Accessing dynamic functional connectivity using l₀-regularized sparse-smooth inverse covariance estimation from fMRI

Inferring dynamic functional connectivity (dFC) from functional magnetic resonance imaging (fMRI) is crucial to understand the time-variant functional inter-relationships among brain regions. Because of the sparse property of functional connectivity networks, sparsity-promoting dFC estimation methods, which are mainly based on l₁-norm regularization, are gaining popularity. However, l₁-norm regularization cannot provide the maximum sparsity solution as the most natural sparsity promoting norm, the l₀-norm. But l₀-norm is seldom used to infer sparse dFC because an efficient algorithm to address the non-convexity problem of l₀-norm is lacking. In this work, we develop a new l₀-norm regularization-based inverse covariance estimation method for estimating dFC from fMRI. This novel method employs l₀-norm regularizations on both spatial and temporal scales to enhance the spatial sparsity and temporal smoothness of dFC estimates. To overcome the non-convexity of l₀-norm, we further propose an effective optimization algorithm based on the coordinate descent (CD). The performance of the proposed l₀-norm-based sparse-smooth regularization (L0-SSR) method is examined using a series of synthetic datasets concerning various types of network topology. We further apply the proposed L0-SSR method to real fMRI data recorded in block-design motor tasks from 45 participants for the exploration of task induced dFC. Results on synthetic and real-world fMRI data show that, the L0-SSR method can achieve more accurate and interpretable dFC estimates than conventional l₁-norm-based dFC estimation methods. Hence, the proposed L0-SSR method could serve as a powerful analytical tool to infer highly complex, variable, and sparse dFC patterns.