Selective minimum-norm solution of the biomagnetic inverse problem
Abstract
A new multidipole estimation method which gives a sparse solution of the biomagnetic inverse problem is proposed. This solution is extracted from the basic feasible solutions of linearly independent data equations. These feasible solutions are obtained by selecting exactly as many dipole-moments as the number of magnetic sensors. By changing the selection, we search for the minimum-norm vector of selected moments. As a result, a practically sparse solution is obtained; computer-simulated solutions for Lp-norm (p = 2, 1, 0.5, 0.2) have a small number of significant moments around the real source-dipoles. In particular, the solution for L1-norm is equivalent to the minimum-L1-norm solution of the original inverse problem. This solution can be uniquely computed by using Linear Programming.
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L1-norm regularization favors sparse source distribution and assumes that sources follow a Laplace prior distribution in Bayesian inference.
“L1-norm regularization favors sparse source distribution (57–60); it assumes that the sources follow a Laplace prior distribution in Bayesian inference.”
From Electrophysiological source imaging: A noninvasive window to brain dynamics (2018) · cites this paper as [57]
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- Authors
- Matsuura, K., & Okabe, Y.
- Affiliations
- Research Center for Advanced Science and Technology, The University of Tokyo (JP)
- ORCID
- Matsuura, K.
- Venue
- IEEE Transactions on Biomedical Engineering
- Published
- 1995-06
- Volume
- 42
- Issue
- 6
- Pages
- 608-615
- ISSN
- 0018-9294 (ISSN-L)
- OpenAlex
- W2165411673
- Cited by
- 243
- References
- 17
- Citations by year
- 2026: 3 · 2025: 8 · 2024: 5 · 2023: 6 · 2022: 2 · 2021: 6 · 2020: 6 · 2019: 9 · 2018: 6 · 2017: 7 · 2016: 7 · 2015: 7 · 2014: 9 · 2013: 13 · 2012: 11
- FWCI
- 4.35
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Biomedical Engineering (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Numerical methods in inverse problems
- Life Sciences › Neuroscience › Cognitive Neuroscience › EEG and Brain-Computer Interfaces
- Physical Sciences › Computer Science › Signal Processing › Direction-of-Arrival Estimation Techniques
- Keywords
- minimum norm solution, sparse solutions, L1 norm, Lp norms, linear programming, magnetic source localization, basic feasible solution, dipole moment
- MeSH terms
- Animals, Humans, Magnetics, Mathematics, Methods, Models, Neurological, Nervous System Physiological Phenomena, Programming, Linear, Artifacts
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