Convolutional Dictionary Learning¶
This example demonstrates the use of
prlcnscdl.ConvBPDNDictLearn_Consensus for learning a
convolutional dictionary from a set of colour training images
[51]. 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)
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.stack((S1, S2, S3, S4, S5), 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, 3, 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 1.24e+03 1.19e+03 2.83e+02
1 9.43e+02 6.77e+02 1.33e+03
2 8.82e+02 4.16e+02 2.33e+03
3 8.43e+02 3.10e+02 2.66e+03
4 7.71e+02 2.67e+02 2.52e+03
5 7.29e+02 2.69e+02 2.30e+03
6 7.10e+02 2.73e+02 2.19e+03
7 6.98e+02 2.65e+02 2.17e+03
8 6.89e+02 2.51e+02 2.19e+03
9 6.82e+02 2.39e+02 2.21e+03
10 6.76e+02 2.32e+02 2.22e+03
11 6.72e+02 2.29e+02 2.21e+03
12 6.68e+02 2.28e+02 2.20e+03
13 6.64e+02 2.28e+02 2.18e+03
14 6.61e+02 2.28e+02 2.17e+03
15 6.58e+02 2.27e+02 2.16e+03
16 6.56e+02 2.25e+02 2.15e+03
17 6.54e+02 2.24e+02 2.15e+03
18 6.52e+02 2.23e+02 2.15e+03
19 6.50e+02 2.22e+02 2.14e+03
20 6.49e+02 2.21e+02 2.14e+03
21 6.47e+02 2.20e+02 2.14e+03
22 6.46e+02 2.19e+02 2.13e+03
23 6.45e+02 2.19e+02 2.13e+03
24 6.44e+02 2.18e+02 2.13e+03
25 6.42e+02 2.18e+02 2.12e+03
26 6.41e+02 2.18e+02 2.12e+03
27 6.40e+02 2.17e+02 2.12e+03
28 6.39e+02 2.17e+02 2.11e+03
29 6.39e+02 2.17e+02 2.11e+03
30 6.38e+02 2.16e+02 2.11e+03
31 6.37e+02 2.16e+02 2.10e+03
32 6.36e+02 2.16e+02 2.10e+03
33 6.35e+02 2.15e+02 2.10e+03
34 6.35e+02 2.15e+02 2.10e+03
35 6.34e+02 2.15e+02 2.10e+03
36 6.33e+02 2.15e+02 2.09e+03
37 6.33e+02 2.15e+02 2.09e+03
38 6.32e+02 2.14e+02 2.09e+03
39 6.32e+02 2.14e+02 2.09e+03
40 6.31e+02 2.14e+02 2.09e+03
41 6.31e+02 2.14e+02 2.08e+03
42 6.30e+02 2.14e+02 2.08e+03
43 6.30e+02 2.14e+02 2.08e+03
44 6.29e+02 2.13e+02 2.08e+03
45 6.29e+02 2.13e+02 2.08e+03
46 6.28e+02 2.13e+02 2.08e+03
47 6.28e+02 2.13e+02 2.07e+03
48 6.27e+02 2.13e+02 2.07e+03
49 6.27e+02 2.13e+02 2.07e+03
50 6.27e+02 2.13e+02 2.07e+03
51 6.26e+02 2.13e+02 2.07e+03
52 6.26e+02 2.12e+02 2.07e+03
53 6.26e+02 2.12e+02 2.07e+03
54 6.25e+02 2.12e+02 2.07e+03
55 6.25e+02 2.12e+02 2.06e+03
56 6.25e+02 2.12e+02 2.06e+03
57 6.24e+02 2.12e+02 2.06e+03
58 6.24e+02 2.12e+02 2.06e+03
59 6.24e+02 2.12e+02 2.06e+03
