Combining sparsity and rotational invariance in EEG/MEG source reconstruction
Abstract
We introduce Focal Vector Field Reconstruction (FVR), a novel technique for the inverse imaging of vector fields. The method was designed to simultaneously achieve two goals: a) invariance with respect to the orientation of the coordinate system, and b) a preference for sparsity of the solutions and their spatial derivatives. This was achieved by defining the regulating penalty function, which renders the solutions unique, as a global l(1)-norm of local l(2)-norms. We show that the method can be successfully used for solving the EEG inverse problem. In the joint localization of 2-3 simulated dipoles, FVR always reliably recovers the true sources. The competing methods have limitations in distinguishing close sources because their estimates are either too smooth (LORETA, Minimum l(1)-norm) or too scattered (Minimum l(2)-norm). In both noiseless and noisy simulations, FVR has the smallest localization error according to the Earth Mover's Distance (EMD), which is introduced here as a meaningful measure to compare arbitrary source distributions. We also apply the method to the simultaneous localization of left and right somatosensory N20 generators from real EEG recordings. Compared to its peers FVR was the only method that delivered correct location of the source in the somatosensory area of each hemisphere in accordance with neurophysiological prior knowledge.
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Sparsity is often assumed to avoid over-fitting in inverse problems and has increasing applications in signal and image processing.
“Sparsity is often assumed to avoid over-fitting in inverse problems, and has increasing applications in signal and image processing (43, 50–54).”
From Electrophysiological source imaging: A noninvasive window to brain dynamics (2018) · cites this paper as [52]
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- Authors
- Haufe, S., Nikulin, V. V., Ziehe, A., Müller, K.-R., & Nolte, G.
- Affiliations
- Technische Universität Berlin (DE)
- Bernstein Center for Computational Neuroscience Berlin (DE)
- Fraunhofer-Gesellschaft (DE)
- Corresponding author
- Haufe, Stefan
- Venue
- NeuroImage
- Publisher
- Elsevier BV
- Published
- 2008-08
- Volume
- 42
- Issue
- 2
- Pages
- 726-738
- ISSN
- 1053-8119 (ISSN-L)
- OpenAlex
- W2007364043
- Cited by
- 130
- References
- 41
- Citations by year
- 2026: 2 · 2025: 4 · 2024: 5 · 2023: 7 · 2022: 6 · 2021: 4 · 2020: 7 · 2019: 8 · 2018: 8 · 2017: 9 · 2016: 13 · 2015: 13 · 2014: 7 · 2013: 8 · 2012: 4
- FWCI
- 4.31
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- NeuroImage (publishedVersion)
- PubMed (publishedVersion)
- Publikationsdatenbank der Fraunhofer-Gesellschaft (Fraunhofer-Gesellschaft) (submittedVersion)
- Fraunhofer-Publica (Fraunhofer-Gesellschaft) (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- Funders
- Bundesministerium für Bildung und Forschung
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › EEG and Brain-Computer Interfaces
- Physical Sciences › Mathematics › Mathematical Physics › Numerical methods in inverse problems
- Physical Sciences › Computer Science › Signal Processing › Direction-of-Arrival Estimation Techniques
- Keywords
- EEG source reconstruction, MEG source reconstruction, rotation invariance, sparse regularization, source localization, Wasserstein distance, dipole source localization, LORETA
- MeSH terms
- Algorithms, Brain, Brain Mapping, Computer Simulation, Diagnosis, Computer-Assisted, Electroencephalography, Humans, Models, Neurological, Magnetoencephalography
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