Parallel CSC with a Spatial Mask¶
This example compares the use of parcbpdn.ParConvBPDN with
cbpdn.ConvBPDNMaskDcpl for convolutional sparse coding with
a spatial mask [50]. The example problem is
inpainting of randomly distributed corruption of a greyscale image.
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 tvl2
from sporco.admm import cbpdn
from sporco.admm import parcbpdn
from sporco import util
from sporco import metric
from sporco import plot
plot.config_notebook_plotting()
Load a reference image.
img = util.ExampleImages().image('monarch.png', zoom=0.25, scaled=True,
gray=True, idxexp=np.s_[:, 160:672])
Create random mask and apply to reference image to obtain test image.
(The call to numpy.random.seed ensures that the pseudo-random noise
is reproducible.)
t = 0.5
np.random.seed(12345)
msk = np.random.randn(*(img.shape))
msk[np.abs(msk) > t] = 1
msk[np.abs(msk) < t] = 0
imgw = msk * img
Define pad and crop functions.
pn = 8
spad = lambda x: np.pad(x, pn, mode='symmetric')
zpad = lambda x: np.pad(x, pn, mode='constant')
crop = lambda x: x[pn:-pn, pn:-pn]
Construct padded mask and test image.
mskp = zpad(msk)
imgwp = spad(imgw)
\(\ell_2\)-TV denoising with a spatial mask as a non-linear lowpass filter. The highpass component is the difference between the test image and the lowpass component, multiplied by the mask for faster convergence of the convolutional sparse coding (see [60]).
lmbda = 0.05
opt = tvl2.TVL2Denoise.Options({'Verbose': False, 'MaxMainIter': 200,
'DFidWeight': mskp, 'gEvalY': False,
'AutoRho': {'Enabled': True}})
b = tvl2.TVL2Denoise(imgwp, lmbda, opt)
sl = b.solve()
sh = mskp * (imgwp - sl)
Load dictionary.
D = util.convdicts()['G:12x12x216']
plot.imview(util.tiledict(D), fgsz=(7, 7))
lmbda = 2e-2
The RelStopTol was chosen for the two different methods to stop with similar functional values
Initialise and run serial CSC solver using masked decoupling [28].
opt = cbpdn.ConvBPDNMaskDcpl.Options({'Verbose': True, 'MaxMainIter': 200,
'HighMemSolve': True, 'RelStopTol': 5e-2,
'AuxVarObj': False, 'RelaxParam': 1.8,
'rho': 5e1*lmbda + 1e-1, 'AutoRho':
{'Enabled': False, 'StdResiduals': False}})
b = cbpdn.ConvBPDNMaskDcpl(D, sh, lmbda, mskp, opt=opt)
X = b.solve()
Itn Fnc DFid Regℓ1 r s
------------------------------------------------------
0 1.20e+01 5.44e-03 5.98e+02 1.06e-01 9.64e-01
1 1.09e+01 3.73e-02 5.44e+02 9.75e-02 1.16e+00
2 1.01e+01 7.97e-02 5.00e+02 9.15e-02 1.16e+00
3 9.65e+00 1.15e-01 4.77e+02 8.79e-02 1.05e+00
4 9.54e+00 1.37e-01 4.70e+02 8.57e-02 9.00e-01
5 9.55e+00 1.50e-01 4.70e+02 8.35e-02 7.61e-01
6 9.50e+00 1.59e-01 4.67e+02 7.97e-02 6.53e-01
7 9.39e+00 1.66e-01 4.61e+02 7.59e-02 5.76e-01
8 9.27e+00 1.73e-01 4.55e+02 7.26e-02 5.16e-01
9 9.20e+00 1.81e-01 4.51e+02 6.98e-02 4.62e-01
10 9.20e+00 1.89e-01 4.51e+02 6.73e-02 4.13e-01
11 9.17e+00 1.98e-01 4.49e+02 6.48e-02 3.72e-01
