Skip to content

Reduce Multi-Measurement-Vector and Boost

Solver ID: ReMBo

Usage

from invert import Solver

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

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

Overview

Randomly reduces a multi-measurement problem to repeated single-measurement OMP-style recovery, then boosts by re-fitting on the recovered joint support.

References

  1. Mishali, M., & Eldar, Y. C. (2008). Reduce and boost: Recovering arbitrary sets of jointly sparse vectors. IEEE Transactions on Signal Processing, 56(10), 4692–4702.
  2. Duarte, M. F., & Eldar, Y. C. (2011). Structured compressed sensing: From theory to applications. IEEE Transactions on Signal Processing, 59(9), 4053–4085.

API Reference

Bases: BaseSolver

Class for the Reduce Multi-Measurement-Vector and Boost (ReMBo) inverse solution [1]. The algorithm as describe in [2] was used for the imlpementation.

References

[1] Mishali, M., & Eldar, Y. C. (2008). Reduce and boost: Recovering arbitrary sets of jointly sparse vectors. IEEE Transactions on Signal Processing, 56(10), 4692-4702. [2] Duarte, M. F., & Eldar, Y. C. (2011). Structured compressed sensing: From theory to applications. IEEE Transactions on signal processing, 59(9), 4053-4085.

Source code in invert/solvers/matching_pursuit/rembo.py 
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
class SolverREMBO(BaseSolver):
    """Class for the Reduce Multi-Measurement-Vector and Boost (ReMBo) inverse
        solution [1]. The algorithm as describe in [2] was used for the
        imlpementation.

    References
    ----------
    [1] Mishali, M., & Eldar, Y. C. (2008). Reduce and boost: Recovering
    arbitrary sets of jointly sparse vectors. IEEE Transactions on Signal
    Processing, 56(10), 4692-4702.
    [2] Duarte, M. F., & Eldar, Y. C. (2011).
    Structured compressed sensing: From theory to applications. IEEE
    Transactions on signal processing, 59(9), 4053-4085.
    """

    meta = SolverMeta(
        acronym="ReMBo",
        full_name="Reduce Multi-Measurement-Vector and Boost",
        category="Matching Pursuit",
        description=(
            "Randomly reduces a multi-measurement problem to repeated single-measurement "
            "OMP-style recovery, then boosts by re-fitting on the recovered joint support."
        ),
        references=[
            "Mishali, M., & Eldar, Y. C. (2008). Reduce and boost: Recovering arbitrary sets of jointly sparse vectors. IEEE Transactions on Signal Processing, 56(10), 4692–4702.",
            "Duarte, M. F., & Eldar, Y. C. (2011). Structured compressed sensing: From theory to applications. IEEE Transactions on Signal Processing, 59(9), 4053–4085.",
        ],
    )

    def __init__(self, name="Reduce Multi-Measurement-Vector and Boost", **kwargs):
        self.name = name
        return super().__init__(**kwargs)

    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.

        Return
        ------
        self : object returns itself for convenience
        """
        super().make_inverse_operator(forward, *args, alpha=alpha, **kwargs)
        self.leadfield_original = self.leadfield.copy()
        self.leadfield_normed = self.robust_normalize_leadfield(self.leadfield)

        self.inverse_operators = []
        return self

    def apply_inverse_operator(self, mne_obj, K="auto") -> mne.SourceEstimate:  # type: ignore
        """Apply the REMBO inverse solution.

        Parameters
        ----------
        mne_obj : [mne.Evoked, mne.Epochs, mne.io.Raw]
            The MNE data object.
        K : ["auto", int]
            The number of atoms to select per iteration.

        Return
        ------
        stc : mne.SourceEstimate
            The source estimate containing the inverse solution.
        """
        data = self.unpack_data_obj(mne_obj)
        source_mat = self.calc_rembo_solution(data, K=K)
        stc = self.source_to_object(source_mat)
        return stc

    def calc_rembo_solution(self, y, K="auto"):
        """Calculate the REMBO inverse solution based on the measurement vector
            y.

        Parameters
        ----------
        y : numpy.ndarray
            The EEG matrix (channels, time)
        K : ["auto", int]
            The number of atoms to select per iteration.

        Return
        ------
        x_hat : numpy.ndarray
            The source matrix (dipoles, time)
        """

        rand = np.random.rand
        n_chans, n_time = y.shape
        if K == "auto":
            K = int(n_chans / 2)
        max_iter = int(n_chans / 2)
        n_dipoles = self.leadfield.shape[1]

        unexplained_variance = np.array(
            [
                calc_residual_variance(np.zeros(y.shape), y),
            ]
        )
        n_sources = np.array(
            [
                0,
            ]
        )
        x_hats = [np.zeros((n_dipoles, n_time))]

        for _i in range(max_iter):
            a = rand(n_time)
            y_vec = y @ a  # sample randomly from the measurement matrix
            x_hat = self.calc_omp_solution(y_vec, K=K)
            S_hat = np.where(x_hat != 0)[0].astype(int)
            As_pinv = np.linalg.pinv(self.leadfield[:, S_hat])

            x_hat = np.zeros((n_dipoles, n_time))
            x_hat[S_hat, :] = As_pinv @ y
            x_hats.append(x_hat)

            unexplained_variance = np.append(
                unexplained_variance, calc_residual_variance(self.leadfield @ x_hat, y)
            )
            n_sources = np.append(n_sources, len(S_hat)).astype(float)

        idc = np.argsort(n_sources)
        n_sources = n_sources[idc]
        unexplained_variance = unexplained_variance[idc]

