"""Compute a Recursively Applied and Projected MUltiple Signal Classification (RAP-MUSIC).""" # noqa # Authors: Yousra Bekhti # Alexandre Gramfort # # License: BSD (3-clause) import numpy as np from scipy import linalg from ..io.pick import pick_channels_evoked from ..cov import compute_whitener from ..utils import logger, verbose from ..dipole import Dipole from ._compute_beamformer import _prepare_beamformer_input, _setup_picks def _apply_rap_music(data, info, times, forward, noise_cov, n_dipoles=2, picks=None): """RAP-MUSIC for evoked data. Parameters ---------- data : array, shape (n_channels, n_times) Evoked data. info : dict Measurement info. times : array Times. forward : instance of Forward Forward operator. noise_cov : instance of Covariance The noise covariance. n_dipoles : int The number of dipoles to estimate. The default value is 2. picks : array-like of int | None Indices (in info) of data channels. If None, MEG and EEG data channels (without bad channels) will be used. Returns ------- dipoles : list of instances of Dipole The dipole fits. explained_data : array | None Data explained by the dipoles using a least square fitting with the selected active dipoles and their estimated orientation. Computed only if return_explained_data is True. """ is_free_ori, ch_names, proj, vertno, G, _ = _prepare_beamformer_input( info, forward, label=None, picks=picks, pick_ori=None) gain = G.copy() # Handle whitening + data covariance whitener, _ = compute_whitener(noise_cov, info, picks) if info['projs']: whitener = np.dot(whitener, proj) # whiten the leadfield and the data G = np.dot(whitener, G) data = np.dot(whitener, data) eig_values, eig_vectors = linalg.eigh(np.dot(data, data.T)) phi_sig = eig_vectors[:, -n_dipoles:] n_orient = 3 if is_free_ori else 1 n_channels = G.shape[0] A = np.empty((n_channels, n_dipoles)) gain_dip = np.empty((n_channels, n_dipoles)) oris = np.empty((n_dipoles, 3)) poss = np.empty((n_dipoles, 3)) G_proj = G.copy() phi_sig_proj = phi_sig.copy() for k in range(n_dipoles): subcorr_max = -1. for i_source in range(G.shape[1] // n_orient): idx_k = slice(n_orient * i_source, n_orient * (i_source + 1)) Gk = G_proj[:, idx_k] if n_orient == 3: Gk = np.dot(Gk, forward['source_nn'][idx_k]) subcorr, ori = _compute_subcorr(Gk, phi_sig_proj) if subcorr > subcorr_max: subcorr_max = subcorr source_idx = i_source source_ori = ori if n_orient == 3 and source_ori[-1] < 0: # make sure ori is relative to surface ori source_ori *= -1 # XXX source_pos = forward['source_rr'][i_source] if n_orient == 1: source_ori = forward['source_nn'][i_source] idx_k = slice(n_orient * source_idx, n_orient * (source_idx + 1)) Ak = G[:, idx_k] if n_orient == 3: Ak = np.dot(Ak, np.dot(forward['source_nn'][idx_k], source_ori)) A[:, k] = Ak.ravel() gain_k = gain[:, idx_k] if n_orient == 3: gain_k = np.dot(gain_k, np.dot(forward['source_nn'][idx_k], source_ori)) gain_dip[:, k] = gain_k.ravel() oris[k] = source_ori poss[k] = source_pos logger.info("source %s found: p = %s" % (k + 1, source_idx)) if n_orient == 3: logger.info("ori = %s %s %s" % tuple(oris[k])) projection = _compute_proj(A[:, :k + 1]) G_proj = np.dot(projection, G) phi_sig_proj = np.dot(projection, phi_sig) sol = linalg.lstsq(A, data)[0] explained_data = np.dot(gain_dip, sol) residual = data - np.dot(whitener, explained_data) gof = 1. - np.sum(residual ** 2, axis=0) / np.sum(data ** 2, axis=0) return _make_dipoles(times, poss, oris, sol, gof), explained_data def _make_dipoles(times, poss, oris, sol, gof): """Instantiate a list of Dipoles. Parameters ---------- times : array, shape (n_times,) The time instants. poss : array, shape (n_dipoles, 3) The