Dual signal subspace projection (DSSP): a novel algorithm for removing large interference in biomagnetic measurements

Abstract

Objective In functional electrophysiological imaging, signals are often contaminated by interference that can be of considerable magnitude compared to the signals of interest. This paper proposes a novel algorithm for removing such interferences that does not require separate noise measurements. Approach The algorithm is based on a dual definition of the signal subspace in the spatial- and time-domains. Since the algorithm makes use of this duality, it is named the dual signal subspace projection (DSSP). The DSSP algorithm first projects the columns of the measured data matrix onto the inside and outside of the spatial-domain signal subspace, creating a set of two preprocessed data matrices. The intersection of the row spans of these two matrices is estimated as the time-domain interference subspace. The original data matrix is projected onto the subspace that is orthogonal to the interference subspace Main results The DSSP algorithm is validated first by using the computer generated data, and then by using two sets of real biomagnetic data: SCEF data measured from a healthy volunteer and MEG data from a patient with a vagus nerve stimulator. Significance The proposed DSSP algorithm is effective for removing overlapped interference in a wide variety of biomagnetic measurements.

Beamspace dual signal space projection (bDSSP): a method for selective detection of deep sources in MEG measurements

“…Using this Π isc as the projector onto the interference subspace ${\mathrm{scriptK}}_{\text{I}}$, the interference removal is achieved and the signal matrix is estimated such that $${\hat{\mathit{B}}}_S=\mathit{B}\left(\mathit{I}-{\mathrm{bold-italic\Pi }}_{isc}\right)=\mathit{B}\left(\mathit{I}-\left[{\psi }_1,\dots ,{\psi }_r\right]{\left[{\psi }_1,\dots ,{\psi }_r\right]}^T\right).$$ The method of removing the interference in a manner described above is called DSSP [24]. Note that since the basis vectors of the intersection, ψ 1 …, ψ r , span only a subset of the interference subspace ${\mathrm{scriptK}}_{\text{I}}$, this method cannot perfectly remove interferences.…”

“…The orthonormal basis set of the intersection, rsp( P deep B ) ∩ rsp(( I − P deep ) B ), can be obtained using the procedure presented in [24, 27, 28]. Denoting these orthonormal basis vectors by ϕ 1, … , ϕ r , the projector onto the intersection is obtained as $${\mathrm{bold-italic\Pi }}_{isc}=\left[{\varphi }_1,\dots ,{\varphi }_r\right]{\left[{\varphi }_1,\dots ,{\varphi }_r\right]}^T.$$ Using this Π isc as the projector onto the signal subspace ${\mathrm{scriptK}}_{\text{sup}}$, the signal from the deep source is estimated by projecting the rows of the data matrix onto the direction orthogonal to ${\mathrm{scriptK}}_{\text{sup}}$, such that $${\hat{\mathit{B}}}_{\text{deep}}=\mathit{B}\left(\mathit{I}-{\mathrm{bold-italic\Pi }}_{isc}\right)=\mathit{B}\left(\mathit{I}-\left[{\varphi }_1,\dots ,{\varphi }_r\right]{\left[{\varphi }_1,\dots ,{\varphi }_r\right]}^T\right).$$ Note that since the basis vectors ϕ 1 ,…, ϕ r span only a part of ${\mathrm{scriptK}}_{\text{sup}}$, the orthogonal projection on the right-hand side of equation (29) cannot perfectly remove B sup .…”

“…The proposed method is a combination of the beamspace processing with the previously-proposed interference suppression method called dual signal space projection (DSSP) [24]. Thus, the proposed method is here called beamspace DSSP (bDSSP).…”

Subspace-based interference removal methods for a multichannel biomagnetic sensor array

“…If the intersection $\text{rsp}\left({bold-italicnormal\breve{P}}_{S}B\right)\cap \text{rsp}\left(\left(I-{bold-italicnormal\breve{P}}_S\right)B\right)$ is a reasonable approximation of ${\mathrm{scriptK}}_I$, this time-domain SSP will be able to remove interferences effectively. The method of removing the interference in a manner as described above is called dual signal subspace projection (DSSP) [11]. …”

“…These methods rely on some implicit assumptions that are generally hidden behind their formulations, but they can be revealed by our analysis using the notion of the time domain SSP. Such methods include adaptive noise canceling [6, 7], sensor noise suppression [8], common temporal subspace projection [9], spatio-temporal signal space separation [10] and the recently-proposed dual signal subspace projection [11]. …”