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IEEE Trans Biomed Eng · Sep 2006
Concentration maximization and local basis expansions (LBEX) for linear inverse problems.
- Partha P Mitra and Hiren Maniar.
- Department of Neuroscience, Cold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724, USA. mitra@cshl.edu
- IEEE Trans Biomed Eng. 2006 Sep 1; 53 (9): 1775-82.
AbstractLinear inverse problems arise in biomedicine electroencephalography and magnetoencephalography (EEG and MEG) and geophysics. The kernels relating sensors to the unknown sources are Green's functions of some partial differential equation. This knowledge is obscured when treating the discretized kernels simply as matrices. Consequently, physical understanding of the fundamental resolution limits has been lacking. We relate the inverse problem to spatial Fourier analysis, and the resolution limits to uncertainty principles, providing conceptual links to underlying physics. Motivated by the spectral concentration problem and multitaper spectral analysis, our approach constructs local basis sets using maximally concentrated linear combinations of the measurement kernels.
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