12 9.15e+00 2.07e-01 4.47e+02 6.24e-02 3.39e-01
13 9.11e+00 2.14e-01 4.45e+02 6.02e-02 3.13e-01
14 9.06e+00 2.18e-01 4.42e+02 5.81e-02 2.93e-01
15 9.00e+00 2.21e-01 4.39e+02 5.62e-02 2.80e-01
16 8.90e+00 2.22e-01 4.34e+02 5.43e-02 2.72e-01
17 8.78e+00 2.22e-01 4.28e+02 5.26e-02 2.67e-01
18 8.63e+00 2.22e-01 4.21e+02 5.09e-02 2.63e-01
19 8.52e+00 2.22e-01 4.15e+02 4.96e-02 2.58e-01
20 8.40e+00 2.24e-01 4.09e+02 4.82e-02 2.52e-01
21 8.28e+00 2.26e-01 4.03e+02 4.69e-02 2.46e-01
22 8.17e+00 2.30e-01 3.97e+02 4.58e-02 2.41e-01
23 8.07e+00 2.33e-01 3.92e+02 4.47e-02 2.35e-01
24 7.98e+00 2.36e-01 3.87e+02 4.37e-02 2.30e-01
25 7.91e+00 2.40e-01 3.83e+02 4.28e-02 2.26e-01
26 7.84e+00 2.43e-01 3.80e+02 4.20e-02 2.22e-01
27 7.77e+00 2.46e-01 3.76e+02 4.11e-02 2.18e-01
28 7.70e+00 2.49e-01 3.73e+02 4.03e-02 2.15e-01
29 7.63e+00 2.52e-01 3.69e+02 3.95e-02 2.12e-01
30 7.55e+00 2.54e-01 3.65e+02 3.88e-02 2.08e-01
31 7.46e+00 2.57e-01 3.60e+02 3.81e-02 2.04e-01
32 7.37e+00 2.60e-01 3.55e+02 3.74e-02 2.00e-01
33 7.27e+00 2.64e-01 3.50e+02 3.67e-02 1.96e-01
34 7.18e+00 2.67e-01 3.46e+02 3.60e-02 1.92e-01
35 7.10e+00 2.70e-01 3.41e+02 3.54e-02 1.87e-01
36 7.02e+00 2.73e-01 3.37e+02 3.47e-02 1.83e-01
37 6.97e+00 2.76e-01 3.35e+02 3.41e-02 1.78e-01
38 6.93e+00 2.79e-01 3.32e+02 3.36e-02 1.73e-01
39 6.89e+00 2.81e-01 3.31e+02 3.30e-02 1.69e-01
40 6.86e+00 2.83e-01 3.29e+02 3.24e-02 1.65e-01
41 6.82e+00 2.85e-01 3.27e+02 3.19e-02 1.62e-01
42 6.78e+00 2.87e-01 3.25e+02 3.14e-02 1.59e-01
43 6.75e+00 2.89e-01 3.23e+02 3.09e-02 1.56e-01
44 6.72e+00 2.90e-01 3.21e+02 3.04e-02 1.53e-01
45 6.68e+00 2.92e-01 3.19e+02 2.99e-02 1.50e-01
46 6.64e+00 2.93e-01 3.17e+02 2.95e-02 1.48e-01
47 6.59e+00 2.94e-01 3.15e+02 2.91e-02 1.46e-01
48 6.53e+00 2.95e-01 3.12e+02 2.86e-02 1.44e-01
49 6.48e+00 2.96e-01 3.09e+02 2.82e-02 1.42e-01
50 6.41e+00 2.97e-01 3.06e+02 2.78e-02 1.41e-01
51 6.36e+00 2.98e-01 3.03e+02 2.74e-02 1.39e-01
52 6.30e+00 3.00e-01 3.00e+02 2.70e-02 1.38e-01
53 6.25e+00 3.01e-01 2.97e+02 2.66e-02 1.37e-01
54 6.20e+00 3.03e-01 2.95e+02 2.62e-02 1.36e-01
55 6.16e+00 3.05e-01 2.93e+02 2.59e-02 1.34e-01
56 6.11e+00 3.06e-01 2.90e+02 2.55e-02 1.33e-01
57 6.07e+00 3.08e-01 2.88e+02 2.52e-02 1.32e-01
58 6.03e+00 3.09e-01 2.86e+02 2.49e-02 1.31e-01
59 5.99e+00 3.11e-01 2.84e+02 2.45e-02 1.29e-01
60 5.97e+00 3.12e-01 2.83e+02 2.42e-02 1.28e-01
61 5.94e+00 3.13e-01 2.81e+02 2.39e-02 1.26e-01
62 5.92e+00 3.14e-01 2.80e+02 2.36e-02 1.24e-01
63 5.90e+00 3.15e-01 2.79e+02 2.33e-02 1.23e-01
64 5.87e+00 3.16e-01 2.78e+02 2.31e-02 1.21e-01
65 5.85e+00 3.17e-01 2.76e+02 2.28e-02 1.19e-01
66 5.82e+00 3.18e-01 2.75e+02 2.25e-02 1.18e-01
67 5.80e+00 3.19e-01 2.74e+02 2.23e-02 1.16e-01
68 5.77e+00 3.19e-01 2.73e+02 2.20e-02 1.14e-01
69 5.75e+00 3.20e-01 2.72e+02 2.17e-02 1.13e-01
70 5.73e+00 3.20e-01 2.71e+02 2.15e-02 1.12e-01
71 5.71e+00 3.21e-01 2.69e+02 2.12e-02 1.10e-01
