Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Spherical wavelets: efficiently representing functions on the sphere
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Multiresolution analysis for surfaces of arbitrary topological type
ACM Transactions on Graphics (TOG)
BLaC-Wavelets: a multiresolution analysis with non-nested spaces
Proceedings of the 7th conference on Visualization '96
Wavelets for computer graphics: theory and applications
Wavelets for computer graphics: theory and applications
Wavelet-Based Progressive Compression Scheme for Triangle Meshes: Wavemesh
IEEE Transactions on Visualization and Computer Graphics
Wavelet-Based Multiresolution Analysis of Irregular Surface Meshes
IEEE Transactions on Visualization and Computer Graphics
Journal of Cognitive Neuroscience
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Uncertainty principles and ideal atomic decomposition
IEEE Transactions on Information Theory
Decoding by linear programming
IEEE Transactions on Information Theory
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Computer Methods and Programs in Biomedicine
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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.