60 6.23e+02 2.12e+02 2.06e+03
61 6.23e+02 2.12e+02 2.06e+03
62 6.23e+02 2.12e+02 2.06e+03
63 6.22e+02 2.11e+02 2.06e+03
64 6.22e+02 2.11e+02 2.05e+03
65 6.22e+02 2.11e+02 2.05e+03
66 6.22e+02 2.11e+02 2.05e+03
67 6.21e+02 2.11e+02 2.05e+03
68 6.21e+02 2.11e+02 2.05e+03
69 6.21e+02 2.11e+02 2.05e+03
70 6.21e+02 2.11e+02 2.05e+03
71 6.21e+02 2.11e+02 2.05e+03
72 6.20e+02 2.11e+02 2.05e+03
73 6.20e+02 2.11e+02 2.05e+03
74 6.20e+02 2.11e+02 2.05e+03
75 6.20e+02 2.11e+02 2.05e+03
76 6.20e+02 2.11e+02 2.04e+03
77 6.19e+02 2.11e+02 2.04e+03
78 6.19e+02 2.10e+02 2.04e+03
79 6.19e+02 2.10e+02 2.04e+03
80 6.19e+02 2.10e+02 2.04e+03
81 6.19e+02 2.10e+02 2.04e+03
82 6.18e+02 2.10e+02 2.04e+03
83 6.18e+02 2.10e+02 2.04e+03
84 6.18e+02 2.10e+02 2.04e+03
85 6.18e+02 2.10e+02 2.04e+03
86 6.18e+02 2.10e+02 2.04e+03
87 6.18e+02 2.10e+02 2.04e+03
88 6.17e+02 2.10e+02 2.04e+03
89 6.17e+02 2.10e+02 2.04e+03
90 6.17e+02 2.10e+02 2.04e+03
91 6.17e+02 2.10e+02 2.04e+03
92 6.17e+02 2.10e+02 2.04e+03
93 6.17e+02 2.10e+02 2.03e+03
94 6.17e+02 2.10e+02 2.03e+03
95 6.16e+02 2.10e+02 2.03e+03
96 6.16e+02 2.10e+02 2.03e+03
97 6.16e+02 2.10e+02 2.03e+03
98 6.16e+02 2.10e+02 2.03e+03
99 6.16e+02 2.10e+02 2.03e+03
100 6.16e+02 2.10e+02 2.03e+03
101 6.16e+02 2.10e+02 2.03e+03
102 6.16e+02 2.10e+02 2.03e+03
103 6.15e+02 2.09e+02 2.03e+03
104 6.15e+02 2.09e+02 2.03e+03
105 6.15e+02 2.09e+02 2.03e+03
106 6.15e+02 2.09e+02 2.03e+03
107 6.15e+02 2.09e+02 2.03e+03
108 6.15e+02 2.09e+02 2.03e+03
109 6.15e+02 2.09e+02 2.03e+03
110 6.15e+02 2.09e+02 2.03e+03
111 6.14e+02 2.09e+02 2.03e+03
112 6.14e+02 2.09e+02 2.03e+03
113 6.14e+02 2.09e+02 2.02e+03
114 6.14e+02 2.09e+02 2.02e+03
115 6.14e+02 2.09e+02 2.02e+03
116 6.14e+02 2.09e+02 2.02e+03
117 6.14e+02 2.09e+02 2.02e+03
118 6.14e+02 2.09e+02 2.02e+03
119 6.14e+02 2.09e+02 2.02e+03
120 6.13e+02 2.09e+02 2.02e+03
121 6.13e+02 2.09e+02 2.02e+03
122 6.13e+02 2.09e+02 2.02e+03
123 6.13e+02 2.09e+02 2.02e+03
124 6.13e+02 2.09e+02 2.02e+03
125 6.13e+02 2.09e+02 2.02e+03
126 6.13e+02 2.09e+02 2.02e+03
127 6.13e+02 2.09e+02 2.02e+03
128 6.13e+02 2.09e+02 2.02e+03
129 6.13e+02 2.09e+02 2.02e+03
130 6.13e+02 2.09e+02 2.02e+03
131 6.12e+02 2.09e+02 2.02e+03
132 6.12e+02 2.09e+02 2.02e+03