72 5.68e+00 3.21e-01 2.68e+02 2.10e-02 1.09e-01
73 5.65e+00 3.21e-01 2.67e+02 2.07e-02 1.08e-01
74 5.63e+00 3.22e-01 2.65e+02 2.05e-02 1.07e-01
75 5.60e+00 3.22e-01 2.64e+02 2.02e-02 1.06e-01
76 5.58e+00 3.22e-01 2.63e+02 2.00e-02 1.05e-01
77 5.56e+00 3.23e-01 2.62e+02 1.98e-02 1.03e-01
78 5.54e+00 3.23e-01 2.61e+02 1.97e-02 1.02e-01
79 5.52e+00 3.24e-01 2.60e+02 1.95e-02 1.01e-01
80 5.50e+00 3.24e-01 2.59e+02 1.93e-02 9.95e-02
81 5.47e+00 3.25e-01 2.57e+02 1.91e-02 9.83e-02
82 5.44e+00 3.25e-01 2.56e+02 1.89e-02 9.73e-02
83 5.41e+00 3.26e-01 2.54e+02 1.87e-02 9.64e-02
84 5.38e+00 3.27e-01 2.52e+02 1.86e-02 9.56e-02
85 5.35e+00 3.27e-01 2.51e+02 1.84e-02 9.49e-02
86 5.32e+00 3.28e-01 2.50e+02 1.82e-02 9.42e-02
87 5.30e+00 3.29e-01 2.48e+02 1.80e-02 9.36e-02
88 5.28e+00 3.30e-01 2.47e+02 1.79e-02 9.30e-02
89 5.26e+00 3.30e-01 2.46e+02 1.77e-02 9.24e-02
90 5.24e+00 3.31e-01 2.45e+02 1.76e-02 9.17e-02
91 5.22e+00 3.31e-01 2.44e+02 1.74e-02 9.11e-02
92 5.20e+00 3.32e-01 2.44e+02 1.73e-02 9.04e-02
93 5.19e+00 3.32e-01 2.43e+02 1.71e-02 8.96e-02
94 5.18e+00 3.33e-01 2.42e+02 1.70e-02 8.89e-02
95 5.17e+00 3.33e-01 2.42e+02 1.69e-02 8.81e-02
96 5.15e+00 3.34e-01 2.41e+02 1.67e-02 8.72e-02
97 5.14e+00 3.34e-01 2.40e+02 1.66e-02 8.64e-02
98 5.13e+00 3.35e-01 2.40e+02 1.65e-02 8.56e-02
99 5.11e+00 3.35e-01 2.39e+02 1.64e-02 8.49e-02
100 5.09e+00 3.36e-01 2.38e+02 1.62e-02 8.42e-02
101 5.07e+00 3.36e-01 2.37e+02 1.61e-02 8.36e-02
102 5.05e+00 3.37e-01 2.36e+02 1.60e-02 8.30e-02
103 5.03e+00 3.38e-01 2.35e+02 1.59e-02 8.25e-02
104 5.01e+00 3.38e-01 2.34e+02 1.57e-02 8.19e-02
105 4.99e+00 3.39e-01 2.33e+02 1.56e-02 8.14e-02
106 4.97e+00 3.39e-01 2.32e+02 1.55e-02 8.08e-02
107 4.96e+00 3.40e-01 2.31e+02 1.53e-02 8.03e-02
108 4.94e+00 3.40e-01 2.30e+02 1.52e-02 7.97e-02
109 4.93e+00 3.41e-01 2.29e+02 1.51e-02 7.91e-02
110 4.91e+00 3.41e-01 2.29e+02 1.50e-02 7.86e-02
111 4.90e+00 3.41e-01 2.28e+02 1.48e-02 7.81e-02
112 4.88e+00 3.42e-01 2.27e+02 1.47e-02 7.76e-02
113 4.87e+00 3.42e-01 2.26e+02 1.46e-02 7.71e-02
114 4.85e+00 3.42e-01 2.25e+02 1.45e-02 7.66e-02
115 4.84e+00 3.43e-01 2.25e+02 1.44e-02 7.62e-02
116 4.82e+00 3.43e-01 2.24e+02 1.43e-02 7.58e-02
117 4.81e+00 3.43e-01 2.23e+02 1.41e-02 7.54e-02
118 4.79e+00 3.43e-01 2.22e+02 1.40e-02 7.50e-02
119 4.78e+00 3.44e-01 2.22e+02 1.39e-02 7.45e-02
120 4.77e+00 3.44e-01 2.21e+02 1.38e-02 7.40e-02
121 4.76e+00 3.44e-01 2.21e+02 1.37e-02 7.35e-02
122 4.75e+00 3.44e-01 2.20e+02 1.36e-02 7.29e-02
123 4.74e+00 3.45e-01 2.20e+02 1.35e-02 7.22e-02
124 4.73e+00 3.45e-01 2.19e+02 1.34e-02 7.15e-02
125 4.72e+00 3.45e-01 2.19e+02 1.33e-02 7.07e-02
126 4.71e+00 3.45e-01 2.18e+02 1.32e-02 6.99e-02
127 4.71e+00 3.45e-01 2.18e+02 1.31e-02 6.92e-02
128 4.70e+00 3.46e-01 2.18e+02 1.30e-02 6.84e-02
129 4.68e+00 3.46e-01 2.17e+02 1.29e-02 6.77e-02
130 4.67e+00 3.46e-01 2.16e+02 1.29e-02 6.71e-02
