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Unit-Noise-Gain Beamformer

Solver ID: UNIT_NOISE_GAIN

Usage

from invert import Solver

# fwd = ...    (mne.Forward object)
# evoked = ... (mne.Evoked object)

solver = Solver("UNIT_NOISE_GAIN")
solver.make_inverse_operator(fwd)
stc = solver.apply_inverse_operator(evoked)
stc.plot()

Overview

Minimum-variance beamformer variant using unit-noise-gain weight normalization (as implemented here).

References

  1. tbd

API Reference

Bases: BaseSolver

Class for the Unit Noise Gain (UNIG) Beamformer inverse solution [1].

References

[1]

Source code in invert/solvers/beamformers/unit_noise_gain.py 
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class SolverUnitNoiseGain(BaseSolver):
    """Class for the Unit Noise Gain (UNIG) Beamformer
    inverse solution [1].

    References
    ----------
    [1]
    """

    meta = SolverMeta(
        slug="unit_noise_gain",
        full_name="Unit-Noise-Gain Beamformer",
        category="Beamformers",
        description=(
            "Minimum-variance beamformer variant using unit-noise-gain weight "
            "normalization (as implemented here)."
        ),
        references=["tbd"],
    )

    def __init__(self, name="UNIG Beamformer", reduce_rank=True, rank="auto", **kwargs):
        self.name = name
        return super().__init__(reduce_rank=reduce_rank, rank=rank, **kwargs)

    def make_inverse_operator(
        self,
        forward,
        mne_obj,
        *args,
        weight_norm=True,
        noise_cov=None,
        alpha="auto",
        verbose=0,
        **kwargs,
    ):
        """Calculate inverse operator.

        Parameters
        ----------
        forward : mne.Forward
            The mne-python Forward model instance.
        mne_obj : [mne.Evoked, mne.Epochs, mne.io.Raw]
            The MNE data object.
        weight_norm : bool
            Normalize the filter weight matrix W to unit length of the columns.
        alpha : float
            The regularization parameter.

        Return
        ------
        self : object returns itself for convenience
        """
        super().make_inverse_operator(forward, *args, alpha=alpha, **kwargs)
        data = self.unpack_data_obj(mne_obj)

        leadfield = self.leadfield
        # leadfield /= np.linalg.norm(leadfield, axis=0)
        n_chans, n_dipoles = leadfield.shape

        if noise_cov is None:
            noise_cov = np.identity(n_chans)

        self.weight_norm = weight_norm

        y = data
        I = np.identity(n_chans)

        # Recompute regularization based on the max eigenvalue of the Covariance
        # Matrix (opposed to that of the leadfield)
        y -= y.mean(axis=1, keepdims=True)
        C = self.data_covariance(y, center=False, ddof=1)
        self.alphas = self.get_alphas(reference=C)
        inverse_operators = []
        for alpha in self.alphas:
            C_inv = np.linalg.inv(C + alpha * I)
            C_inv_sq = C_inv @ C_inv
            leadfield_C_inv_sq = leadfield.T @ C_inv_sq

            # Use np.einsum to compute the diagonal elements
            diag_elements = np.einsum("ij,ji->i", leadfield_C_inv_sq, leadfield)

            # W = C_inv @ leadfield * (1.0 / diag_elements)
            W = C_inv @ leadfield * (1 / np.sqrt(diag_elements))

            # W = C_inv @ leadfield @ np.linalg.pinv(leadfield.T @ C_inv @ leadfield)

            if self.weight_norm:
                W /= np.linalg.norm(W, axis=0)

            inverse_operator = W.T
            inverse_operators.append(inverse_operator)

        self.inverse_operators = [
            InverseOperator(inverse_operator, self.name)
            for inverse_operator in inverse_operators
        ]

        return self

__init__ 

__init__(
    name="UNIG Beamformer",
    reduce_rank=True,
    rank="auto",
    **kwargs,
)
Source code in invert/solvers/beamformers/unit_noise_gain.py 
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def __init__(self, name="UNIG Beamformer", reduce_rank=True, rank="auto", **kwargs):
    self.name = name
    return super().__init__(reduce_rank=reduce_rank, rank=rank, **kwargs)

make_inverse_operator 

make_inverse_operator(
    forward,
    mne_obj,
    *args,
    weight_norm=True,
    noise_cov=None,
    alpha="auto",
    verbose=0,
    **kwargs,
)

Calculate inverse operator.

Parameters:

Name Type Description Default
forward Forward

The mne-python Forward model instance.

 required
mne_obj [Evoked, Epochs, Raw]

The MNE data object.

 required
weight_norm bool

Normalize the filter weight matrix W to unit length of the columns.

 True
alpha float

The regularization parameter.

 'auto'
Return

self : object returns itself for convenience

Source code in invert/solvers/beamformers/unit_noise_gain.py 
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def make_inverse_operator(
    self,
    forward,
    mne_obj,
    *args,
    weight_norm=True,
    noise_cov=None,
    alpha="auto",
    verbose=0,
    **kwargs,
):
    """Calculate inverse operator.

    Parameters
    ----------
    forward : mne.Forward
        The mne-python Forward model instance.
    mne_obj : [mne.Evoked, mne.Epochs, mne.io.Raw]
        The MNE data object.
    weight_norm : bool
        Normalize the filter weight matrix W to unit length of the columns.
    alpha : float
        The regularization parameter.

    Return
    ------
    self : object returns itself for convenience
    """
    super().make_inverse_operator(forward, *args, alpha=alpha, **kwargs)
    data = self.unpack_data_obj(mne_obj)

    leadfield = self.leadfield
    # leadfield /= np.linalg.norm(leadfield, axis=0)
    n_chans, n_dipoles = leadfield.shape

    if noise_cov is None:
        noise_cov = np.identity(n_chans)

    self.weight_norm = weight_norm

    y = data
    I = np.identity(n_chans)

    # Recompute regularization based on the max eigenvalue of the Covariance
    # Matrix (opposed to that of the leadfield)
    y -= y.mean(axis=1, keepdims=True)
    C = self.data_covariance(y, center=False, ddof=1)
    self.alphas = self.get_alphas(reference=C)
    inverse_operators = []
    for alpha in self.alphas:
        C_inv = np.linalg.inv(C + alpha * I)
        C_inv_sq = C_inv @ C_inv
        leadfield_C_inv_sq = leadfield.T @ C_inv_sq

        # Use np.einsum to compute the diagonal elements
        diag_elements = np.einsum("ij,ji->i", leadfield_C_inv_sq, leadfield)

        # W = C_inv @ leadfield * (1.0 / diag_elements)
        W = C_inv @ leadfield * (1 / np.sqrt(diag_elements))

        # W = C_inv @ leadfield @ np.linalg.pinv(leadfield.T @ C_inv @ leadfield)

        if self.weight_norm:
            W /= np.linalg.norm(W, axis=0)

        inverse_operator = W.T
        inverse_operators.append(inverse_operator)

    self.inverse_operators = [
        InverseOperator(inverse_operator, self.name)
        for inverse_operator in inverse_operators
    ]

    return self