Multi-channel CSC¶
This example demonstrates convolutional sparse coding of a colour signal with a product dictionary [25]
\[\mathrm{argmin}_X \; \left\| D X B^T - S \right\|_1 + \lambda \| X \|_1\]
where \(D\) is a convolutional dictionary, \(B\) is a standard dictionary, and \(S\) is a multi-channel input image.
This example uses the GPU accelerated version of admm.pdcsc
within the sporco.cupy subpackage.
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 import util
from sporco import signal
from sporco import fft
from sporco import linalg
from sporco import plot
plot.config_notebook_plotting()
from sporco import metric
from sporco.cupy import (cupy_enabled, np2cp, cp2np, select_device_by_load,
gpu_info)
from sporco.cupy.admm import pdcsc
from sporco.dictlrn import bpdndl
Load example image.
img = util.ExampleImages().image('kodim23.png', scaled=True,
idxexp=np.s_[160:416,60:316])
Highpass filter example image.
npd = 16
fltlmbd = 10
slc, shc = signal.tikhonov_filter(img, fltlmbd, npd)
Load greyscale convolutional dictionary.
D = util.convdicts()['G:8x8x64']
Learn a standard dictionary \(B\) to represent all pixel colours in the example image. Since the standard dictionary is a \(3 \times 6\) matrix, the sparse representation \(X\) has 6 pseudo-channels, which are converted to the 3 channels of the example image by right-multiplication by the dictionary \(B\), giving \(XB\).
S = shc.reshape((-1, shc.shape[-1])).T
np.random.seed(12345)
B0 = np.random.randn(S.shape[0], 6)
lmbda = 1e-2
opt = bpdndl.BPDNDictLearn.Options(
{'Verbose': True, 'MaxMainIter': 100,
'BPDN': {'rho': 10.0*lmbda, 'AutoRho': {'Enabled': False}},
'CMOD': {'rho': S.shape[1] / 3e2, 'AutoRho': {'Enabled': False}}})
d = bpdndl.BPDNDictLearn(B0, S, lmbda, opt)
B = d.solve()
Itn Fnc DFid ℓ1 Cnstr r_X s_X ρ_X r_D s_D ρ_D
--------------------------------------------------------------------------------------------------------
0 1.28e+02 9.77e+01 3.00e+03 9.28e-02 4.88e-01 1.20e+00 1.00e-01 5.53e-02 1.34e+00 2.18e+02
1 9.43e+01 5.17e+01 4.25e+03 1.18e-01 3.37e-01 6.04e-01 1.00e-01 7.91e-02 1.50e+00 2.18e+02
2 6.24e+01 2.38e+01 3.86e+03 1.15e-01 2.43e-01 3.39e-01 1.00e-01 5.40e-02 1.46e+00 2.18e+02
3 5.59e+01 1.59e+01 4.00e+03 8.68e-02 1.94e-01 1.62e-01 1.00e-01 3.63e-02 8.59e-01 2.18e+02
4 5.48e+01 1.28e+01 4.20e+03 6.08e-02 1.48e-01 1.40e-01 1.00e-01 2.53e-02 3.12e-01 2.18e+02
5 5.23e+01 1.08e+01 4.14e+03 5.07e-02 1.12e-01 1.25e-01 1.00e-01 2.05e-02 1.05e-01 2.18e+02
6 5.09e+01 8.96e+00 4.20e+03 4.02e-02 8.93e-02 7.65e-02 1.00e-01 1.66e-02 9.90e-02 2.18e+02
7 5.05e+01 7.72e+00 4.28e+03 3.05e-02 7.18e-02 5.68e-02 1.00e-01 1.28e-02 1.39e-01 2.18e+02