131 4.66e+00 3.46e-01 2.16e+02 1.28e-02 6.65e-02
132 4.65e+00 3.47e-01 2.15e+02 1.27e-02 6.60e-02
133 4.63e+00 3.47e-01 2.14e+02 1.26e-02 6.55e-02
134 4.62e+00 3.47e-01 2.14e+02 1.25e-02 6.52e-02
135 4.61e+00 3.47e-01 2.13e+02 1.24e-02 6.49e-02
136 4.59e+00 3.47e-01 2.12e+02 1.23e-02 6.46e-02
137 4.58e+00 3.47e-01 2.11e+02 1.22e-02 6.44e-02
138 4.56e+00 3.48e-01 2.11e+02 1.21e-02 6.42e-02
139 4.55e+00 3.48e-01 2.10e+02 1.21e-02 6.39e-02
140 4.54e+00 3.48e-01 2.09e+02 1.20e-02 6.37e-02
141 4.53e+00 3.48e-01 2.09e+02 1.19e-02 6.34e-02
142 4.52e+00 3.49e-01 2.08e+02 1.18e-02 6.31e-02
143 4.51e+00 3.49e-01 2.08e+02 1.18e-02 6.27e-02
144 4.50e+00 3.49e-01 2.08e+02 1.17e-02 6.23e-02
145 4.50e+00 3.49e-01 2.07e+02 1.16e-02 6.18e-02
146 4.49e+00 3.50e-01 2.07e+02 1.15e-02 6.13e-02
147 4.49e+00 3.50e-01 2.07e+02 1.15e-02 6.08e-02
148 4.48e+00 3.50e-01 2.07e+02 1.14e-02 6.03e-02
149 4.48e+00 3.50e-01 2.06e+02 1.13e-02 5.98e-02
150 4.47e+00 3.50e-01 2.06e+02 1.13e-02 5.94e-02
151 4.46e+00 3.50e-01 2.05e+02 1.12e-02 5.90e-02
152 4.45e+00 3.50e-01 2.05e+02 1.11e-02 5.87e-02
153 4.44e+00 3.51e-01 2.04e+02 1.10e-02 5.85e-02
154 4.42e+00 3.51e-01 2.04e+02 1.10e-02 5.83e-02
155 4.41e+00 3.51e-01 2.03e+02 1.09e-02 5.82e-02
156 4.40e+00 3.51e-01 2.02e+02 1.08e-02 5.81e-02
157 4.38e+00 3.51e-01 2.02e+02 1.07e-02 5.80e-02
158 4.37e+00 3.51e-01 2.01e+02 1.07e-02 5.79e-02
159 4.36e+00 3.52e-01 2.01e+02 1.06e-02 5.78e-02
160 4.35e+00 3.52e-01 2.00e+02 1.05e-02 5.76e-02
161 4.34e+00 3.52e-01 2.00e+02 1.05e-02 5.74e-02
162 4.34e+00 3.52e-01 1.99e+02 1.04e-02 5.71e-02
163 4.33e+00 3.52e-01 1.99e+02 1.04e-02 5.68e-02
164 4.32e+00 3.53e-01 1.98e+02 1.03e-02 5.65e-02
165 4.31e+00 3.53e-01 1.98e+02 1.03e-02 5.62e-02
166 4.31e+00 3.53e-01 1.98e+02 1.02e-02 5.58e-02
167 4.30e+00 3.53e-01 1.97e+02 1.01e-02 5.55e-02
168 4.29e+00 3.53e-01 1.97e+02 1.01e-02 5.53e-02
169 4.28e+00 3.54e-01 1.96e+02 1.00e-02 5.50e-02
170 4.27e+00 3.54e-01 1.96e+02 9.97e-03 5.48e-02
171 4.26e+00 3.54e-01 1.95e+02 9.91e-03 5.46e-02
172 4.25e+00 3.54e-01 1.95e+02 9.86e-03 5.43e-02
173 4.24e+00 3.54e-01 1.94e+02 9.80e-03 5.41e-02
174 4.24e+00 3.54e-01 1.94e+02 9.74e-03 5.38e-02
175 4.23e+00 3.55e-01 1.94e+02 9.69e-03 5.36e-02
176 4.22e+00 3.55e-01 1.93e+02 9.63e-03 5.33e-02
177 4.22e+00 3.55e-01 1.93e+02 9.58e-03 5.29e-02
178 4.21e+00 3.55e-01 1.93e+02 9.53e-03 5.26e-02
179 4.21e+00 3.55e-01 1.93e+02 9.48e-03 5.22e-02
180 4.20e+00 3.55e-01 1.92e+02 9.44e-03 5.19e-02
181 4.20e+00 3.55e-01 1.92e+02 9.39e-03 5.15e-02
182 4.19e+00 3.56e-01 1.92e+02 9.34e-03 5.12e-02
183 4.19e+00 3.56e-01 1.92e+02 9.29e-03 5.08e-02
184 4.18e+00 3.56e-01 1.91e+02 9.24e-03 5.05e-02
185 4.18e+00 3.56e-01 1.91e+02 9.19e-03 5.02e-02
186 4.17e+00 3.56e-01 1.91e+02 9.14e-03 4.98e-02
------------------------------------------------------
Initialise and run parallel CSC solver using an ADMM dictionary partition [42].
