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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 ..utils import logger, warn, verbose
from ..io.meas_info import _simplify_info
from ..io.pick import pick_types, pick_channels, pick_info
from ..surface import _normalize_vectors
from ..forward import _map_meg_or_eeg_channels
from ..utils import _check_option, _validate_type
def _calc_h(cosang, stiffness=4, n_legendre_terms=50):
"""Calculate spherical spline h function between points on a sphere.
Parameters
----------
cosang : array-like | float
cosine of angles between pairs of points on a spherical surface. This
is equivalent to the dot product of unit vectors.
stiffness : float
stiffnes of the spline. Also referred to as ``m``.
n_legendre_terms : int
number of Legendre terms to evaluate.
"""
factors = [(2 * n + 1) /
(n ** (stiffness - 1) * (n + 1) ** (stiffness - 1) * 4 * np.pi)
for n in range(1, n_legendre_terms + 1)]
return legval(cosang, [0] + factors)
def _calc_g(cosang, stiffness=4, n_legendre_terms=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.
n_legendre_terms : 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, n_legendre_terms + 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.
"""
from scipy import linalg
pos_from = pos_from.copy()
pos_to = pos_to.copy()
n_from = pos_from.shape[0]
n_to = pos_to.shape[0]
# 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)
assert G_from.shape == (n_from, n_from)
assert G_to_from.shape == (n_to, n_from)
if alpha is not None:
G_from.flat[::len(G_from) + 1] += alpha
C = np.vstack([np.hstack([G_from, np.ones((n_from, 1))]),
np.hstack([np.ones((1, n_from)), [[0]]])])
C_inv = linalg.pinv(C)
interpolation = np.hstack([G_to_from, np.ones((n_to, 1))]) @ C_inv[:, :-1]
assert interpolation.shape == (n_to, n_from)
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
_validate_type(inst, (BaseRaw, BaseEpochs, Evoked), 'inst')
inst._data[..., bads_idx, :] = np.matmul(
interpolation, inst._data[..., goods_idx, :])
@verbose
def _interpolate_bads_eeg(inst, origin, exclude=None, verbose=None):
if exclude is None:
exclude = list()
bads_idx = np.zeros(len(inst.ch_names), dtype=bool)
goods_idx = np.zeros(len(inst.ch_names), dtype=bool)
picks = pick_types(inst.info, meg=False, eeg=True, exclude=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]
# test spherical fit
distance = np.linalg.norm(pos - origin, axis=-1)
distance = np.mean(distance / np.mean(distance))
if np.abs(1. - distance) > 0.1:
warn('Your spherical fit is poor, interpolation results are '
'likely to be inaccurate.')
pos_good = pos[goods_idx_pos] - origin
pos_bad = pos[bads_idx_pos] - origin
logger.info('Computing interpolation matrix from {} sensor '
'positions'.format(len(pos_good)))
interpolation = _make_interpolation_matrix(pos_good, pos_bad)
logger.info('Interpolating {} sensors'.format(len(pos_bad)))
_do_interp_dots(inst, interpolation, goods_idx, bads_idx)
def _interpolate_bads_meg(inst, mode='accurate', origin=(0., 0., 0.04),
verbose=None, ref_meg=False):
return _interpolate_bads_meeg(
inst, mode, origin, ref_meg=ref_meg, eeg=False, verbose=verbose)
@verbose
def _interpolate_bads_meeg(inst, mode='accurate', origin=(0., 0., 0.04),
meg=True, eeg=True, ref_meg=False,
exclude=(), verbose=None):
bools = dict(meg=meg, eeg=eeg)
info = _simplify_info(inst.info)
for ch_type, do in bools.items():
if not do:
continue
kw = dict(meg=False, eeg=False)
kw[ch_type] = True
picks_type = pick_types(info, ref_meg=ref_meg, exclude=exclude, **kw)
picks_good = pick_types(info, ref_meg=ref_meg, exclude='bads', **kw)
use_ch_names = [inst.info['ch_names'][p] for p in picks_type]
bads_type = [ch for ch in inst.info['bads'] if ch in use_ch_names]
if len(bads_type) == 0 or len(picks_type) == 0:
continue
# select the bad channels to be interpolated
picks_bad = pick_channels(inst.info['ch_names'], bads_type,
exclude=[])
if ch_type == 'eeg':
picks_to = picks_type
bad_sel = np.in1d(picks_type, picks_bad)
else:
picks_to = picks_bad
bad_sel = slice(None)
info_from = pick_info(inst.info, picks_good)
info_to = pick_info(inst.info, picks_to)
mapping = _map_meg_or_eeg_channels(
info_from, info_to, mode=mode, origin=origin)
mapping = mapping[bad_sel]
_do_interp_dots(inst, mapping, picks_good, picks_bad)
@verbose
def _interpolate_bads_nirs(inst, method='nearest', exclude=(), verbose=None):
from scipy.spatial.distance import pdist, squareform
from mne.preprocessing.nirs import _validate_nirs_info
if len(pick_types(inst.info, fnirs=True, exclude=())) == 0:
return
# Returns pick of all nirs and ensures channels are correctly ordered
picks_nirs = _validate_nirs_info(inst.info)
nirs_ch_names = [inst.info['ch_names'][p] for p in picks_nirs]
nirs_ch_names = [ch for ch in nirs_ch_names if ch not in exclude]
bads_nirs = [ch for ch in inst.info['bads'] if ch in nirs_ch_names]
if len(bads_nirs) == 0:
return
picks_bad = pick_channels(inst.info['ch_names'], bads_nirs, exclude=[])
bads_mask = [p in picks_bad for p in picks_nirs]
chs = [inst.info['chs'][i] for i in picks_nirs]
locs3d = np.array([ch['loc'][:3] for ch in chs])
_check_option('fnirs_method', method, ['nearest'])
if method == 'nearest':
dist = pdist(locs3d)
dist = squareform(dist)
for bad in picks_bad:
dists_to_bad = dist[bad]
# Ignore distances to self
dists_to_bad[dists_to_bad == 0] = np.inf
# Ignore distances to other bad channels
dists_to_bad[bads_mask] = np.inf
# Find closest remaining channels for same frequency
closest_idx = np.argmin(dists_to_bad) + (bad % 2)
inst._data[bad] = inst._data[closest_idx]
inst.info['bads'] = [ch for ch in inst.info['bads'] if ch in exclude]
return inst
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