Convolutional Constained MOD¶
This example demonstrates the use of pgm.ccmod.ConvCnstrMOD
for computing a convolutional dictionary update via the convolutional
constrained method of optimal directions problem
[26]. It also illustrates the use of
pgm.momentum.MomentumNesterov,
pgm.momentum.MomentumLinear and
pgm.momentum.MomentumGenLinear to adapt the momentum
coefficients of PGM. This problem is mainly useful as a component within
convolutional dictionary learning, but its use is demonstrated here
since a user may wish to construct such objects as part of a custom
convolutional dictionary learning algorithm, using
dictlrn.DictLearn.
from __future__ import print_function
from builtins import input
import pyfftw # See https://github.com/pyFFTW/pyFFTW/issues/40
import numpy as np
from sporco.admm import cbpdn
from sporco.pgm import ccmod
from sporco.pgm.momentum import MomentumLinear, MomentumGenLinear
from sporco import util
from sporco import signal
from sporco import plot
plot.config_notebook_plotting()
Load training images.
exim = util.ExampleImages(scaled=True, zoom=0.25, gray=True)
S1 = exim.image('barbara.png', idxexp=np.s_[10:522, 100:612])
S2 = exim.image('kodim23.png', idxexp=np.s_[:, 60:572])
S3 = exim.image('monarch.png', idxexp=np.s_[:, 160:672])
S4 = exim.image('sail.png', idxexp=np.s_[:, 210:722])
S5 = exim.image('tulips.png', idxexp=np.s_[:, 30:542])
S = np.dstack((S1, S2, S3, S4, S5))
Highpass filter training images.
npd = 16
fltlmbd = 5
sl, sh = signal.tikhonov_filter(S, fltlmbd, npd)
Load initial dictionary.
D0 = util.convdicts()['G:12x12x36']
Compute sparse representation on current dictionary.
lmbda = 0.1
opt = cbpdn.ConvBPDN.Options({'Verbose': True, 'MaxMainIter': 100,
'HighMemSolve': True})
c = cbpdn.ConvBPDN(D0, sh, lmbda, opt)
X = c.solve()
Itn Fnc DFid Regℓ1 r s ρ
----------------------------------------------------------------
0 4.13e+02 2.48e+01 3.88e+03 9.11e-01 1.90e-01 6.00e+00
1 3.31e+02 7.06e+01 2.60e+03 6.12e-01 2.76e-01 6.00e+00
2 2.99e+02 7.08e+01 2.28e+03 3.06e-01 2.46e-01 6.00e+00
3 3.00e+02 6.52e+01 2.35e+03 2.25e-01 1.88e-01 4.73e+00
4 3.08e+02 5.90e+01 2.49e+03 1.96e-01 1.31e-01 3.66e+00
5 2.97e+02 5.68e+01 2.40e+03 1.70e-01 9.63e-02 3.17e+00
6 2.71e+02 5.55e+01 2.15e+03 1.38e-01 7.91e-02 3.17e+00
7 2.48e+02 5.56e+01 1.92e+03 1.14e-01 6.64e-02 3.17e+00
8 2.33e+02 5.59e+01 1.77e+03 9.44e-02 5.49e-02 3.17e+00
9 2.23e+02 5.63e+01 1.67e+03 7.90e-02 4.64e-02 3.17e+00
10 2.16e+02 5.66e+01 1.60e+03 6.63e-02 4.07e-02 3.17e+00
11 2.13e+02 5.68e+01 1.56e+03 6.01e-02 3.63e-02 2.86e+00
12 2.12e+02 5.67e+01 1.55e+03 5.51e-02 3.23e-02 2.60e+00
13 2.11e+02 5.66e+01 1.54e+03 4.83e-02 2.86e-02 2.60e+00
14 2.09e+02 5.64e+01 1.52e+03 4.27e-02 2.56e-02 2.60e+00