opt_par = parcbpdn.ParConvBPDN.Options({'Verbose': True, 'MaxMainIter': 200,
'HighMemSolve': True, 'RelStopTol': 1e-2,
'AuxVarObj': False, 'RelaxParam': 1.8,
'rho': 5e1*lmbda + 1e-1, 'alpha': 1.5,
'AutoRho': {'Enabled': False,
'StdResiduals': False}})
b_par = parcbpdn.ParConvBPDN(D, sh, lmbda, mskp, opt=opt_par)
X_par = b_par.solve()
Itn Fnc DFid Regl1 r s
------------------------------------------------------
0 5.80e+01 3.10e+01 1.35e+03 1.19e+00 1.19e+00
1 2.01e+01 1.35e+00 9.35e+02 9.84e-01 8.14e-01
2 3.60e+01 1.52e+01 1.04e+03 8.17e-01 6.34e-01
3 1.50e+01 3.53e-01 7.32e+02 7.28e-01 5.97e-01
4 2.47e+01 7.06e+00 8.82e+02 6.43e-01 5.43e-01
5 1.49e+01 1.03e+00 6.92e+02 6.03e-01 5.24e-01
6 1.89e+01 3.71e+00 7.60e+02 5.57e-01 5.45e-01
7 1.41e+01 1.13e+00 6.51e+02 5.33e-01 5.85e-01
8 1.52e+01 1.80e+00 6.69e+02 5.07e-01 6.23e-01
9 1.38e+01 1.08e+00 6.34e+02 4.90e-01 6.41e-01
10 1.40e+01 1.15e+00 6.42e+02 4.73e-01 6.34e-01
11 1.40e+01 1.10e+00 6.44e+02 4.57e-01 6.04e-01
12 1.39e+01 1.04e+00 6.43e+02 4.41e-01 5.64e-01
13 1.39e+01 1.12e+00 6.39e+02 4.25e-01 5.26e-01
14 1.35e+01 1.02e+00 6.23e+02 4.09e-01 4.98e-01
15 1.31e+01 1.02e+00 6.04e+02 3.94e-01 4.82e-01
16 1.25e+01 8.76e-01 5.80e+02 3.80e-01 4.73e-01
17 1.20e+01 7.96e-01 5.59e+02 3.65e-01 4.65e-01
18 1.15e+01 6.66e-01 5.40e+02 3.52e-01 4.55e-01
19 1.11e+01 5.90e-01 5.24e+02 3.40e-01 4.44e-01
20 1.07e+01 5.11e-01 5.11e+02 3.29e-01 4.30e-01
21 1.05e+01 4.70e-01 5.00e+02 3.18e-01 4.15e-01
22 1.03e+01 4.33e-01 4.92e+02 3.08e-01 4.00e-01
23 1.01e+01 4.21e-01 4.84e+02 2.99e-01 3.86e-01
24 9.96e+00 4.13e-01 4.77e+02 2.91e-01 3.74e-01
25 9.83e+00 4.20e-01 4.71e+02 2.84e-01 3.64e-01
26 9.73e+00 4.32e-01 4.65e+02 2.77e-01 3.55e-01
27 9.66e+00 4.52e-01 4.60e+02 2.70e-01 3.47e-01
28 9.59e+00 4.72e-01 4.56e+02 2.64e-01 3.40e-01
29 9.53e+00 4.94e-01 4.52e+02 2.58e-01 3.33e-01
30 9.47e+00 5.11e-01 4.48e+02 2.52e-01 3.26e-01
31 9.41e+00 5.24e-01 4.44e+02 2.47e-01 3.18e-01
32 9.33e+00 5.31e-01 4.40e+02 2.42e-01 3.11e-01
33 9.23e+00 5.33e-01 4.35e+02 2.37e-01 3.05e-01
34 9.12e+00 5.28e-01 4.30e+02 2.32e-01 2.99e-01
35 9.01e+00 5.19e-01 4.24e+02 2.27e-01 2.93e-01
36 8.89e+00 5.07e-01 4.19e+02 2.22e-01 2.86e-01
37 8.76e+00 4.92e-01 4.13e+02 2.18e-01 2.80e-01
38 8.61e+00 4.76e-01 4.06e+02 2.14e-01 2.75e-01
39 8.46e+00 4.60e-01 4.00e+02 2.09e-01 2.71e-01
40 8.32e+00 4.43e-01 3.94e+02 2.05e-01 2.67e-01
41 8.19e+00 4.27e-01 3.88e+02 2.02e-01 2.62e-01
42 8.08e+00 4.12e-01 3.84e+02 1.98e-01 2.57e-01
43 7.99e+00 4.00e-01 3.79e+02 1.94e-01 2.51e-01
44 7.90e+00 3.90e-01 3.75e+02 1.91e-01 2.46e-01
45 7.81e+00 3.82e-01 3.71e+02 1.87e-01 2.40e-01
46 7.71e+00 3.75e-01 3.67e+02 1.84e-01 2.36e-01
