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

Mitra, P. P., Maniar, H. (September 2006) Concentration maximization and local basis expansions (LBEX) for linear inverse problems. IEEE Trans Biomed Eng, 53 (9). pp. 1775-82. ISSN 0018-9294 (Print)

DOI: 10.1109/TBME.2006.876629


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.

Item Type: Paper
Uncontrolled Keywords: Algorithms Brain physiology Brain Mapping methods Computer Simulation Diagnosis Computer-Assisted methods Electroencephalography methods Evoked Potentials physiology Humans Likelihood Functions Linear Models Magnetoencephalography methods Models Neurological
Subjects: organs, tissues, organelles, cell types and functions > organs types and functions > brain
bioinformatics > computational biology
bioinformatics > quantitative biology > fourier analysis
CSHL Authors:
Communities: CSHL labs > Mitra lab
Depositing User: CSHL Librarian
Date: September 2006
Date Deposited: 12 Dec 2011 20:49
Last Modified: 19 Apr 2018 18:59
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