  Magnetoencephalography (MEG) is a noninvasive method for measuring magnetic
flux signals caused by brain activity using sensor arrays located on or above
the scalp. A common strategy for monitoring brain activity is to place sensors
on a nearly uniform grid, or sensor array, around the head. By increasing the
total number of sensors, higher spatial-frequency components of brain activity
can be resolved as dictated by Nyquist sampling theory. Currently, there are
few principled mathematical architectures for sensor placement aside from
Nyquist considerations. However, global brain activity often exhibits
low-dimensional patterns of spatio-temporal dynamics. The low-dimensional
global patterns can be computed from the singular value decomposition and can
be leveraged to select a small number of sensors optimized for reconstructing
brain signals and localizing brain sources. Moreover, a smaller number of
sensors which are systematically chosen can outperform the entire sensor array
when considering noisy measurements. We propose a greedy selection algorithm
based upon the QR decomposition that is computationally efficient to implement
for MEG. We demonstrate the performance of the sensor selection algorithm for
the tasks of signal reconstruction and localization. The performance is
dependent upon source localization, with shallow sources easily identified and
reconstructed, and deep sources more difficult to locate. Our findings suggest
that principled methods for sensor selection can improve MEG capabilities and
potentially add cost savings for monitoring brain-wide activity.
