Convolutional Dictionary Learning¶
This example demonstrating the use of dictlrn.DictLearn to
construct a dictionary learning algorithm with the flexibility of
choosing the sparse coding and dictionary update classes. In this case
they are cbpdn.ConvBPDNJoint and
admm.ccmod.ConvCnstrMOD respectively, so the resulting
dictionary learning algorithm is not equivalent to
dictlrn.cbpdndl.ConvBPDNDictLearn. The example uses colour
input images and a greyscale dictionary
[51].
from __future__ import division
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.admm import ccmod
from sporco.dictlrn import dictlrn
from sporco import cnvrep
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=0.5)
img1 = exim.image('barbara.png', idxexp=np.s_[10:522, 100:612])
img2 = exim.image('kodim23.png', idxexp=np.s_[:, 60:572])
img3 = exim.image('monarch.png', idxexp=np.s_[:, 160:672])
S = np.stack((img1, img2, img3), axis=3)
Highpass filter training images.
npd = 16
fltlmbd = 5
sl, sh = signal.tikhonov_filter(S, fltlmbd, npd)
Construct initial dictionary.
np.random.seed(12345)
D0 = np.random.randn(8, 8, 64)
Construct object representing problem dimensions.
cri = cnvrep.CDU_ConvRepIndexing(D0.shape, sh)
Define X and D update options.
lmbda = 0.2
mu = 0.1
optx = cbpdn.ConvBPDNJoint.Options({'Verbose': False, 'MaxMainIter': 1,
'rho': 50.0*lmbda + 0.5, 'AutoRho': {'Period': 10,
'AutoScaling': False, 'RsdlRatio': 10.0, 'Scaling': 2.0,
'RsdlTarget': 1.0}})
optd = ccmod.ConvCnstrMODOptions({'Verbose': False, 'MaxMainIter': 1,
'rho': 10.0*cri.K, 'AutoRho': {'Period': 10, 'AutoScaling': False,
'RsdlRatio': 10.0, 'Scaling': 2.0, 'RsdlTarget': 1.0}},
method='ism')
Normalise dictionary according to dictionary Y update options.
D0n = cnvrep.Pcn(D0, D0.shape, cri.Nv, dimN=2, dimC=0, crp=True,
zm=optd['ZeroMean'])
Update D update options to include initial values for Y and U.
optd.update({'Y0': cnvrep.zpad(cnvrep.stdformD(D0n, cri.Cd, cri.M), cri.Nv),
'U0': np.zeros(cri.shpD)})
Create X update object.
xstep = cbpdn.ConvBPDNJoint(D0n, sh, lmbda, mu, optx)
Create D update object.
dstep = ccmod.ConvCnstrMOD(None, sh, D0.shape, optd, method='ism')
Create DictLearn object and solve.
opt = dictlrn.DictLearn.Options({'Verbose': True, 'MaxMainIter': 100})
d = dictlrn.DictLearn(xstep, dstep, opt)
D1 = d.solve()
print("DictLearn solve time: %.2fs" % d.timer.elapsed('solve'), "\n")
Itn FncX r_X s_X ρ_X FncD r_D s_D ρ_D
------------------------------------------------------------------------------------
0 6.28e+03 1.00e+00 8.33e-05 1.05e+01 1.91e+03 1.75e-04 7.10e-02 3.00e+01
1 4.85e+03 9.94e-01 2.16e-02 1.05e+01 1.86e+03 1.01e-01 2.44e-01 3.00e+01
2 3.80e+03 9.17e-01 8.41e-02 1.05e+01 1.32e+03 2.65e-01 1.97e-01 3.00e+01
