Neuroelectric source imaging using 3SCO: A space coding algorithm based on particle swarm optimization and l0 norm constraint

The electroencephalogram (EEG) neuroelectric sources inverse problem is usually underdetermined and lacks a unique solution, which is due to both the electromagnetism Helmholtz theorem and the fact that there are fewer observations than the unknown variables. One potential choice to tackle this issue is to solve the underdetermined system for a sparse solution. Aiming to the sparse solution, a novel algorithm termed 3SCO (Solution Space Sparse Coding Optimization) is presented in this paper. In 3SCO, after the solution space is coded with some particles, the particle-coded space is compressed by the evolution of particle swarm optimization algorithm, where an l0 constrained fitness function is introduced to guarantee the selection of a suitable sparse solution for the underdetermined system. 3SCO was first tested by localizing simulated EEG sources with different configurations on a realistic head model, and the comparisons with minimum norm (MN), LORETA (low resolution electromagnetic tomography), l1 norm solution and FOCUSS (focal underdetermined system solver) confirmed that a good sparse solution for EEG source imaging could be achieved with 3SCO. Finally, 3SCO was applied to localize the neuroelectric sources in a visual stimuli related experiment and the localized areas were basically consistent with those reported in previous studies.