This paper introduces a novel time-varying sparse inverse covariance estimation method based on dual l₀-penalties (DLP). The new DLP method estimates the sparse inverse covariance by minimizing an l₀-penalized log-likelihood function and an extra l₀ penalty on temporal homogeneity. A cyclic descent optimization algorithm is further developed to localize the minimum of the objective function. Experiment results on simulated signals show that the proposed DLP method can achieve better performance than conventional l₁-penalized methods in estimating time-varying sparse network structures under different scenarios.