One effect of a maximum possible current strength Page: 4 of 6
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If there are no constraints on the current, this situation can easily arise whenever the number of source parameters
(dipole moments) is large compared to the number of measurements. Here we examine the extent to which a con-
straint on the maximum possible dipole moment per unit area can reduce this ambiguity.
To see why this might happen: Suppose there really is current in region I; a particular reconstruction algo-
rithm may miss that current but still fit the data, by assigning extra current in region H1. In this case, a constraint on
the maximum possible dipole moment per unit area may be able to prevent this from happening, especially if region I
Source Space and Sensor Array
To take a first look at this question, we have chosen the simple source space and sensor array shown in Fig.2.
Fig.2. The two planes of the source space,
ABC and ACD, and the array of
magnetic field sensors.
The source space contains portions of two perpendicular planes, ABC and ACD. Each one is 5cm x 5cm and
divided into 28 x 28 pixels. The dipoles are normal to the planes (tangential). The total number of dipole moments
for this source space is 2 x 28 x 28 = 1,568. A spherical head model is assumed in our calculation. The sensor array
forms a hemisphere 12 cm from the origin, and 127 radially oriented magnetic field sensors have been assigned to the
The number of parameters available to describe a current source (1,568) is very much larger than the number
of measurements (127); consequently any given data set can be explained with a very large number (1,568 - 127 =
1,441) of different currents. This leads to a large degree of ambiguity for the inverse problem.
We place a source in the center of the ABC plane as shown in Fig.3. The magnetic field produced by this
source is then calculated at all the sensors. There is no noise added to the data. Note that the dipole moment per unit
area of this source does not exceed I per pixel area. We take this to be the maximum allowed value for the dipole
moment per unit area.
Here is the central question: Given this simulated magnetic field data, can we be certain that there is current
in the central region of the ABC plane, if the only constraint is a maximum allowed value for the dipole moment per
unit area? To answer this question, we perform the following steps. Force the current to be zero in the
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Huang, M. & Heller, L. One effect of a maximum possible current strength, article, June 1, 1996; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc668720/m1/4/: accessed April 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.