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Minimum Norm Estimate

Solver ID: MNE

Usage

from invert import Solver

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

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

Overview

Classic L2 minimum-norm inverse solution. Estimates source currents by minimising the L2 norm of the source distribution subject to the data fit constraint.

References

  1. Hämäläinen, M. S., & Ilmoniemi, R. J. (1994). Interpreting magnetic fields of the brain: minimum norm estimates. Medical & Biological Engineering & Computing, 32(1), 35–42.

API Reference

Bases: BaseSolver

Class for the Minimum Norm Estimate (MNE) inverse solution [1].

The formulas provided by [2] were used for implementation.

References

[1] Pascual-Marqui, R. D. (1999). Review of methods for solving the EEG inverse problem. International journal of bioelectromagnetism, 1(1), 75-86.

[2] Grech, R., Cassar, T., Muscat, J., Camilleri, K. P., Fabri, S. G., Zervakis, M., ... & Vanrumste, B. (2008). Review on solving the inverse problem in EEG source analysis. Journal of neuroengineering and rehabilitation, 5(1), 1-33.

Source code in invert/solvers/minimum_norm/mne.py 
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class SolverMNE(BaseSolver):
    """Class for the Minimum Norm Estimate (MNE) inverse solution [1].

    The formulas provided by [2] were used for implementation.

    References
    ----------
    [1] Pascual-Marqui, R. D. (1999). Review of methods for solving the EEG
        inverse problem. International journal of bioelectromagnetism, 1(1), 75-86.

    [2] Grech, R., Cassar, T., Muscat, J., Camilleri, K. P., Fabri, S. G.,
        Zervakis, M., ... & Vanrumste, B. (2008). Review on solving the inverse
        problem in EEG source analysis. Journal of neuroengineering and
        rehabilitation, 5(1), 1-33.
    """

    meta = SolverMeta(
        acronym="MNE",
        full_name="Minimum Norm Estimate",
        category="Minimum Norm",
        description=(
            "Classic L2 minimum-norm inverse solution. Estimates source currents "
            "by minimising the L2 norm of the source distribution subject to the "
            "data fit constraint."
        ),
        references=[
            "Hämäläinen, M. S., & Ilmoniemi, R. J. (1994). Interpreting magnetic fields of the brain: minimum norm estimates. Medical & Biological Engineering & Computing, 32(1), 35–42.",
        ],
    )

    def __init__(self, name="Minimum Norm Estimate", **kwargs):
        self.name = name
        super().__init__(**kwargs)
        self.require_recompute = False
        self.require_data = False

    def make_inverse_operator(self, forward, *args, alpha="auto", verbose=0, **kwargs):
        """Calculate inverse operator.

        Parameters
        ----------
        forward : mne.Forward
            The mne-python Forward model instance.
        alpha : float
            The regularization parameter. When set to a float, it is scaled
            by the largest eigenvalue of L @ L.T.

        Return
        ------
        self : object returns itself for convenience
        """
        super().make_inverse_operator(
            forward, *args, reference=None, alpha=alpha, **kwargs
        )

        leadfield = self.leadfield
        n_chans, _ = leadfield.shape

        LLT = leadfield @ leadfield.T
        inverse_operators = []
        for alpha in self.alphas:
            inverse_operator = np.linalg.solve(
                LLT + alpha * np.identity(n_chans), leadfield
            ).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='Minimum Norm Estimate', **kwargs)
Source code in invert/solvers/minimum_norm/mne.py 
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def __init__(self, name="Minimum Norm Estimate", **kwargs):
    self.name = name
    super().__init__(**kwargs)
    self.require_recompute = False
    self.require_data = False

make_inverse_operator 

make_inverse_operator(
    forward, *args, alpha="auto", verbose=0, **kwargs
)

Calculate inverse operator.

Parameters:

Name Type Description Default
forward Forward

The mne-python Forward model instance.

 required
alpha float

The regularization parameter. When set to a float, it is scaled by the largest eigenvalue of L @ L.T.

 'auto'
Return

self : object returns itself for convenience

Source code in invert/solvers/minimum_norm/mne.py 
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def make_inverse_operator(self, forward, *args, alpha="auto", verbose=0, **kwargs):
    """Calculate inverse operator.

    Parameters
    ----------
    forward : mne.Forward
        The mne-python Forward model instance.
    alpha : float
        The regularization parameter. When set to a float, it is scaled
        by the largest eigenvalue of L @ L.T.

    Return
    ------
    self : object returns itself for convenience
    """
    super().make_inverse_operator(
        forward, *args, reference=None, alpha=alpha, **kwargs
    )

    leadfield = self.leadfield
    n_chans, _ = leadfield.shape

    LLT = leadfield @ leadfield.T
    inverse_operators = []
    for alpha in self.alphas:
        inverse_operator = np.linalg.solve(
            LLT + alpha * np.identity(n_chans), leadfield
        ).T
        inverse_operators.append(inverse_operator)

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