Convolutional Dictionary Learning¶
This example demonstrates the use of
prlcnscdl.ConvBPDNDictLearn_Consensus for learning a
convolutional dictionary from a set of training images. The dictionary
learning algorithm is based on the ADMM consensus dictionary update
[1] [26].
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.dictlrn import prlcnscdl
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)
Construct initial dictionary.
np.random.seed(12345)
D0 = np.random.randn(8, 8, 64)
Set regularization parameter and options for dictionary learning solver.
lmbda = 0.2
opt = prlcnscdl.ConvBPDNDictLearn_Consensus.Options({'Verbose': True,
'MaxMainIter': 200,
'CBPDN': {'rho': 50.0*lmbda + 0.5},
'CCMOD': {'rho': 1.0, 'ZeroMean': True}})
Create solver object and solve.
d = prlcnscdl.ConvBPDNDictLearn_Consensus(D0, sh, lmbda, opt)
D1 = d.solve()
print("ConvBPDNDictLearn_Consensus solve time: %.2fs" %
d.timer.elapsed('solve'))
Itn Fnc DFid Regℓ1
----------------------------------
0 4.18e+02 4.18e+02 1.97e-01
1 4.01e+02 3.92e+02 4.45e+01
2 3.50e+02 3.00e+02 2.48e+02
3 3.23e+02 2.10e+02 5.66e+02
4 3.13e+02 1.53e+02 7.99e+02
5 3.03e+02 1.22e+02 9.04e+02
6 2.91e+02 1.10e+02 9.03e+02
7 2.79e+02 1.09e+02 8.53e+02
8 2.71e+02 1.11e+02 8.00e+02
9 2.66e+02 1.13e+02 7.62e+02
10 2.62e+02 1.14e+02 7.43e+02
11 2.60e+02 1.13e+02 7.35e+02
12 2.58e+02 1.11e+02 7.34e+02
13 2.56e+02 1.09e+02 7.35e+02
14 2.55e+02 1.07e+02 7.37e+02
15 2.53e+02 1.06e+02 7.38e+02
16 2.52e+02 1.05e+02 7.38e+02
17 2.51e+02 1.04e+02 7.37e+02
18 2.50e+02 1.03e+02 7.35e+02
19 2.50e+02 1.03e+02 7.33e+02
20 2.49e+02 1.03e+02 7.31e+02
21 2.48e+02 1.03e+02 7.28e+02
22 2.48e+02 1.02e+02 7.26e+02
23 2.47e+02 1.02e+02 7.25e+02
24 2.47e+02 1.02e+02 7.24e+02
25 2.46e+02 1.02e+02 7.23e+02
26 2.46e+02 1.01e+02 7.22e+02
27 2.45e+02 1.01e+02 7.21e+02
28 2.45e+02 1.01e+02 7.21e+02
29 2.45e+02 1.01e+02 7.20e+02
30 2.44e+02 1.00e+02 7.20e+02
31 2.44e+02 1.00e+02 7.19e+02
32 2.44e+02 1.00e+02 7.18e+02
33 2.43e+02 1.00e+02 7.17e+02
34 2.43e+02 9.98e+01 7.17e+02
35 2.43e+02 9.97e+01 7.16e+02
36 2.43e+02 9.96e+01 7.15e+02
37 2.42e+02 9.94e+01 7.15e+02
38 2.42e+02 9.93e+01 7.14e+02
39 2.42e+02 9.91e+01 7.14e+02
40 2.42e+02 9.90e+01 7.13e+02
41 2.41e+02 9.89e+01 7.13e+02
42 2.41e+02 9.88e+01 7.12e+02
43 2.41e+02 9.87e+01 7.12e+02
44 2.41e+02 9.85e+01 7.12e+02
45 2.41e+02 9.84e+01 7.11e+02
46 2.41e+02 9.83e+01 7.11e+02
47 2.40e+02 9.83e+01 7.11e+02
48 2.40e+02 9.82e+01 7.10e+02
49 2.40e+02 9.81e+01 7.10e+02
