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# Authors: Denis Engemann <denis.engemann@gmail.com>
#
# License: BSD (3-clause)
import numpy as np
from numpy.polynomial.legendre import legval
from scipy import linalg
from ..fixes import einsum
from ..utils import logger, warn, verbose
from ..io.pick import pick_types, pick_channels, pick_info
from ..surface import _normalize_vectors
from ..bem import _fit_sphere
from ..forward import _map_meg_channels
def _calc_g(cosang, stiffness=4, num_lterms=50):
"""Calculate spherical spline g function between points on a sphere.
Parameters
----------
cosang : array-like of float, shape(n_channels, n_channels)
cosine of angles between pairs of points on a spherical surface. This
is equivalent to the dot product of unit vectors.
stiffness : float
stiffness of the spline.
num_lterms : int
number of Legendre terms to evaluate.
Returns
-------
G : np.ndrarray of float, shape(n_channels, n_channels)
The G matrix.
"""
factors = [(2 * n + 1) / (n ** stiffness * (n + 1) ** stiffness *
4 * np.pi) for n in range(1, num_lterms + 1)]
return legval(cosang, [0] + factors)
def _make_interpolation_matrix(pos_from, pos_to, alpha=1e-5):
"""Compute interpolation matrix based on spherical splines.
Implementation based on [1]
Parameters
----------
pos_from : np.ndarray of float, shape(n_good_sensors, 3)
The positions to interpoloate from.
pos_to : np.ndarray of float, shape(n_bad_sensors, 3)
The positions to interpoloate.
alpha : float
Regularization parameter. Defaults to 1e-5.
Returns
-------
interpolation : np.ndarray of float, shape(len(pos_from), len(pos_to))
The interpolation matrix that maps good signals to the location
of bad signals.
References
----------
[1] Perrin, F., Pernier, J., Bertrand, O. and Echallier, JF. (1989).
Spherical splines for scalp potential and current density mapping.
Electroencephalography Clinical Neurophysiology, Feb; 72(2):184-7.
"""
pos_from = pos_from.copy()
pos_to = pos_to.copy()
# normalize sensor positions to sphere
_normalize_vectors(pos_from)
_normalize_vectors(pos_to)
# cosine angles between source positions
cosang_from = pos_from.dot(pos_from.T)
cosang_to_from = pos_to.dot(pos_from.T)
G_from = _calc_g(cosang_from)
G_to_from = _calc_g(cosang_to_from)
if alpha is not None:
G_from.flat[::len(G_from) + 1] += alpha
n_channels = G_from.shape[0] # G_from should be square matrix
C = np.r_[np.c_[G_from, np.ones((n_channels, 1))],
np.c_[np.ones((1, n_channels)), 0]]
C_inv = linalg.pinv(C)
interpolation = np.c_[G_to_from,
np.ones((G_to_from.shape[0], 1))].dot(C_inv[:, :-1])
return interpolation
def _do_interp_dots(inst, interpolation, goods_idx, bads_idx):
"""Dot product of channel mapping matrix to channel data."""
from ..io.base import BaseRaw
from ..epochs import BaseEpochs
from ..evoked import Evoked
if isinstance(inst, (BaseRaw, Evoked)):
inst._data[bads_idx] = interpolation.dot(inst._data[goods_idx])
elif isinstance(inst, BaseEpochs):
inst._data[:, bads_idx, :] = einsum(
'ij,xjy->xiy', interpolation, inst._data[:, goods_idx, :])
else:
raise ValueError('Inputs of type {0} are not supported'
.format(type(inst)))
@verbose
def _interpolate_bads_eeg(inst, verbose=None):
"""Interpolate bad EEG channels.
Operates in place.
Parameters
----------
inst : mne.io.Raw, mne.Epochs or mne.Evoked
The data to interpolate. Must be preloaded.
"""
bads_idx = np.zeros(len(inst.ch_names), dtype=np.bool)
goods_idx = np.zeros(len(inst.ch_names), dtype=np.bool)
picks = pick_types(inst.info, meg=False, eeg=True, exclude=[])
inst.info._check_consistency()
bads_idx[picks] = [inst.ch_names[ch] in inst.info['bads'] for ch in picks]
if len(picks) == 0 or bads_idx.sum() == 0:
return
goods_idx[picks] = True
goods_idx[bads_idx] = False
pos = inst._get_channel_positions(picks)
# Make sure only EEG are used
bads_idx_pos = bads_idx[picks]
goods_idx_pos = goods_idx[picks]
pos_good = pos[goods_idx_pos]
pos_bad = pos[bads_idx_pos]
# test spherical fit
radius, center = _fit_sphere(pos_good)
distance = np.sqrt(np.sum((pos_good - center) ** 2, 1))
distance = np.mean(distance / radius)
if np.abs(1. - distance) > 0.1:
warn('Your spherical fit is poor, interpolation results are '
'likely to be inaccurate.')
logger.info('Computing interpolation matrix from {0} sensor '
'positions'.format(len(pos_good)))
interpolation = _make_interpolation_matrix(pos_good, pos_bad)
logger.info('Interpolating {0} sensors'.format(len(pos_bad)))
_do_interp_dots(inst, interpolation, goods_idx, bads_idx)
@verbose
def _interpolate_bads_meg(inst, mode='accurate', origin=(0., 0., 0.04),
verbose=None):
"""Interpolate bad channels from data in good channels.
Parameters
----------
inst : mne.io.Raw, mne.Epochs or mne.Evoked
The data to interpolate. Must be preloaded.
mode : str
Either `'accurate'` or `'fast'`, determines the quality of the
Legendre polynomial expansion used for interpolation. `'fast'` should
be sufficient for most applications.
origin : array-like, shape (3,) | str
Origin of the sphere in the head coordinate frame and in meters.
Can be ``'auto'``, which means a head-digitization-based origin
fit. Default is ``(0., 0., 0.04)``.
verbose : bool, str, int, or None
If not None, override default verbose level (see :func:`mne.verbose`
and :ref:`Logging documentation <tut_logging>` for more).
"""
picks_meg = pick_types(inst.info, meg=True, eeg=False,
ref_meg=True, exclude=[])
picks_good = pick_types(inst.info, meg=True, eeg=False,
ref_meg=True, exclude='bads')
meg_ch_names = [inst.info['ch_names'][p] for p in picks_meg]
bads_meg = [ch for ch in inst.info['bads'] if ch in meg_ch_names]
# select the bad meg channel to be interpolated
if len(bads_meg) == 0:
picks_bad = []
else:
picks_bad = pick_channels(inst.info['ch_names'], bads_meg,
exclude=[])
# return without doing anything if there are no meg channels
if len(picks_meg) == 0 or len(picks_bad) == 0:
return
info_from = pick_info(inst.info, picks_good)
info_to = pick_info(inst.info, picks_bad)
mapping = _map_meg_channels(info_from, info_to, mode=mode)
_do_interp_dots(inst, mapping, picks_good, picks_bad)
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