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Mathematical analysis of lead field expansions (1999)
| Content Provider | CiteSeerX |
|---|---|
| Author | Taylor, John G. Ioannides, Reas A. Müller-Gärtner, Hans-Wilhem |
| Abstract | Abstract—The solution to the bioelectromagnetic inverse problem is discussed in terms of a generalized lead field expansion, extended to weights depending polynomially on the current strength. The expansion coefficients are obtained from the resulting system of equations which relate the lead field expansion to the data. The framework supports a family of algorithms which include the class of minimum norm solutions and those of weighted minimum norm, including FOCUSS (suitably modified to conform to requirements of rotational invariance). The weighted-minimum-norm family is discussed in some detail, making explicit the dependence (or independence) of the weighting scheme on the modulus of the unknown current density vector. For all but the linear case, and with a single power in the weight, a highly nonlinear system of equations results. These are analyzed and their solution reduced to tractable problems for a finite number of degrees of freedom. In the simplest magnetic field tomography (MFT) case, this is shown to possess expected properties for localized distributed sources. A sensitivity analysis supports this conclusion. Index Terms—Biomagnetic inverse problem, magnetic field tomography, magnetoencephalography. I. |
| File Format | |
| Journal | IEEE Transactions on Medical Imaging |
| Language | English |
| Publisher Date | 1999-01-01 |
| Access Restriction | Open |
| Subject Keyword | Lead Field Expansion Mathematical Analysis Magnetic Field Tomography Linear Case Weighted-minimum-norm Family Minimum Norm Solution Single Power Unknown Current Density Vector Expected Property Sensitivity Analysis Generalized Lead Field Expansion Distributed Source Index Term Biomagnetic Inverse Problem Current Strength Expansion Coefficient Nonlinear System Rotational Invariance Equation Result Bioelectromagnetic Inverse Problem Weighted Minimum Norm Finite Number |
| Content Type | Text |
| Resource Type | Article |
