title: A new wavelet transform to sparsely represent cortical current densities for EEG/MEG inverse problems.
abstract: The present study investigated the use of transform sparseness of cortical current density on human brain surface to improve electroencephalography/magnetoencephalography (EEG/MEG) inverse solutions. Transform sparseness was assessed by evaluating compressibility of cortical current densities in transform domains. To do that, a structure compression method from computer graphics was first adopted to compress cortical surface structure, either regular or irregular, into hierarchical multi-resolution meshes. Then, a new face-based wavelet method based on generated multi-resolution meshes was proposed to compress current density functions defined on cortical surfaces. Twelve cortical surface models were built by three EEG/MEG softwares and their structural compressibility was evaluated and compared by the proposed method. Monte Carlo simulations were implemented to evaluate the performance of the proposed wavelet method in compressing various cortical current density distributions as compared to other two available vertex-based wavelet methods. The present results indicate that the face-based wavelet method can achieve higher transform sparseness than vertex-based wavelet methods. Furthermore, basis functions from the face-based wavelet method have lower coherence against typical EEG and MEG measurement systems than vertex-based wavelet methods. Both high transform sparseness and low coherent measurements suggest that the proposed face-based wavelet method can improve the performance of L1-norm regularized EEG/MEG inverse solutions, which was further demonstrated in simulations and experimental setups using MEG data. Thus, this new transform on complicated cortical structure is promising to significantly advance EEG/MEG inverse source imaging technologies.
authors.affiliation: School of Electrical and Computer Engineering, University of Oklahoma, Norman, OK, USA.
authors.forename: Ke
authors.initials: K
authors.lastname: Liao
authors.forename: Min
authors.initials: M
authors.lastname: Zhu
authors.forename: Lei
authors.initials: L
authors.lastname: Ding
mesh_terms: D000465:Algorithms; D019540:Area Under Curve; D001931:Brain Mapping / Q000379:methods; D002540:Cerebral Cortex / Q000473:pathology; D003196:Computer Graphics; D003198:Computer Simulation; D044962:Data Compression; D004569:Electroencephalography / Q000379:methods*; D004827:Epilepsy / Q000503:physiopathology; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D007802:Language; D015225:Magnetoencephalography / Q000379:methods*; D015233:Models, Statistical; D009010:Monte Carlo Method; D012984:Software; D058067:Wavelet Analysis
keywords: Compressed sensing; Compressibility; EEG/MEG; Inverse problem; Sparseness; Wavelet transform