133 6.12e+02 2.09e+02 2.02e+03
134 6.12e+02 2.09e+02 2.02e+03
135 6.12e+02 2.09e+02 2.02e+03
136 6.12e+02 2.09e+02 2.02e+03
137 6.12e+02 2.09e+02 2.02e+03
138 6.12e+02 2.09e+02 2.02e+03
139 6.12e+02 2.09e+02 2.02e+03
140 6.12e+02 2.08e+02 2.02e+03
141 6.12e+02 2.08e+02 2.02e+03
142 6.11e+02 2.08e+02 2.02e+03
143 6.11e+02 2.08e+02 2.01e+03
144 6.11e+02 2.08e+02 2.01e+03
145 6.11e+02 2.08e+02 2.01e+03
146 6.11e+02 2.08e+02 2.01e+03
147 6.11e+02 2.08e+02 2.01e+03
148 6.11e+02 2.08e+02 2.01e+03
149 6.11e+02 2.08e+02 2.01e+03
150 6.11e+02 2.08e+02 2.01e+03
151 6.11e+02 2.08e+02 2.01e+03
152 6.11e+02 2.08e+02 2.01e+03
153 6.11e+02 2.08e+02 2.01e+03
154 6.11e+02 2.08e+02 2.01e+03
155 6.11e+02 2.08e+02 2.01e+03
156 6.10e+02 2.08e+02 2.01e+03
157 6.10e+02 2.08e+02 2.01e+03
158 6.10e+02 2.08e+02 2.01e+03
159 6.10e+02 2.08e+02 2.01e+03
160 6.10e+02 2.08e+02 2.01e+03
161 6.10e+02 2.08e+02 2.01e+03
162 6.10e+02 2.08e+02 2.01e+03
163 6.10e+02 2.08e+02 2.01e+03
164 6.10e+02 2.08e+02 2.01e+03
165 6.10e+02 2.08e+02 2.01e+03
166 6.10e+02 2.08e+02 2.01e+03
167 6.10e+02 2.08e+02 2.01e+03
168 6.10e+02 2.08e+02 2.01e+03
169 6.10e+02 2.08e+02 2.01e+03
170 6.10e+02 2.08e+02 2.01e+03
171 6.09e+02 2.08e+02 2.01e+03
172 6.09e+02 2.08e+02 2.01e+03
173 6.09e+02 2.08e+02 2.01e+03
174 6.09e+02 2.08e+02 2.01e+03
175 6.09e+02 2.08e+02 2.01e+03
176 6.09e+02 2.08e+02 2.01e+03
177 6.09e+02 2.08e+02 2.01e+03
178 6.09e+02 2.08e+02 2.01e+03
179 6.09e+02 2.08e+02 2.01e+03
180 6.09e+02 2.08e+02 2.01e+03
181 6.09e+02 2.08e+02 2.01e+03
182 6.09e+02 2.08e+02 2.01e+03
183 6.09e+02 2.08e+02 2.01e+03
184 6.09e+02 2.08e+02 2.01e+03
185 6.09e+02 2.08e+02 2.01e+03
186 6.09e+02 2.08e+02 2.01e+03
187 6.09e+02 2.08e+02 2.01e+03
188 6.09e+02 2.08e+02 2.01e+03
189 6.08e+02 2.08e+02 2.00e+03
190 6.08e+02 2.07e+02 2.00e+03
191 6.08e+02 2.07e+02 2.00e+03
192 6.08e+02 2.07e+02 2.00e+03
193 6.08e+02 2.07e+02 2.00e+03
194 6.08e+02 2.07e+02 2.00e+03
195 6.08e+02 2.07e+02 2.00e+03
196 6.08e+02 2.07e+02 2.00e+03
197 6.08e+02 2.07e+02 2.00e+03
198 6.08e+02 2.07e+02 2.00e+03
199 6.08e+02 2.07e+02 2.00e+03
----------------------------------
ConvBPDNDictLearn_Consensus solve time: 75.80s
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')
