Linear transformations of data space in MEG

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Abstract
Magnetoencephalography (MEG) is a method which allows the non-invasive measurement of the minute magnetic field which is generated by ion currents in the brain. Due to the complex sensitivity profile of the sensors, the measured data are a non-trivial representation of the currents where information specific to local generators is distributed across many channels and each channel contains a mixture of contributions from many such generators. We propose a framework which generates a new representation of the data through a linear transformation which is designed so that some desired property is optimized in one or more new virtual channel(s). First figures of merit are suggested to describe the relation between the measured data and the underlying currents. Within this context the new framework is established by first showing how the transformation matrix itself is designed and then by its application to real and simulated data. The results demonstrate that the proposed linear transformations of data space provide a computationally efficient tool for analysis and a very much needed dimensional reduction of the data.