50 2.40e+02 9.80e+01 7.09e+02
51 2.40e+02 9.79e+01 7.09e+02
52 2.40e+02 9.79e+01 7.09e+02
53 2.39e+02 9.78e+01 7.08e+02
54 2.39e+02 9.77e+01 7.08e+02
55 2.39e+02 9.77e+01 7.08e+02
56 2.39e+02 9.76e+01 7.07e+02
57 2.39e+02 9.76e+01 7.07e+02
58 2.39e+02 9.75e+01 7.07e+02
59 2.39e+02 9.75e+01 7.06e+02
60 2.39e+02 9.74e+01 7.06e+02
61 2.38e+02 9.74e+01 7.06e+02
62 2.38e+02 9.73e+01 7.05e+02
63 2.38e+02 9.73e+01 7.05e+02
64 2.38e+02 9.72e+01 7.05e+02
65 2.38e+02 9.71e+01 7.05e+02
66 2.38e+02 9.71e+01 7.04e+02
67 2.38e+02 9.70e+01 7.04e+02
68 2.38e+02 9.70e+01 7.04e+02
69 2.38e+02 9.69e+01 7.04e+02
70 2.38e+02 9.69e+01 7.04e+02
71 2.38e+02 9.69e+01 7.03e+02
72 2.37e+02 9.68e+01 7.03e+02
73 2.37e+02 9.68e+01 7.03e+02
74 2.37e+02 9.67e+01 7.03e+02
75 2.37e+02 9.66e+01 7.03e+02
76 2.37e+02 9.66e+01 7.03e+02
77 2.37e+02 9.66e+01 7.03e+02
78 2.37e+02 9.65e+01 7.03e+02
79 2.37e+02 9.65e+01 7.02e+02
80 2.37e+02 9.64e+01 7.02e+02
81 2.37e+02 9.64e+01 7.02e+02
82 2.37e+02 9.63e+01 7.02e+02
83 2.37e+02 9.63e+01 7.02e+02
84 2.37e+02 9.63e+01 7.02e+02
85 2.37e+02 9.62e+01 7.02e+02
86 2.36e+02 9.62e+01 7.01e+02
87 2.36e+02 9.62e+01 7.01e+02
88 2.36e+02 9.62e+01 7.01e+02
89 2.36e+02 9.61e+01 7.01e+02
90 2.36e+02 9.61e+01 7.01e+02
91 2.36e+02 9.61e+01 7.01e+02
92 2.36e+02 9.61e+01 7.00e+02
93 2.36e+02 9.61e+01 7.00e+02
94 2.36e+02 9.60e+01 7.00e+02
95 2.36e+02 9.60e+01 7.00e+02
96 2.36e+02 9.60e+01 7.00e+02
97 2.36e+02 9.60e+01 7.00e+02
98 2.36e+02 9.60e+01 6.99e+02
99 2.36e+02 9.60e+01 6.99e+02
100 2.36e+02 9.59e+01 6.99e+02
101 2.36e+02 9.59e+01 6.99e+02
102 2.36e+02 9.59e+01 6.99e+02
103 2.36e+02 9.59e+01 6.99e+02
104 2.36e+02 9.59e+01 6.98e+02
105 2.36e+02 9.59e+01 6.98e+02
106 2.35e+02 9.59e+01 6.98e+02
107 2.35e+02 9.58e+01 6.98e+02
108 2.35e+02 9.58e+01 6.98e+02
109 2.35e+02 9.58e+01 6.98e+02
110 2.35e+02 9.58e+01 6.97e+02
111 2.35e+02 9.58e+01 6.97e+02
112 2.35e+02 9.58e+01 6.97e+02
113 2.35e+02 9.58e+01 6.97e+02
114 2.35e+02 9.58e+01 6.97e+02
115 2.35e+02 9.57e+01 6.97e+02
116 2.35e+02 9.57e+01 6.97e+02
117 2.35e+02 9.57e+01 6.97e+02
118 2.35e+02 9.57e+01 6.97e+02
119 2.35e+02 9.57e+01 6.96e+02
120 2.35e+02 9.57e+01 6.96e+02
121 2.35e+02 9.57e+01 6.96e+02
122 2.35e+02 9.56e+01 6.96e+02
123 2.35e+02 9.56e+01 6.96e+02
124 2.35e+02 9.56e+01 6.96e+02
125 2.35e+02 9.56e+01 6.96e+02
126 2.35e+02 9.56e+01 6.96e+02
127 2.35e+02 9.56e+01 6.95e+02
128 2.35e+02 9.56e+01 6.95e+02
129 2.35e+02 9.56e+01 6.95e+02
130 2.35e+02 9.56e+01 6.95e+02