3 3.60e+03 5.50e-01 1.46e-01 1.05e+01 9.77e+02 2.03e-01 1.55e-01 3.00e+01
4 3.88e+03 3.65e-01 1.33e-01 1.05e+01 7.60e+02 1.86e-01 1.18e-01 3.00e+01
5 3.70e+03 2.77e-01 1.15e-01 1.05e+01 6.06e+02 1.83e-01 1.02e-01 3.00e+01
6 3.54e+03 2.39e-01 1.15e-01 1.05e+01 5.29e+02 1.71e-01 8.56e-02 3.00e+01
7 3.31e+03 2.11e-01 1.05e-01 1.05e+01 5.06e+02 1.61e-01 7.13e-02 3.00e+01
8 2.98e+03 1.78e-01 8.58e-02 1.05e+01 5.08e+02 1.42e-01 6.21e-02 3.00e+01
9 2.73e+03 1.53e-01 7.33e-02 1.05e+01 5.17e+02 1.28e-01 5.80e-02 3.00e+01
10 2.54e+03 1.37e-01 6.80e-02 1.05e+01 5.24e+02 1.18e-01 5.40e-02 3.00e+01
11 2.41e+03 1.21e-01 5.98e-02 1.05e+01 5.31e+02 1.04e-01 4.70e-02 3.00e+01
12 2.28e+03 1.04e-01 5.20e-02 1.05e+01 5.35e+02 9.10e-02 4.08e-02 3.00e+01
13 2.16e+03 9.06e-02 4.75e-02 1.05e+01 5.34e+02 8.05e-02 3.58e-02 3.00e+01
14 2.06e+03 7.97e-02 4.34e-02 1.05e+01 5.31e+02 7.17e-02 3.16e-02 3.00e+01
15 1.98e+03 7.07e-02 3.99e-02 1.05e+01 5.28e+02 6.44e-02 2.83e-02 3.00e+01
16 1.90e+03 6.34e-02 3.70e-02 1.05e+01 5.25e+02 5.83e-02 2.57e-02 3.00e+01
17 1.84e+03 5.74e-02 3.42e-02 1.05e+01 5.24e+02 5.30e-02 2.36e-02 3.00e+01
18 1.79e+03 5.24e-02 3.18e-02 1.05e+01 5.23e+02 4.89e-02 2.20e-02 3.00e+01
19 1.74e+03 4.79e-02 2.97e-02 1.05e+01 5.22e+02 4.50e-02 2.04e-02 3.00e+01
20 1.70e+03 4.40e-02 2.81e-02 1.05e+01 5.21e+02 4.20e-02 1.91e-02 3.00e+01
21 1.66e+03 4.07e-02 2.65e-02 1.05e+01 5.20e+02 3.90e-02 1.77e-02 3.00e+01
22 1.63e+03 3.77e-02 2.52e-02 1.05e+01 5.19e+02 3.68e-02 1.64e-02 3.00e+01
23 1.60e+03 3.51e-02 2.41e-02 1.05e+01 5.17e+02 3.47e-02 1.53e-02 3.00e+01
24 1.57e+03 3.28e-02 2.31e-02 1.05e+01 5.15e+02 3.30e-02 1.43e-02 3.00e+01
25 1.55e+03 3.07e-02 2.22e-02 1.05e+01 5.14e+02 3.14e-02 1.35e-02 3.00e+01
26 1.53e+03 2.90e-02 2.13e-02 1.05e+01 5.12e+02 3.00e-02 1.28e-02 3.00e+01
27 1.51e+03 2.74e-02 2.05e-02 1.05e+01 5.11e+02 2.86e-02 1.21e-02 3.00e+01
28 1.49e+03 2.59e-02 1.98e-02 1.05e+01 5.09e+02 2.75e-02 1.14e-02 3.00e+01
29 1.47e+03 2.46e-02 1.91e-02 1.05e+01 5.08e+02 2.64e-02 1.09e-02 3.00e+01
30 1.45e+03 2.34e-02 1.84e-02 1.05e+01 5.07e+02 2.54e-02 1.04e-02 3.00e+01
31 1.44e+03 2.23e-02 1.79e-02 1.05e+01 5.06e+02 2.45e-02 1.00e-02 3.00e+01
32 1.43e+03 2.14e-02 1.74e-02 1.05e+01 5.06e+02 2.38e-02 9.66e-03 3.00e+01
33 1.42e+03 2.06e-02 1.69e-02 1.05e+01 5.05e+02 2.30e-02 9.34e-03 3.00e+01
34 1.41e+03 1.99e-02 1.64e-02 1.05e+01 5.04e+02 2.23e-02 9.01e-03 3.00e+01
35 1.40e+03 1.91e-02 1.59e-02 1.05e+01 5.04e+02 2.17e-02 8.71e-03 3.00e+01
36 1.39e+03 1.85e-02 1.55e-02 1.05e+01 5.03e+02 2.11e-02 8.43e-03 3.00e+01
37 1.38e+03 1.78e-02 1.51e-02 1.05e+01 5.02e+02 2.05e-02 8.14e-03 3.00e+01
38 1.37e+03 1.72e-02 1.47e-02 1.05e+01 5.02e+02 2.00e-02 7.88e-03 3.00e+01
39 1.36e+03 1.67e-02 1.44e-02 1.05e+01 5.01e+02 1.95e-02 7.63e-03 3.00e+01
