We introduced spatial filtering methods in the spherical harmonics domain for constraining magnetoencephalographic (MEG) multichannel measurements to any user-specified spherical region of interest (ROI) inside the head. The main idea of the spatial filtering is to emphasize those signals arising from an ROI, while suppressing the signals coming from outside the ROI. We exploit a well-known method called the signal space separation (SSS), which can decompose MEG data into a signal component generated by neurobiological sources and a noise component generated by external sources outside the head. The novel methods presented in this work, expanded SSS (exSSS) and generalized expanded SSS (genexSSS) utilize a beamspace optimization criterion in order to linearly transform the inner signal SSS coefficients to represent the sources belonging to the ROI. The filters mainly depend on the radius and the center of the ROI. The simplicity of the derived formulations of our methods stems from the natural appropriateness to spherical domain and orthogonality properties of the SSS basis functions that are intimately related to the vector spherical harmonics.

ExSSS scheme: The ROI is represented by the black sphere.
GenexSSS scheme: The ROI is represented by the red sphere. The boundary between internal space and external space is represented by a red dashed circle and the virtual sphere is represented by the inside part of the blue dashed circle.

Experiment results using a rewards-based stimulation paradigm. In this paradigm, each trial proceeds as follows. The user views their current wager, is asked whether they wish to bet the entire wager for double-or-nothing (if win, wager doubles; if lose, lose entire wager) or pocket current winnings, and then is shown the outcome of the die roll.
Top Left: 102 MEG magnetometer traces ranging from the 500 ms preceeding a decision to the 800 ms following. This data has been
processed by bandpass filter, averaging, but without the exSSS processing. Note the lack of any significant visible activity.
Top Right: The same data processed with the exSSS algorithm. Note the presence of significant activity between 200ms and 350ms that was uncovered by the exSSS method.