47 7.62e+00 3.70e-01 3.62e+02 1.81e-01 2.32e-01
48 7.54e+00 3.66e-01 3.59e+02 1.78e-01 2.29e-01
49 7.48e+00 3.63e-01 3.56e+02 1.75e-01 2.26e-01
50 7.43e+00 3.63e-01 3.53e+02 1.72e-01 2.22e-01
51 7.37e+00 3.64e-01 3.50e+02 1.69e-01 2.18e-01
52 7.31e+00 3.66e-01 3.47e+02 1.67e-01 2.14e-01
53 7.25e+00 3.70e-01 3.44e+02 1.64e-01 2.11e-01
54 7.20e+00 3.74e-01 3.41e+02 1.61e-01 2.09e-01
55 7.16e+00 3.78e-01 3.39e+02 1.59e-01 2.05e-01
56 7.12e+00 3.81e-01 3.37e+02 1.57e-01 2.02e-01
57 7.07e+00 3.84e-01 3.34e+02 1.54e-01 1.99e-01
58 7.02e+00 3.86e-01 3.32e+02 1.52e-01 1.96e-01
59 6.97e+00 3.87e-01 3.29e+02 1.50e-01 1.93e-01
60 6.92e+00 3.87e-01 3.26e+02 1.48e-01 1.90e-01
61 6.86e+00 3.87e-01 3.24e+02 1.46e-01 1.87e-01
62 6.80e+00 3.87e-01 3.21e+02 1.43e-01 1.85e-01
63 6.74e+00 3.85e-01 3.18e+02 1.41e-01 1.82e-01
64 6.68e+00 3.83e-01 3.15e+02 1.39e-01 1.80e-01
65 6.63e+00 3.81e-01 3.12e+02 1.38e-01 1.78e-01
66 6.58e+00 3.78e-01 3.10e+02 1.36e-01 1.75e-01
67 6.53e+00 3.75e-01 3.08e+02 1.34e-01 1.73e-01
68 6.48e+00 3.72e-01 3.05e+02 1.32e-01 1.70e-01
69 6.43e+00 3.70e-01 3.03e+02 1.30e-01 1.68e-01
70 6.38e+00 3.68e-01 3.01e+02 1.29e-01 1.65e-01
71 6.33e+00 3.67e-01 2.98e+02 1.27e-01 1.63e-01
72 6.29e+00 3.67e-01 2.96e+02 1.25e-01 1.61e-01
73 6.25e+00 3.67e-01 2.94e+02 1.24e-01 1.59e-01
74 6.21e+00 3.67e-01 2.92e+02 1.22e-01 1.57e-01
75 6.18e+00 3.68e-01 2.90e+02 1.20e-01 1.55e-01
76 6.14e+00 3.68e-01 2.89e+02 1.19e-01 1.53e-01
77 6.10e+00 3.68e-01 2.87e+02 1.17e-01 1.51e-01
78 6.06e+00 3.69e-01 2.85e+02 1.16e-01 1.49e-01
79 6.02e+00 3.69e-01 2.83e+02 1.15e-01 1.48e-01
80 5.99e+00 3.69e-01 2.81e+02 1.13e-01 1.46e-01
81 5.95e+00 3.69e-01 2.79e+02 1.12e-01 1.44e-01
82 5.92e+00 3.69e-01 2.78e+02 1.10e-01 1.43e-01
83 5.89e+00 3.69e-01 2.76e+02 1.09e-01 1.41e-01
84 5.86e+00 3.69e-01 2.74e+02 1.08e-01 1.39e-01
85 5.83e+00 3.68e-01 2.73e+02 1.07e-01 1.37e-01
86 5.79e+00 3.68e-01 2.71e+02 1.05e-01 1.35e-01
87 5.76e+00 3.68e-01 2.70e+02 1.04e-01 1.34e-01
88 5.73e+00 3.68e-01 2.68e+02 1.03e-01 1.32e-01
89 5.69e+00 3.68e-01 2.66e+02 1.02e-01 1.31e-01
90 5.65e+00 3.67e-01 2.64e+02 1.01e-01 1.29e-01
91 5.62e+00 3.67e-01 2.62e+02 9.95e-02 1.28e-01
92 5.59e+00 3.66e-01 2.61e+02 9.84e-02 1.27e-01
93 5.56e+00 3.66e-01 2.60e+02 9.73e-02 1.26e-01
94 5.54e+00 3.66e-01 2.59e+02 9.62e-02 1.24e-01
95 5.52e+00 3.66e-01 2.58e+02 9.51e-02 1.22e-01
96 5.49e+00 3.67e-01 2.56e+02 9.41e-02 1.21e-01
97 5.46e+00 3.68e-01 2.55e+02 9.30e-02 1.19e-01
98 5.43e+00 3.69e-01 2.53e+02 9.20e-02 1.18e-01
99 5.40e+00 3.69e-01 2.51e+02 9.11e-02 1.17e-01
100 5.38e+00 3.70e-01 2.50e+02 9.01e-02 1.16e-01
101 5.36e+00 3.71e-01 2.49e+02 8.91e-02 1.15e-01
102 5.34e+00 3.71e-01 2.49e+02 8.82e-02 1.14e-01