15 2.05e+02 5.63e+01 1.49e+03 3.80e-02 2.35e-02 2.60e+00
16 2.02e+02 5.63e+01 1.46e+03 3.61e-02 2.17e-02 2.34e+00
17 2.00e+02 5.64e+01 1.44e+03 3.46e-02 1.97e-02 2.14e+00
18 1.98e+02 5.64e+01 1.42e+03 3.16e-02 1.77e-02 2.14e+00
19 1.97e+02 5.65e+01 1.40e+03 2.90e-02 1.61e-02 2.14e+00
20 1.95e+02 5.65e+01 1.39e+03 2.67e-02 1.49e-02 2.14e+00
21 1.94e+02 5.66e+01 1.37e+03 2.46e-02 1.38e-02 2.14e+00
22 1.92e+02 5.66e+01 1.36e+03 2.27e-02 1.29e-02 2.14e+00
23 1.91e+02 5.66e+01 1.34e+03 2.11e-02 1.21e-02 2.14e+00
24 1.89e+02 5.66e+01 1.33e+03 1.97e-02 1.14e-02 2.14e+00
25 1.88e+02 5.66e+01 1.31e+03 1.84e-02 1.07e-02 2.14e+00
26 1.87e+02 5.66e+01 1.30e+03 1.72e-02 1.01e-02 2.14e+00
27 1.86e+02 5.67e+01 1.29e+03 1.62e-02 9.53e-03 2.14e+00
28 1.85e+02 5.67e+01 1.28e+03 1.52e-02 9.02e-03 2.14e+00
29 1.84e+02 5.67e+01 1.27e+03 1.44e-02 8.57e-03 2.14e+00
30 1.83e+02 5.68e+01 1.26e+03 1.36e-02 8.14e-03 2.14e+00
31 1.82e+02 5.68e+01 1.26e+03 1.29e-02 7.73e-03 2.14e+00
32 1.82e+02 5.68e+01 1.25e+03 1.22e-02 7.33e-03 2.14e+00
33 1.81e+02 5.68e+01 1.25e+03 1.21e-02 6.95e-03 1.95e+00
34 1.81e+02 5.68e+01 1.24e+03 1.16e-02 6.54e-03 1.95e+00
35 1.81e+02 5.69e+01 1.24e+03 1.10e-02 6.15e-03 1.95e+00
36 1.80e+02 5.69e+01 1.23e+03 1.05e-02 5.79e-03 1.95e+00
37 1.80e+02 5.69e+01 1.23e+03 1.00e-02 5.48e-03 1.95e+00
38 1.79e+02 5.69e+01 1.22e+03 9.57e-03 5.21e-03 1.95e+00
39 1.79e+02 5.69e+01 1.22e+03 9.12e-03 4.96e-03 1.95e+00
40 1.78e+02 5.70e+01 1.21e+03 8.70e-03 4.74e-03 1.95e+00
41 1.78e+02 5.70e+01 1.21e+03 8.29e-03 4.52e-03 1.95e+00
42 1.78e+02 5.70e+01 1.21e+03 7.91e-03 4.30e-03 1.95e+00
43 1.77e+02 5.70e+01 1.20e+03 7.56e-03 4.10e-03 1.95e+00
44 1.77e+02 5.70e+01 1.20e+03 7.22e-03 3.92e-03 1.95e+00
45 1.76e+02 5.70e+01 1.19e+03 6.90e-03 3.75e-03 1.95e+00
46 1.76e+02 5.70e+01 1.19e+03 6.59e-03 3.58e-03 1.95e+00
47 1.76e+02 5.71e+01 1.19e+03 6.31e-03 3.41e-03 1.95e+00
48 1.76e+02 5.71e+01 1.19e+03 6.03e-03 3.26e-03 1.95e+00
49 1.75e+02 5.71e+01 1.18e+03 5.77e-03 3.12e-03 1.95e+00
50 1.75e+02 5.71e+01 1.18e+03 5.52e-03 2.99e-03 1.95e+00
51 1.75e+02 5.71e+01 1.18e+03 5.28e-03 2.87e-03 1.95e+00
52 1.74e+02 5.71e+01 1.17e+03 5.05e-03 2.75e-03 1.95e+00
53 1.74e+02 5.71e+01 1.17e+03 4.84e-03 2.63e-03 1.95e+00
54 1.74e+02 5.71e+01 1.17e+03 4.64e-03 2.51e-03 1.95e+00
55 1.74e+02 5.71e+01 1.17e+03 4.44e-03 2.41e-03 1.95e+00
56 1.74e+02 5.71e+01 1.16e+03 4.26e-03 2.31e-03 1.95e+00
57 1.73e+02 5.71e+01 1.16e+03 4.09e-03 2.22e-03 1.95e+00
58 1.73e+02 5.72e+01 1.16e+03 3.93e-03 2.12e-03 1.95e+00
59 1.73e+02 5.72e+01 1.16e+03 3.78e-03 2.03e-03 1.95e+00
60 1.73e+02 5.72e+01 1.16e+03 3.63e-03 1.94e-03 1.95e+00
61 1.73e+02 5.72e+01 1.16e+03 3.48e-03 1.87e-03 1.95e+00