40 1.36e+03 1.61e-02 1.40e-02 1.05e+01 5.01e+02 1.90e-02 7.41e-03 3.00e+01
41 1.35e+03 1.56e-02 1.37e-02 1.05e+01 5.00e+02 1.85e-02 7.22e-03 3.00e+01
42 1.34e+03 1.52e-02 1.34e-02 1.05e+01 5.00e+02 1.81e-02 7.06e-03 3.00e+01
43 1.34e+03 1.48e-02 1.31e-02 1.05e+01 4.99e+02 1.77e-02 6.91e-03 3.00e+01
44 1.33e+03 1.44e-02 1.29e-02 1.05e+01 4.99e+02 1.74e-02 6.80e-03 3.00e+01
45 1.33e+03 1.40e-02 1.26e-02 1.05e+01 4.99e+02 1.70e-02 6.68e-03 3.00e+01
46 1.32e+03 1.37e-02 1.23e-02 1.05e+01 4.98e+02 1.67e-02 6.55e-03 3.00e+01
47 1.32e+03 1.34e-02 1.21e-02 1.05e+01 4.98e+02 1.64e-02 6.44e-03 3.00e+01
48 1.31e+03 1.31e-02 1.18e-02 1.05e+01 4.97e+02 1.61e-02 6.34e-03 3.00e+01
49 1.31e+03 1.29e-02 1.16e-02 1.05e+01 4.97e+02 1.58e-02 6.26e-03 3.00e+01
50 1.31e+03 1.26e-02 1.15e-02 1.05e+01 4.97e+02 1.55e-02 6.21e-03 3.00e+01
51 1.30e+03 1.24e-02 1.13e-02 1.05e+01 4.97e+02 1.53e-02 6.17e-03 3.00e+01
52 1.30e+03 1.22e-02 1.11e-02 1.05e+01 4.96e+02 1.51e-02 6.15e-03 3.00e+01
53 1.30e+03 1.20e-02 1.09e-02 1.05e+01 4.96e+02 1.49e-02 6.13e-03 3.00e+01
54 1.29e+03 1.19e-02 1.08e-02 1.05e+01 4.96e+02 1.47e-02 6.11e-03 3.00e+01
55 1.29e+03 1.17e-02 1.06e-02 1.05e+01 4.95e+02 1.45e-02 6.07e-03 3.00e+01
56 1.29e+03 1.15e-02 1.05e-02 1.05e+01 4.95e+02 1.43e-02 6.02e-03 3.00e+01
57 1.29e+03 1.14e-02 1.04e-02 1.05e+01 4.95e+02 1.42e-02 5.95e-03 3.00e+01
58 1.28e+03 1.12e-02 1.03e-02 1.05e+01 4.95e+02 1.41e-02 5.90e-03 3.00e+01
59 1.28e+03 1.11e-02 1.02e-02 1.05e+01 4.94e+02 1.39e-02 5.81e-03 3.00e+01
60 1.28e+03 1.09e-02 1.01e-02 1.05e+01 4.94e+02 1.37e-02 5.71e-03 3.00e+01
61 1.28e+03 1.07e-02 9.96e-03 1.05e+01 4.94e+02 1.35e-02 5.59e-03 3.00e+01
62 1.27e+03 1.06e-02 9.87e-03 1.05e+01 4.93e+02 1.34e-02 5.48e-03 3.00e+01
63 1.27e+03 1.04e-02 9.74e-03 1.05e+01 4.93e+02 1.31e-02 5.34e-03 3.00e+01
64 1.27e+03 1.02e-02 9.61e-03 1.05e+01 4.93e+02 1.29e-02 5.20e-03 3.00e+01
65 1.27e+03 1.00e-02 9.46e-03 1.05e+01 4.93e+02 1.27e-02 5.03e-03 3.00e+01
66 1.26e+03 9.79e-03 9.35e-03 1.05e+01 4.92e+02 1.25e-02 4.88e-03 3.00e+01
67 1.26e+03 9.60e-03 9.20e-03 1.05e+01 4.92e+02 1.23e-02 4.72e-03 3.00e+01
68 1.26e+03 9.37e-03 9.08e-03 1.05e+01 4.92e+02 1.21e-02 4.57e-03 3.00e+01
69 1.25e+03 9.18e-03 8.96e-03 1.05e+01 4.92e+02 1.19e-02 4.43e-03 3.00e+01
70 1.25e+03 8.98e-03 8.83e-03 1.05e+01 4.91e+02 1.17e-02 4.31e-03 3.00e+01
71 1.25e+03 8.81e-03 8.69e-03 1.05e+01 4.91e+02 1.15e-02 4.18e-03 3.00e+01
72 1.25e+03 8.61e-03 8.52e-03 1.05e+01 4.91e+02 1.13e-02 4.04e-03 3.00e+01
73 1.24e+03 8.41e-03 8.37e-03 1.05e+01 4.91e+02 1.11e-02 3.89e-03 3.00e+01
74 1.24e+03 8.17e-03 8.26e-03 1.05e+01 4.91e+02 1.08e-02 3.75e-03 3.00e+01
75 1.24e+03 7.98e-03 8.11e-03 1.05e+01 4.91e+02 1.06e-02 3.62e-03 3.00e+01