103 5.32e+00 3.72e-01 2.47e+02 8.73e-02 1.12e-01
104 5.29e+00 3.71e-01 2.46e+02 8.63e-02 1.11e-01
105 5.27e+00 3.71e-01 2.45e+02 8.54e-02 1.10e-01
106 5.23e+00 3.70e-01 2.43e+02 8.46e-02 1.09e-01
107 5.20e+00 3.70e-01 2.42e+02 8.37e-02 1.08e-01
108 5.17e+00 3.69e-01 2.40e+02 8.28e-02 1.07e-01
109 5.15e+00 3.68e-01 2.39e+02 8.20e-02 1.06e-01
110 5.13e+00 3.67e-01 2.38e+02 8.11e-02 1.05e-01
111 5.12e+00 3.66e-01 2.38e+02 8.03e-02 1.03e-01
112 5.10e+00 3.65e-01 2.37e+02 7.95e-02 1.02e-01
113 5.08e+00 3.64e-01 2.36e+02 7.87e-02 1.00e-01
114 5.04e+00 3.63e-01 2.34e+02 7.79e-02 9.93e-02
115 5.01e+00 3.63e-01 2.32e+02 7.71e-02 9.86e-02
116 4.98e+00 3.62e-01 2.31e+02 7.64e-02 9.82e-02
117 4.96e+00 3.62e-01 2.30e+02 7.56e-02 9.76e-02
118 4.94e+00 3.61e-01 2.29e+02 7.49e-02 9.68e-02
119 4.92e+00 3.61e-01 2.28e+02 7.41e-02 9.58e-02
120 4.91e+00 3.61e-01 2.28e+02 7.34e-02 9.45e-02
121 4.90e+00 3.60e-01 2.27e+02 7.27e-02 9.32e-02
122 4.88e+00 3.60e-01 2.26e+02 7.20e-02 9.20e-02
123 4.85e+00 3.60e-01 2.25e+02 7.13e-02 9.11e-02
124 4.83e+00 3.60e-01 2.23e+02 7.06e-02 9.04e-02
125 4.81e+00 3.61e-01 2.22e+02 7.00e-02 8.98e-02
126 4.79e+00 3.61e-01 2.22e+02 6.93e-02 8.91e-02
127 4.78e+00 3.62e-01 2.21e+02 6.87e-02 8.84e-02
128 4.76e+00 3.63e-01 2.20e+02 6.80e-02 8.76e-02
129 4.75e+00 3.64e-01 2.19e+02 6.74e-02 8.68e-02
130 4.73e+00 3.64e-01 2.18e+02 6.68e-02 8.59e-02
131 4.72e+00 3.65e-01 2.18e+02 6.62e-02 8.51e-02
132 4.70e+00 3.66e-01 2.17e+02 6.56e-02 8.43e-02
133 4.68e+00 3.66e-01 2.16e+02 6.50e-02 8.35e-02
134 4.67e+00 3.66e-01 2.15e+02 6.44e-02 8.27e-02
135 4.65e+00 3.67e-01 2.14e+02 6.38e-02 8.20e-02
136 4.64e+00 3.67e-01 2.14e+02 6.32e-02 8.12e-02
137 4.63e+00 3.67e-01 2.13e+02 6.27e-02 8.04e-02
138 4.61e+00 3.67e-01 2.12e+02 6.21e-02 7.96e-02
139 4.60e+00 3.67e-01 2.11e+02 6.15e-02 7.89e-02
140 4.58e+00 3.67e-01 2.10e+02 6.10e-02 7.83e-02
141 4.56e+00 3.67e-01 2.10e+02 6.04e-02 7.78e-02
142 4.54e+00 3.67e-01 2.09e+02 5.99e-02 7.73e-02
143 4.53e+00 3.67e-01 2.08e+02 5.94e-02 7.66e-02
144 4.52e+00 3.67e-01 2.08e+02 5.89e-02 7.58e-02
145 4.51e+00 3.67e-01 2.07e+02 5.84e-02 7.49e-02
146 4.50e+00 3.67e-01 2.07e+02 5.78e-02 7.40e-02
147 4.48e+00 3.67e-01 2.06e+02 5.73e-02 7.32e-02
148 4.47e+00 3.67e-01 2.05e+02 5.68e-02 7.26e-02
149 4.45e+00 3.67e-01 2.04e+02 5.64e-02 7.21e-02
150 4.43e+00 3.67e-01 2.03e+02 5.59e-02 7.17e-02
151 4.42e+00 3.67e-01 2.03e+02 5.54e-02 7.12e-02
152 4.41e+00 3.67e-01 2.02e+02 5.49e-02 7.07e-02
153 4.40e+00 3.67e-01 2.01e+02 5.45e-02 7.01e-02
154 4.38e+00 3.68e-01 2.01e+02 5.40e-02 6.95e-02
155 4.37e+00 3.68e-01 2.00e+02 5.35e-02 6.89e-02
156 4.36e+00 3.68e-01 2.00e+02 5.31e-02 6.83e-02