62 1.73e+02 5.72e+01 1.15e+03 3.34e-03 1.80e-03 1.95e+00
63 1.72e+02 5.72e+01 1.15e+03 3.21e-03 1.73e-03 1.95e+00
64 1.72e+02 5.72e+01 1.15e+03 3.09e-03 1.66e-03 1.95e+00
65 1.72e+02 5.72e+01 1.15e+03 2.97e-03 1.59e-03 1.95e+00
66 1.72e+02 5.72e+01 1.15e+03 2.86e-03 1.53e-03 1.95e+00
67 1.72e+02 5.72e+01 1.15e+03 2.75e-03 1.47e-03 1.95e+00
68 1.72e+02 5.72e+01 1.15e+03 2.65e-03 1.42e-03 1.95e+00
69 1.72e+02 5.72e+01 1.14e+03 2.54e-03 1.36e-03 1.95e+00
70 1.71e+02 5.72e+01 1.14e+03 2.45e-03 1.32e-03 1.95e+00
71 1.71e+02 5.72e+01 1.14e+03 2.36e-03 1.27e-03 1.95e+00
72 1.71e+02 5.72e+01 1.14e+03 2.27e-03 1.23e-03 1.95e+00
73 1.71e+02 5.72e+01 1.14e+03 2.19e-03 1.19e-03 1.95e+00
74 1.71e+02 5.72e+01 1.14e+03 2.11e-03 1.14e-03 1.95e+00
75 1.71e+02 5.72e+01 1.14e+03 2.03e-03 1.09e-03 1.95e+00
76 1.71e+02 5.72e+01 1.14e+03 1.96e-03 1.05e-03 1.95e+00
77 1.71e+02 5.72e+01 1.14e+03 1.88e-03 1.00e-03 1.95e+00
78 1.71e+02 5.72e+01 1.14e+03 1.81e-03 9.68e-04 1.95e+00
79 1.71e+02 5.72e+01 1.13e+03 1.75e-03 9.34e-04 1.95e+00
80 1.71e+02 5.72e+01 1.13e+03 1.69e-03 9.00e-04 1.95e+00
81 1.71e+02 5.73e+01 1.13e+03 1.63e-03 8.65e-04 1.95e+00
82 1.70e+02 5.73e+01 1.13e+03 1.57e-03 8.31e-04 1.95e+00
83 1.70e+02 5.73e+01 1.13e+03 1.51e-03 7.98e-04 1.95e+00
84 1.70e+02 5.73e+01 1.13e+03 1.46e-03 7.68e-04 1.95e+00
85 1.70e+02 5.73e+01 1.13e+03 1.41e-03 7.41e-04 1.95e+00
86 1.70e+02 5.73e+01 1.13e+03 1.36e-03 7.16e-04 1.95e+00
87 1.70e+02 5.73e+01 1.13e+03 1.31e-03 6.93e-04 1.95e+00
88 1.70e+02 5.73e+01 1.13e+03 1.26e-03 6.71e-04 1.95e+00
89 1.70e+02 5.73e+01 1.13e+03 1.22e-03 6.49e-04 1.95e+00
90 1.70e+02 5.73e+01 1.13e+03 1.18e-03 6.26e-04 1.95e+00
91 1.70e+02 5.73e+01 1.13e+03 1.14e-03 6.04e-04 1.95e+00
92 1.70e+02 5.73e+01 1.13e+03 1.10e-03 5.81e-04 1.95e+00
93 1.70e+02 5.73e+01 1.13e+03 1.06e-03 5.61e-04 1.95e+00
94 1.70e+02 5.73e+01 1.13e+03 1.03e-03 5.41e-04 1.95e+00
95 1.70e+02 5.73e+01 1.13e+03 9.94e-04 5.25e-04 1.95e+00
----------------------------------------------------------------
Update dictionary for training image set. Nesterov momentum coefficients [6].
opt = ccmod.ConvCnstrMOD.Options({'Verbose': True,
'MaxMainIter': 100, 'L': 50})
c1 = ccmod.ConvCnstrMOD(X, sh, D0.shape, opt)
c1.solve()
D11 = c1.getdict().squeeze()
print("ConvCnstrMOD solve time: %.2fs" % c1.timer.elapsed('solve'))
Itn DFid Cnstr Rsdl
----------------------------------
0 6.32e+01 5.88e-07 3.60e+01
1 5.68e+01 9.74e-07 1.45e-01
2 5.31e+01 7.99e-07 5.24e-02
3 5.12e+01 7.77e-07 1.76e-02
4 5.03e+01 9.09e-07 5.86e-03
5 4.99e+01 9.62e-07 2.38e-03
6 4.98e+01 8.14e-07 1.30e-03
7 4.97e+01 7.91e-07 7.65e-04
----------------------------------
ConvCnstrMOD solve time: 1.45s
Update dictionary for training image set. Linear momentum coefficients [14].