8 5.01e+01 7.89e+00 4.23e+03 2.38e-02 5.74e-02 5.19e-02 1.00e-01 1.02e-02 1.19e-01 2.18e+02
9 4.98e+01 7.07e+00 4.27e+03 1.76e-02 4.67e-02 3.94e-02 1.00e-01 7.79e-03 1.09e-01 2.18e+02
10 4.96e+01 6.78e+00 4.28e+03 1.23e-02 3.91e-02 2.95e-02 1.00e-01 6.05e-03 1.18e-01 2.18e+02
11 4.95e+01 6.78e+00 4.27e+03 1.02e-02 3.35e-02 2.74e-02 1.00e-01 5.49e-03 1.23e-01 2.18e+02
12 4.93e+01 6.43e+00 4.29e+03 7.38e-03 2.95e-02 2.33e-02 1.00e-01 4.87e-03 1.29e-01 2.18e+02
13 4.92e+01 6.28e+00 4.30e+03 6.19e-03 2.61e-02 1.99e-02 1.00e-01 4.72e-03 1.35e-01 2.18e+02
14 4.91e+01 6.25e+00 4.29e+03 4.46e-03 2.42e-02 1.86e-02 1.00e-01 4.52e-03 1.39e-01 2.18e+02
15 4.91e+01 6.10e+00 4.30e+03 3.63e-03 2.26e-02 1.72e-02 1.00e-01 4.53e-03 1.43e-01 2.18e+02
16 4.90e+01 6.01e+00 4.30e+03 2.56e-03 2.16e-02 1.61e-02 1.00e-01 4.47e-03 1.46e-01 2.18e+02
17 4.89e+01 5.96e+00 4.30e+03 2.21e-03 2.10e-02 1.56e-02 1.00e-01 4.54e-03 1.49e-01 2.18e+02
18 4.88e+01 5.81e+00 4.30e+03 1.45e-03 2.06e-02 1.61e-02 1.00e-01 4.83e-03 1.62e-01 2.18e+02
19 4.88e+01 5.75e+00 4.30e+03 1.67e-03 2.14e-02 1.85e-02 1.00e-01 5.36e-03 1.81e-01 2.18e+02
20 4.87e+01 5.67e+00 4.30e+03 9.83e-04 2.34e-02 2.22e-02 1.00e-01 5.73e-03 1.96e-01 2.18e+02
21 4.86e+01 5.51e+00 4.31e+03 1.07e-03 2.61e-02 2.47e-02 1.00e-01 6.00e-03 2.05e-01 2.18e+02
22 4.86e+01 5.47e+00 4.31e+03 1.18e-03 2.86e-02 2.30e-02 1.00e-01 6.34e-03 2.16e-01 2.18e+02
23 4.85e+01 5.52e+00 4.30e+03 5.24e-04 2.92e-02 1.90e-02 1.00e-01 6.65e-03 2.27e-01 2.18e+02
24 4.84e+01 5.46e+00 4.29e+03 1.39e-03 2.77e-02 1.66e-02 1.00e-01 6.39e-03 2.17e-01 2.18e+02
25 4.82e+01 5.30e+00 4.29e+03 1.72e-03 2.46e-02 1.62e-02 1.00e-01 5.63e-03 1.91e-01 2.18e+02
26 4.80e+01 5.17e+00 4.28e+03 7.31e-04 2.13e-02 1.55e-02 1.00e-01 4.84e-03 1.67e-01 2.18e+02
27 4.79e+01 5.09e+00 4.28e+03 7.83e-04 1.87e-02 1.36e-02 1.00e-01 4.36e-03 1.51e-01 2.18e+02
28 4.78e+01 5.01e+00 4.28e+03 1.02e-03 1.68e-02 1.23e-02 1.00e-01 4.13e-03 1.44e-01 2.18e+02
29 4.77e+01 4.95e+00 4.27e+03 8.75e-04 1.59e-02 1.21e-02 1.00e-01 4.03e-03 1.42e-01 2.18e+02
30 4.76e+01 4.92e+00 4.27e+03 5.01e-04 1.57e-02 1.16e-02 1.00e-01 4.02e-03 1.43e-01 2.18e+02
31 4.76e+01 4.90e+00 4.27e+03 2.28e-04 1.57e-02 1.06e-02 1.00e-01 4.06e-03 1.45e-01 2.18e+02
32 4.75e+01 4.87e+00 4.27e+03 1.44e-04 1.55e-02 9.78e-03 1.00e-01 4.03e-03 1.44e-01 2.18e+02
33 4.75e+01 4.82e+00 4.27e+03 2.93e-04 1.48e-02 9.41e-03 1.00e-01 3.89e-03 1.39e-01 2.18e+02
34 4.74e+01 4.76e+00 4.27e+03 4.30e-04 1.39e-02 8.77e-03 1.00e-01 3.66e-03 1.31e-01 2.18e+02
35 4.74e+01 4.71e+00 4.27e+03 5.41e-04 1.29e-02 8.11e-03 1.00e-01 3.41e-03 1.23e-01 2.18e+02