157 4.35e+00 3.68e-01 1.99e+02 5.26e-02 6.77e-02
158 4.34e+00 3.68e-01 1.98e+02 5.22e-02 6.71e-02
159 4.32e+00 3.68e-01 1.98e+02 5.18e-02 6.65e-02
160 4.31e+00 3.68e-01 1.97e+02 5.13e-02 6.59e-02
161 4.30e+00 3.67e-01 1.97e+02 5.09e-02 6.53e-02
162 4.29e+00 3.67e-01 1.96e+02 5.05e-02 6.47e-02
163 4.28e+00 3.67e-01 1.95e+02 5.01e-02 6.42e-02
164 4.26e+00 3.67e-01 1.95e+02 4.97e-02 6.37e-02
165 4.25e+00 3.66e-01 1.94e+02 4.93e-02 6.32e-02
166 4.23e+00 3.66e-01 1.93e+02 4.89e-02 6.28e-02
167 4.22e+00 3.66e-01 1.93e+02 4.85e-02 6.24e-02
168 4.21e+00 3.66e-01 1.92e+02 4.81e-02 6.20e-02
------------------------------------------------------
Report runtimes of different methods of solving the same problem.
print("ConvBPDNMaskDcpl solve time: %.2fs" % b.timer.elapsed('solve_wo_rsdl'))
print("ParConvBPDN solve time: %.2fs" % b_par.timer.elapsed('solve_wo_rsdl'))
print("ParConvBPDN was %.2f times faster than ConvBPDNMaskDcpl\n" %
(b.timer.elapsed('solve_wo_rsdl')/b_par.timer.elapsed('solve_wo_rsdl')))
ConvBPDNMaskDcpl solve time: 80.13s
ParConvBPDN solve time: 9.94s
ParConvBPDN was 8.06 times faster than ConvBPDNMaskDcpl
Reconstruct images from sparse representations.
imgr = crop(sl + b.reconstruct().squeeze())
imgr_par = crop(sl + b_par.reconstruct().squeeze())
Report performances of different methods of solving the same problem.
print("Corrupted image PSNR: %5.2f dB" % metric.psnr(img, imgw))
print("Serial Reconstruction PSNR: %5.2f dB" % metric.psnr(img, imgr))
print("Parallel Reconstruction PSNR: %5.2f dB\n" % metric.psnr(img, imgr_par))
Corrupted image PSNR: 10.07 dB
Serial Reconstruction PSNR: 21.82 dB
Parallel Reconstruction PSNR: 21.82 dB
Display reference, test, and reconstructed images
fig = plot.figure(figsize=(14, 14))
plot.subplot(2, 2, 1)
plot.imview(img, fig=fig, title='Reference Image')
plot.subplot(2, 2, 2)
plot.imview(imgw, fig=fig, title=('Corrupted Image PSNR: %5.2f dB' %
metric.psnr(img, imgw)))
plot.subplot(2, 2, 3)
plot.imview(imgr, fig=fig, title=('Serial reconstruction PSNR: %5.2f dB' %
metric.psnr(img, imgr)))
plot.subplot(2, 2, 4)
plot.imview(imgr_par, fig=fig, title=('Parallel reconstruction PSNR: %5.2f dB' %
metric.psnr(img, imgr_par)))
fig.show()
Display lowpass component and sparse representation
fig = plot.figure(figsize=(21, 7))
plot.subplot(1, 3, 1)
plot.imview(sl, fig=fig, cmap=plot.cm.Blues, title='Lowpass component')
plot.subplot(1, 3, 2)
plot.imview(np.squeeze(np.sum(abs(X), axis=b.cri.axisM)), fig=fig,
cmap=plot.cm.Blues, title='Serial sparse representation')
plot.subplot(1, 3, 3)
plot.imview(np.squeeze(np.sum(abs(X_par), axis=b.cri.axisM)), fig=fig,
cmap=plot.cm.Blues, title='Parallel sparse representation')
fig.show()