opt = ccmod.ConvCnstrMOD.Options({'Verbose': True, 'MaxMainIter': 100,
'Momentum': MomentumLinear(), 'L': 50})
c2 = ccmod.ConvCnstrMOD(X, sh, D0.shape, opt)
c2.solve()
D12 = c2.getdict().squeeze()
print("ConvCnstrMOD solve time: %.2fs" % c2.timer.elapsed('solve'))
Itn DFid Cnstr Rsdl
----------------------------------
0 6.32e+01 5.88e-07 3.60e+01
1 5.68e+01 9.74e-07 1.45e-01
2 5.38e+01 7.33e-07 6.77e-02
3 5.18e+01 1.00e-06 2.87e-02
4 5.08e+01 8.41e-07 1.13e-02
5 5.02e+01 9.21e-07 4.37e-03
6 4.99e+01 1.00e-06 1.86e-03
7 4.97e+01 7.00e-07 9.30e-04
----------------------------------
ConvCnstrMOD solve time: 0.26s
Update dictionary for training image set. Generalized linear momentum coefficients [40].
opt = ccmod.ConvCnstrMOD.Options({'Verbose': True, 'MaxMainIter': 100,
'Momentum': MomentumGenLinear(), 'L': 50})
c3 = ccmod.ConvCnstrMOD(X, sh, D0.shape, opt)
c3.solve()
D13 = c3.getdict().squeeze()
print("ConvCnstrMOD solve time: %.2fs" % c3.timer.elapsed('solve'))
Itn DFid Cnstr Rsdl
----------------------------------
0 6.32e+01 5.88e-07 3.60e+01
1 5.68e+01 9.74e-07 1.45e-01
2 5.19e+01 6.85e-07 2.92e-02
3 5.03e+01 6.77e-07 1.63e-02
4 5.04e+01 7.02e-07 2.49e-02
5 5.06e+01 8.34e-07 2.50e-02
6 5.04e+01 7.66e-07 1.64e-02
7 5.02e+01 9.86e-07 8.65e-03
8 5.00e+01 8.62e-07 5.02e-03
9 4.99e+01 8.40e-07 3.72e-03
10 4.99e+01 9.54e-07 3.00e-03
11 4.98e+01 7.62e-07 2.34e-03
12 4.98e+01 6.03e-07 1.72e-03
13 4.97e+01 9.23e-07 1.20e-03
14 4.97e+01 9.22e-07 8.39e-04
----------------------------------
ConvCnstrMOD solve time: 0.34s
Display initial and final dictionaries.
fig = plot.figure(figsize=(7, 7))
plot.subplot(2, 2, 1)
plot.imview(util.tiledict(D0), title='D0', fig=fig)
plot.subplot(2, 2, 2)
plot.imview(util.tiledict(D11), title='D1 Nesterov', fig=fig)
plot.subplot(2, 2, 3)
plot.imview(util.tiledict(D12), title='D1 Linear', fig=fig)
plot.subplot(2, 2, 4)
plot.imview(util.tiledict(D13), title='D1 GenLinear', fig=fig)
fig.show()
Get iterations statistics from CCMOD solver object and plot functional value, and residuals.
its1 = c1.getitstat()
its2 = c2.getitstat()
its3 = c3.getitstat()
fig = plot.figure(figsize=(15, 5))
plot.subplot(1, 2, 1)
plot.plot(its1.DFid, xlbl='Iterations', ylbl='Functional', fig=fig)
plot.plot(its2.DFid, xlbl='Iterations', ylbl='Functional', fig=fig)
plot.plot(its3.DFid, xlbl='Iterations', ylbl='Functional',
lgnd=['Nesterov', 'Linear', 'GenLinear'], fig=fig)
plot.subplot(1, 2, 2)
plot.plot(its1.Rsdl, ptyp='semilogy', xlbl='Iterations', ylbl='Residual',
fig=fig)
plot.plot(its2.Rsdl, ptyp='semilogy', xlbl='Iterations', ylbl='Residual',
fig=fig)
plot.plot(its3.Rsdl, ptyp='semilogy', xlbl='Iterations', ylbl='Residual',
lgnd=['Nesterov', 'Linear', 'GenLinear'], fig=fig)
fig.show()
