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

Li Zhang, Zening Fu, Wenwen Zhang, Gan Huang, Zhen Liang, Linling Li, Bharat B. Biswal, Vince D. Calhoun, Zhiguo Zhang

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)147-161
Number of pages15
StatePublished - Jul 5 2021

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Cognitive Neuroscience
  • Artificial Intelligence


  • Dynamic functional connectivity
  • Inverse covariance estimation
  • Sparse network
  • Spatial–temporal smoothness constraints
  • l-regularization


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