Concentration maximization and local basis expansions (LBEX) for linear inverse problems.

Partha P Mitra; Hiren Maniar

doi:10.1109/tbme.2006.876629

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Concentration maximization and local basis expansions (LBEX) for linear inverse problems.

Partha P Mitra·Hiren Maniar

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Abstract

Linear 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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Algorithms Brain Brain Mapping Computer Simulation Diagnosis, Computer-Assisted Electroencephalography Evoked Potentials Humans Likelihood Functions Linear Models Magnetoencephalography Models, Neurological Journal Article Research Support, Non-U.S. Gov't

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Partha P Mitra, Hiren Maniar. 2006. Concentration maximization and local basis expansions (LBEX) for linear inverse problems.. https://doi.org/10.1109/tbme.2006.876629

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