36 4.73e+01 4.67e+00 4.27e+03 5.86e-04 1.20e-02 7.76e-03 1.00e-01 3.25e-03 1.18e-01 2.18e+02
37 4.73e+01 4.64e+00 4.26e+03 5.70e-04 1.14e-02 7.56e-03 1.00e-01 3.18e-03 1.16e-01 2.18e+02
38 4.72e+01 4.62e+00 4.26e+03 3.90e-04 1.10e-02 7.29e-03 1.00e-01 3.16e-03 1.16e-01 2.18e+02
39 4.72e+01 4.61e+00 4.26e+03 2.14e-04 1.09e-02 7.04e-03 1.00e-01 3.15e-03 1.16e-01 2.18e+02
40 4.72e+01 4.59e+00 4.26e+03 1.49e-04 1.08e-02 6.85e-03 1.00e-01 3.12e-03 1.15e-01 2.18e+02
41 4.71e+01 4.57e+00 4.26e+03 1.66e-04 1.07e-02 6.46e-03 1.00e-01 3.06e-03 1.13e-01 2.18e+02
42 4.71e+01 4.55e+00 4.26e+03 2.86e-04 1.04e-02 6.03e-03 1.00e-01 2.99e-03 1.10e-01 2.18e+02
43 4.71e+01 4.52e+00 4.26e+03 4.05e-04 9.99e-03 5.70e-03 1.00e-01 2.92e-03 1.08e-01 2.18e+02
44 4.71e+01 4.50e+00 4.26e+03 4.49e-04 9.56e-03 5.52e-03 1.00e-01 2.84e-03 1.05e-01 2.18e+02
45 4.70e+01 4.48e+00 4.25e+03 4.09e-04 9.19e-03 5.37e-03 1.00e-01 2.78e-03 1.04e-01 2.18e+02
46 4.70e+01 4.46e+00 4.25e+03 3.26e-04 8.93e-03 5.14e-03 1.00e-01 2.73e-03 1.02e-01 2.18e+02
47 4.70e+01 4.45e+00 4.25e+03 2.52e-04 8.76e-03 4.96e-03 1.00e-01 2.70e-03 1.01e-01 2.18e+02
48 4.69e+01 4.44e+00 4.25e+03 1.81e-04 8.66e-03 4.87e-03 1.00e-01 2.67e-03 1.00e-01 2.18e+02
49 4.69e+01 4.43e+00 4.25e+03 1.66e-04 8.61e-03 4.78e-03 1.00e-01 2.64e-03 9.93e-02 2.18e+02
50 4.69e+01 4.42e+00 4.25e+03 1.83e-04 8.55e-03 4.65e-03 1.00e-01 2.61e-03 9.84e-02 2.18e+02
51 4.69e+01 4.41e+00 4.25e+03 2.29e-04 8.44e-03 4.49e-03 1.00e-01 2.58e-03 9.76e-02 2.18e+02
52 4.69e+01 4.40e+00 4.25e+03 2.71e-04 8.31e-03 4.41e-03 1.00e-01 2.56e-03 9.69e-02 2.18e+02
53 4.68e+01 4.39e+00 4.25e+03 2.84e-04 8.17e-03 4.34e-03 1.00e-01 2.54e-03 9.64e-02 2.18e+02
54 4.68e+01 4.38e+00 4.24e+03 2.68e-04 8.05e-03 4.23e-03 1.00e-01 2.51e-03 9.58e-02 2.18e+02
55 4.68e+01 4.37e+00 4.24e+03 2.38e-04 7.96e-03 4.10e-03 1.00e-01 2.49e-03 9.50e-02 2.18e+02
56 4.68e+01 4.36e+00 4.24e+03 2.05e-04 7.87e-03 4.06e-03 1.00e-01 2.46e-03 9.43e-02 2.18e+02
57 4.68e+01 4.35e+00 4.24e+03 1.83e-04 7.80e-03 4.06e-03 1.00e-01 2.44e-03 9.36e-02 2.18e+02
58 4.67e+01 4.35e+00 4.24e+03 1.87e-04 7.77e-03 4.00e-03 1.00e-01 2.42e-03 9.31e-02 2.18e+02
59 4.67e+01 4.34e+00 4.24e+03 1.92e-04 7.74e-03 3.90e-03 1.00e-01 2.40e-03 9.24e-02 2.18e+02
60 4.67e+01 4.34e+00 4.24e+03 2.14e-04 7.70e-03 3.85e-03 1.00e-01 2.38e-03 9.18e-02 2.18e+02
61 4.67e+01 4.33e+00 4.24e+03 2.30e-04 7.64e-03 3.85e-03 1.00e-01 2.36e-03 9.11e-02 2.18e+02
62 4.67e+01 4.32e+00 4.23e+03 2.36e-04 7.58e-03 3.81e-03 1.00e-01 2.33e-03 9.04e-02 2.18e+02
63 4.66e+01 4.31e+00 4.23e+03 2.30e-04 7.52e-03 3.71e-03 1.00e-01 2.31e-03 8.97e-02 2.18e+02