131 2.35e+02 9.56e+01 6.95e+02
132 2.35e+02 9.56e+01 6.95e+02
133 2.34e+02 9.56e+01 6.95e+02
134 2.34e+02 9.56e+01 6.95e+02
135 2.34e+02 9.56e+01 6.94e+02
136 2.34e+02 9.55e+01 6.94e+02
137 2.34e+02 9.55e+01 6.94e+02
138 2.34e+02 9.55e+01 6.94e+02
139 2.34e+02 9.55e+01 6.94e+02
140 2.34e+02 9.55e+01 6.94e+02
141 2.34e+02 9.55e+01 6.94e+02
142 2.34e+02 9.55e+01 6.94e+02
143 2.34e+02 9.55e+01 6.93e+02
144 2.34e+02 9.55e+01 6.93e+02
145 2.34e+02 9.55e+01 6.93e+02
146 2.34e+02 9.55e+01 6.93e+02
147 2.34e+02 9.55e+01 6.93e+02
148 2.34e+02 9.55e+01 6.93e+02
149 2.34e+02 9.55e+01 6.93e+02
150 2.34e+02 9.55e+01 6.92e+02
151 2.34e+02 9.55e+01 6.92e+02
152 2.34e+02 9.55e+01 6.92e+02
153 2.34e+02 9.55e+01 6.92e+02
154 2.34e+02 9.55e+01 6.92e+02
155 2.34e+02 9.55e+01 6.92e+02
156 2.34e+02 9.55e+01 6.92e+02
157 2.34e+02 9.55e+01 6.92e+02
158 2.34e+02 9.55e+01 6.92e+02
159 2.34e+02 9.55e+01 6.91e+02
160 2.34e+02 9.55e+01 6.91e+02
161 2.34e+02 9.55e+01 6.91e+02
162 2.34e+02 9.55e+01 6.91e+02
163 2.34e+02 9.55e+01 6.91e+02
164 2.34e+02 9.54e+01 6.91e+02
165 2.34e+02 9.54e+01 6.91e+02
166 2.34e+02 9.54e+01 6.91e+02
167 2.34e+02 9.54e+01 6.91e+02
168 2.34e+02 9.54e+01 6.90e+02
169 2.33e+02 9.54e+01 6.90e+02
170 2.33e+02 9.54e+01 6.90e+02
171 2.33e+02 9.54e+01 6.90e+02
172 2.33e+02 9.54e+01 6.90e+02
173 2.33e+02 9.54e+01 6.90e+02
174 2.33e+02 9.54e+01 6.90e+02
175 2.33e+02 9.54e+01 6.90e+02
176 2.33e+02 9.54e+01 6.90e+02
177 2.33e+02 9.54e+01 6.90e+02
178 2.33e+02 9.54e+01 6.89e+02
179 2.33e+02 9.53e+01 6.89e+02
180 2.33e+02 9.53e+01 6.89e+02
181 2.33e+02 9.53e+01 6.89e+02
182 2.33e+02 9.53e+01 6.89e+02
183 2.33e+02 9.53e+01 6.89e+02
184 2.33e+02 9.53e+01 6.89e+02
185 2.33e+02 9.53e+01 6.89e+02
186 2.33e+02 9.53e+01 6.89e+02
187 2.33e+02 9.53e+01 6.89e+02
188 2.33e+02 9.53e+01 6.89e+02
189 2.33e+02 9.53e+01 6.88e+02
190 2.33e+02 9.53e+01 6.88e+02
191 2.33e+02 9.52e+01 6.88e+02
192 2.33e+02 9.52e+01 6.88e+02
193 2.33e+02 9.52e+01 6.88e+02
194 2.33e+02 9.52e+01 6.88e+02
195 2.33e+02 9.52e+01 6.88e+02
196 2.33e+02 9.52e+01 6.88e+02
197 2.33e+02 9.52e+01 6.88e+02
198 2.33e+02 9.52e+01 6.88e+02
199 2.33e+02 9.52e+01 6.88e+02
----------------------------------
ConvBPDNDictLearn_Consensus solve time: 29.26s
Display initial and final 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()
Get iterations statistics from solver object and plot functional value
its = d.getitstat()
plot.plot(its.ObjFun, xlbl='Iterations', ylbl='Functional')