76 1.23e+03 7.76e-03 7.98e-03 1.05e+01 4.90e+02 1.04e-02 3.51e-03 3.00e+01
77 1.23e+03 7.58e-03 7.84e-03 1.05e+01 4.90e+02 1.02e-02 3.40e-03 3.00e+01
78 1.23e+03 7.39e-03 7.72e-03 1.05e+01 4.90e+02 1.00e-02 3.30e-03 3.00e+01
79 1.23e+03 7.22e-03 7.57e-03 1.05e+01 4.90e+02 9.86e-03 3.21e-03 3.00e+01
80 1.22e+03 7.06e-03 7.45e-03 1.05e+01 4.90e+02 9.68e-03 3.12e-03 3.00e+01
81 1.22e+03 6.91e-03 7.32e-03 1.05e+01 4.90e+02 9.51e-03 3.03e-03 3.00e+01
82 1.22e+03 6.76e-03 7.19e-03 1.05e+01 4.90e+02 9.34e-03 2.94e-03 3.00e+01
83 1.22e+03 6.62e-03 7.09e-03 1.05e+01 4.90e+02 9.20e-03 2.87e-03 3.00e+01
84 1.21e+03 6.49e-03 7.00e-03 1.05e+01 4.89e+02 9.05e-03 2.81e-03 3.00e+01
85 1.21e+03 6.36e-03 6.89e-03 1.05e+01 4.89e+02 8.93e-03 2.75e-03 3.00e+01
86 1.21e+03 6.23e-03 6.77e-03 1.05e+01 4.89e+02 8.75e-03 2.69e-03 3.00e+01
87 1.21e+03 6.10e-03 6.67e-03 1.05e+01 4.89e+02 8.63e-03 2.63e-03 3.00e+01
88 1.21e+03 5.98e-03 6.55e-03 1.05e+01 4.89e+02 8.49e-03 2.58e-03 3.00e+01
89 1.20e+03 5.86e-03 6.44e-03 1.05e+01 4.89e+02 8.35e-03 2.53e-03 3.00e+01
90 1.20e+03 5.75e-03 6.32e-03 1.05e+01 4.89e+02 8.20e-03 2.48e-03 3.00e+01
91 1.20e+03 5.62e-03 6.21e-03 1.05e+01 4.89e+02 8.04e-03 2.43e-03 3.00e+01
92 1.20e+03 5.51e-03 6.09e-03 1.05e+01 4.89e+02 7.90e-03 2.37e-03 3.00e+01
93 1.20e+03 5.39e-03 5.97e-03 1.05e+01 4.89e+02 7.76e-03 2.30e-03 3.00e+01
94 1.20e+03 5.27e-03 5.89e-03 1.05e+01 4.89e+02 7.65e-03 2.26e-03 3.00e+01
95 1.19e+03 5.17e-03 5.80e-03 1.05e+01 4.88e+02 7.53e-03 2.22e-03 3.00e+01
96 1.19e+03 5.07e-03 5.71e-03 1.05e+01 4.88e+02 7.41e-03 2.19e-03 3.00e+01
97 1.19e+03 4.98e-03 5.62e-03 1.05e+01 4.88e+02 7.30e-03 2.16e-03 3.00e+01
98 1.19e+03 4.90e-03 5.55e-03 1.05e+01 4.88e+02 7.21e-03 2.13e-03 3.00e+01
99 1.19e+03 4.83e-03 5.47e-03 1.05e+01 4.88e+02 7.10e-03 2.11e-03 3.00e+01
------------------------------------------------------------------------------------
DictLearn solve time: 401.74s
Display dictionaries.
D1 = D1.squeeze()
fig = plot.figure(figsize=(14, 7))
plot.subplot(1, 2, 1)
plot.imview(util.tiledict(D0), title='D0', fig=fig)
plot.subplot(1, 2, 2)
plot.imview(util.tiledict(D1), title='D1', fig=fig)
fig.show()
Plot functional value and residuals.
itsx = xstep.getitstat()
itsd = dstep.getitstat()
fig = plot.figure(figsize=(20, 5))
plot.subplot(1, 3, 1)
plot.plot(itsx.ObjFun, xlbl='Iterations', ylbl='Functional', fig=fig)
plot.subplot(1, 3, 2)
plot.plot(np.vstack((itsx.PrimalRsdl, itsx.DualRsdl, itsd.PrimalRsdl,
itsd.DualRsdl)).T, ptyp='semilogy', xlbl='Iterations',
ylbl='Residual', lgnd=['X Primal', 'X Dual', 'D Primal', 'D Dual'],
fig=fig)
plot.subplot(1, 3, 3)
plot.plot(np.vstack((itsx.Rho, itsd.Rho)).T, xlbl='Iterations',
ylbl='Penalty Parameter', ptyp='semilogy', lgnd=['Rho', 'Sigma'],
fig=fig)
fig.show()