        # REFACTOR THIS:
        unique_sources = np.sort(np.unique(n_sources))
        n_sources_new = []
        unexp_new = []
        x_hats_new = []
        for k in unique_sources:
            idc = np.where(n_sources == k)[0]
            values = unexplained_variance[idc]
            min_sidx = np.argmin(values)
            good_index = idc[min_sidx]

            n_sources_new.append(k)
            unexp_new.append(values.min())
            x_hats_new.append(x_hats[good_index])
        n_sources = np.array(n_sources_new)[1:]
        unexplained_variance = np.array(unexp_new)[1:]
        x_hats = x_hats_new[1:]
        corner_idx = find_corner(n_sources, unexplained_variance)

        # corner_idx = find_corner(n_sources[1:], unexplained_variance[1:])+1
        # corner_idx = idc[corner_idx]
        x_hat = x_hats[corner_idx]
        # import matplotlib.pyplot as plt
        # plt.figure()
        # plt.plot(n_sources, unexplained_variance, 'k*')
        # plt.plot(n_sources[corner_idx], unexplained_variance[corner_idx], 'ro')

        return x_hat

    def calc_omp_solution(self, y, K="auto"):
        """Calculates the Orthogonal Matching Pursuit (OMP) inverse solution.
        (Used by REMBO algorithm)

        Parameters
        ----------
        y : numpy.ndarray
            The data matrix (channels,).
        K : ["auto", int]
            The number of atoms to select per iteration.

        Return
        ------
        x_hat : numpy.ndarray
            The inverse solution (dipoles,)
        """
        n_chans = len(y)
        _, n_dipoles = self.leadfield.shape

        if K == "auto":
            K = int(n_chans / 2)

        x_hat = np.zeros(n_dipoles)
        x_hats = [deepcopy(x_hat)]
        source_norms = np.array(
            [
                0,
            ]
        )

        omega = np.array([])
        r = deepcopy(y)
        residuals = np.array(
            [
                np.linalg.norm(y - self.leadfield_original @ x_hat),
            ]
        )
        x_hats = [
            deepcopy(x_hat),
        ]

        for _i in range(n_chans):
            # Use original leadfield for both selection and estimation (REMBO variant)
            b = self.leadfield_original.T @ r
            b_thresh = thresholding(b, K)
            new_atoms = np.where(b_thresh != 0)[0]
            omega = np.append(omega, new_atoms)
            omega = np.unique(omega.astype(int))

            # Use robust inverse from base class for coefficient estimation
            if len(omega) > 0:
                L_omega = self.leadfield_original[:, omega]
                x_hat[omega] = self.robust_inverse_solution(L_omega, y)

            r = y - self.leadfield_original @ x_hat

            residuals = np.append(residuals, np.linalg.norm(r))
            source_norms = np.append(source_norms, np.sum(x_hat**2))
            x_hats.append(deepcopy(x_hat))

            # Early stopping if residual starts increasing
            if len(residuals) > 1 and residuals[-1] > residuals[-2]:
                break

        iters = np.arange(len(residuals)).astype(float)
        corner_idx = find_corner(iters, residuals)
        x_hat = x_hats[corner_idx]
        return x_hat

__init__ 

__init__(
    name="Reduce Multi-Measurement-Vector and Boost",
    **kwargs,
)
Source code in invert/solvers/matching_pursuit/rembo.py 
46
47
48
def __init__(self, name="Reduce Multi-Measurement-Vector and Boost", **kwargs):
    self.name = name
    return super().__init__(**kwargs)

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.

 'auto'
Return

self : object returns itself for convenience

Source code in invert/solvers/matching_pursuit/rembo.py 
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
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.

    Return
    ------
    self : object returns itself for convenience
    """
    super().make_inverse_operator(forward, *args, alpha=alpha, **kwargs)
    self.leadfield_original = self.leadfield.copy()
    self.leadfield_normed = self.robust_normalize_leadfield(self.leadfield)

    self.inverse_operators = []
    return self

apply_inverse_operator 

apply_inverse_operator(
    mne_obj, K="auto"
) -> mne.SourceEstimate

Apply the REMBO inverse solution.

Parameters:

Name Type Description Default
mne_obj [Evoked, Epochs, Raw]

The MNE data object.

 required
K [auto, int]

The number of atoms to select per iteration.

 'auto'
Return

stc : mne.SourceEstimate The source estimate containing the inverse solution.

Source code in invert/solvers/matching_pursuit/rembo.py 
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
def apply_inverse_operator(self, mne_obj, K="auto") -> mne.SourceEstimate:  # type: ignore
    """Apply the REMBO inverse solution.

    Parameters
    ----------
    mne_obj : [mne.Evoked, mne.Epochs, mne.io.Raw]
        The MNE data object.
    K : ["auto", int]
        The number of atoms to select per iteration.

    Return
    ------
    stc : mne.SourceEstimate
        The source estimate containing the inverse solution.
    """
    data = self.unpack_data_obj(mne_obj)
    source_mat = self.calc_rembo_solution(data, K=K)
    stc = self.source_to_object(source_mat)
    return stc