wiener_filter_curvature.py 3.71 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.
#
# Copyright(C) 2013-2018 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.

Martin Reinecke's avatar
Martin Reinecke committed
19
20
from ..operators.endomorphic_operator import EndomorphicOperator
from ..operators.inversion_enabler import InversionEnabler
21
22
from ..field import Field, sqrt
from ..sugar import power_analyze, power_synthesize
23

Martin Reinecke's avatar
PEP8    
Martin Reinecke committed
24

Martin Reinecke's avatar
Martin Reinecke committed
25
class WienerFilterCurvature(EndomorphicOperator):
Jakob Knollmueller's avatar
Jakob Knollmueller committed
26
27
28
29
    """The curvature of the WienerFilterEnergy.

    This operator implements the second derivative of the
    WienerFilterEnergy used in some minimization algorithms or
30
31
    for error estimates of the posterior maps. It is the
    inverse of the propagator operator.
Jakob Knollmueller's avatar
Jakob Knollmueller committed
32
33
34
35

    Parameters
    ----------
    R: LinearOperator,
Martin Reinecke's avatar
Martin Reinecke committed
36
37
38
       The response operator of the Wiener filter measurement.
    N: EndomorphicOperator
       The noise covariance.
Jakob Knollmueller's avatar
Jakob Knollmueller committed
39
    S: DiagonalOperator,
Martin Reinecke's avatar
Martin Reinecke committed
40
       The prior signal covariance
Jakob Knollmueller's avatar
Jakob Knollmueller committed
41
42
    """

43
    def __init__(self, R, N, S, inverter):
Martin Reinecke's avatar
Martin Reinecke committed
44
        super(WienerFilterCurvature, self).__init__()
45
46
47
        self.R = R
        self.N = N
        self.S = S
Philipp Arras's avatar
Philipp Arras committed
48
        op = R.adjoint * N.inverse * R + S.inverse
Martin Reinecke's avatar
Martin Reinecke committed
49
        self._op = InversionEnabler(op, inverter, S.times)
50

51
52
    @property
    def domain(self):
Martin Reinecke's avatar
Martin Reinecke committed
53
        return self._op.domain
54
55

    @property
Martin Reinecke's avatar
Martin Reinecke committed
56
57
    def capability(self):
        return self._op.capability
58

Martin Reinecke's avatar
Martin Reinecke committed
59
60
    def apply(self, x, mode):
        return self._op.apply(x, mode)
61

Martin Reinecke's avatar
Martin Reinecke committed
62
    def generate_posterior_sample(self):
63
64
65
66
67
68
69
70
71
72
73
74
75
76
        """ Generates a posterior sample from a Gaussian distribution with
        given mean and covariance.

        This method generates samples by setting up the observation and
        reconstruction of a mock signal in order to obtain residuals of the
        right correlation which are added to the given mean.

        Returns
        -------
        sample : Field
            Returns the a sample from the Gaussian of given mean and
            covariance.
        """

77
        power = power_analyze(sqrt(self.S.diagonal()))
78
79
        mock_signal = power_synthesize(power, real_signal=True)

80
        noise = self.N.diagonal()
81
82

        mock_noise = Field.from_random(random_type="normal",
Martin Reinecke's avatar
tweaks    
Martin Reinecke committed
83
                                       domain=self.N.domain, dtype=noise.dtype)
84
85
86
87
88
89
        mock_noise *= sqrt(noise)

        mock_data = self.R(mock_signal) + mock_noise

        mock_j = self.R.adjoint_times(self.N.inverse_times(mock_data))
        mock_m = self.inverse_times(mock_j)
Martin Reinecke's avatar
Martin Reinecke committed
90
        return mock_signal - mock_m
91
92
93

    def generate_posterior_sample2(self):
        power = self.S.diagonal()
Philipp Arras's avatar
Philipp Arras committed
94
95
96
97
        mock_signal = Field.from_random(
            random_type="normal",
            domain=self.S.domain,
            dtype=power.dtype)
98
99
100
101
102
103
104
105
106
107
108
109
        mock_signal *= sqrt(power)

        noise = self.N.diagonal()
        mock_noise = Field.from_random(random_type="normal",
                                       domain=self.N.domain, dtype=noise.dtype)
        mock_noise *= sqrt(noise)

        mock_data = self.R(mock_signal) + mock_noise

        mock_j = self.R.adjoint_times(self.N.inverse_times(mock_data))
        mock_m = self.inverse_times(mock_j)
        return mock_signal - mock_m