dipoles' positions. oris : array, shape (n_dipoles, 3) The dipoles' orientations. sol : array, shape (n_times,) The dipoles' amplitudes over time. gof : array, shape (n_times,) The goodness of fit of the dipoles. Shared between all dipoles. Returns ------- dipoles : list The list of Dipole instances. """ oris = np.array(oris) dipoles = [] for i_dip in range(poss.shape[0]): i_pos = poss[i_dip][np.newaxis, :].repeat(len(times), axis=0) i_ori = oris[i_dip][np.newaxis, :].repeat(len(times), axis=0) dipoles.append(Dipole(times, i_pos, sol[i_dip], i_ori, gof)) return dipoles def _compute_subcorr(G, phi_sig): """Compute the subspace correlation.""" Ug, Sg, Vg = linalg.svd(G, full_matrices=False) # Now we look at the actual rank of the forward fields # in G and handle the fact that it might be rank defficient # eg. when using MEG and a sphere model for which the # radial component will be truly 0. rank = np.sum(Sg > (Sg[0] * 1e-6)) if rank == 0: return 0, np.zeros(len(G)) rank = max(rank, 2) # rank cannot be 1 Ug, Sg, Vg = Ug[:, :rank], Sg[:rank], Vg[:rank] tmp = np.dot(Ug.T.conjugate(), phi_sig) Uc, Sc, _ = linalg.svd(tmp, full_matrices=False) X = np.dot(Vg.T / Sg[None, :], Uc[:, 0]) # subcorr return Sc[0], X / linalg.norm(X) def _compute_proj(A): """Compute the orthogonal projection operation for a manifold vector A.""" U, _, _ = linalg.svd(A, full_matrices=False) return np.identity(A.shape[0]) - np.dot(U, U.T.conjugate()) @verbose def rap_music(evoked, forward, noise_cov, n_dipoles=5, return_residual=False, verbose=None): """RAP-MUSIC source localization method. Compute Recursively Applied and Projected MUltiple SIgnal Classification (RAP-MUSIC) on evoked data. .. note:: The goodness of fit (GOF) of all the returned dipoles is the same and corresponds to the GOF of the full set of dipoles. Parameters ---------- evoked : instance of Evoked Evoked data to localize. forward : instance of Forward Forward operator. noise_cov : instance of Covariance The noise covariance. n_dipoles : int The number of dipoles to look for. The default value is 5. return_residual : bool If True, the residual is returned as an Evoked instance. verbose : bool, str, int, or None If not None, override default verbose level (see :func:`mne.verbose` and :ref:`Logging documentation ` for more). Returns ------- dipoles : list of instance of Dipole The dipole fits. residual : instance of Evoked The residual a.k.a. data not explained by the dipoles. Only returned if return_residual is True. See Also -------- mne.fit_dipole Notes ----- The references are: J.C. Mosher and R.M. Leahy. 1999. Source localization using recursively applied and projected (RAP) MUSIC. Signal Processing, IEEE Trans. 47, 2 (February 1999), 332-340. DOI=10.1109/78.740118 https://doi.org/10.1109/78.740118 Mosher, J.C.; Leahy, R.M., EEG and MEG source localization using recursively applied (RAP) MUSIC, Signals, Systems and Computers, 1996. pp.1201,1207 vol.2, 3-6 Nov. 1996 doi: 10.1109/ACSSC.1996.599135 .. versionadded:: 0.9.0 """ info = evoked.info data = evoked.data times = evoked.times picks = _setup_picks(info, forward, data_cov=None, noise_cov=noise_cov) data = data[picks] dipoles, explained_data = _apply_rap_music(data, info, times, forward, noise_cov, n_dipoles, picks) if return_residual: residual = evoked.copy() selection = [info['ch_names'][p] for p in picks] residual = pick_channels_evoked(residual, include=selection) residual.data -= explained_data active_projs = [p for p in residual.info['projs'] if p['active']] for p in active_projs: p['active'] = False residual.add_proj(active_projs, remove_existing=True) residual.apply_proj() return dipoles, residual else: return dipoles