64 4.66e+01 4.31e+00 4.23e+03 2.20e-04 7.46e-03 3.63e-03 1.00e-01 2.28e-03 8.87e-02 2.18e+02
65 4.66e+01 4.30e+00 4.23e+03 2.03e-04 7.39e-03 3.59e-03 1.00e-01 2.25e-03 8.77e-02 2.18e+02
66 4.66e+01 4.30e+00 4.23e+03 1.96e-04 7.33e-03 3.52e-03 1.00e-01 2.21e-03 8.66e-02 2.18e+02
67 4.66e+01 4.29e+00 4.23e+03 2.01e-04 7.26e-03 3.43e-03 1.00e-01 2.18e-03 8.53e-02 2.18e+02
68 4.66e+01 4.28e+00 4.23e+03 2.00e-04 7.17e-03 3.33e-03 1.00e-01 2.14e-03 8.39e-02 2.18e+02
69 4.66e+01 4.27e+00 4.23e+03 2.13e-04 7.06e-03 3.28e-03 1.00e-01 2.10e-03 8.27e-02 2.18e+02
70 4.65e+01 4.26e+00 4.23e+03 2.20e-04 6.97e-03 3.41e-03 1.00e-01 2.06e-03 8.12e-02 2.18e+02
71 4.65e+01 4.25e+00 4.23e+03 2.54e-04 6.90e-03 3.77e-03 1.00e-01 2.02e-03 7.97e-02 2.18e+02
72 4.65e+01 4.24e+00 4.23e+03 2.27e-04 6.91e-03 4.12e-03 1.00e-01 1.98e-03 7.84e-02 2.18e+02
73 4.65e+01 4.23e+00 4.23e+03 2.04e-04 6.97e-03 4.27e-03 1.00e-01 1.96e-03 7.80e-02 2.18e+02
74 4.65e+01 4.22e+00 4.23e+03 2.06e-04 7.04e-03 4.20e-03 1.00e-01 1.95e-03 7.79e-02 2.18e+02
75 4.65e+01 4.22e+00 4.23e+03 1.84e-04 7.06e-03 3.89e-03 1.00e-01 1.93e-03 7.71e-02 2.18e+02
76 4.65e+01 4.21e+00 4.23e+03 1.90e-04 6.99e-03 3.54e-03 1.00e-01 1.89e-03 7.57e-02 2.18e+02
77 4.65e+01 4.20e+00 4.23e+03 1.97e-04 6.81e-03 3.29e-03 1.00e-01 1.84e-03 7.39e-02 2.18e+02
78 4.64e+01 4.20e+00 4.22e+03 2.09e-04 6.57e-03 3.14e-03 1.00e-01 1.79e-03 7.19e-02 2.18e+02
79 4.64e+01 4.19e+00 4.22e+03 2.17e-04 6.32e-03 3.02e-03 1.00e-01 1.73e-03 6.97e-02 2.18e+02
80 4.64e+01 4.18e+00 4.22e+03 2.15e-04 6.07e-03 2.87e-03 1.00e-01 1.67e-03 6.76e-02 2.18e+02
81 4.64e+01 4.17e+00 4.22e+03 2.23e-04 5.85e-03 2.71e-03 1.00e-01 1.63e-03 6.58e-02 2.18e+02
82 4.64e+01 4.17e+00 4.22e+03 2.25e-04 5.66e-03 2.62e-03 1.00e-01 1.59e-03 6.44e-02 2.18e+02
83 4.64e+01 4.16e+00 4.22e+03 2.18e-04 5.52e-03 2.54e-03 1.00e-01 1.56e-03 6.32e-02 2.18e+02
84 4.64e+01 4.15e+00 4.22e+03 2.09e-04 5.40e-03 2.49e-03 1.00e-01 1.52e-03 6.21e-02 2.18e+02
85 4.64e+01 4.15e+00 4.22e+03 2.04e-04 5.30e-03 2.42e-03 1.00e-01 1.49e-03 6.10e-02 2.18e+02
86 4.64e+01 4.14e+00 4.22e+03 1.92e-04 5.19e-03 2.34e-03 1.00e-01 1.46e-03 5.99e-02 2.18e+02
87 4.64e+01 4.14e+00 4.22e+03 1.86e-04 5.08e-03 2.26e-03 1.00e-01 1.43e-03 5.87e-02 2.18e+02
88 4.64e+01 4.13e+00 4.22e+03 1.82e-04 4.95e-03 2.18e-03 1.00e-01 1.40e-03 5.75e-02 2.18e+02
89 4.64e+01 4.13e+00 4.22e+03 1.81e-04 4.80e-03 2.13e-03 1.00e-01 1.37e-03 5.64e-02 2.18e+02
90 4.63e+01 4.13e+00 4.22e+03 1.86e-04 4.66e-03 2.11e-03 1.00e-01 1.34e-03 5.54e-02 2.18e+02
91 4.63e+01 4.12e+00 4.22e+03 1.84e-04 4.52e-03 2.07e-03 1.00e-01 1.32e-03 5.44e-02 2.18e+02
92 4.63e+01 4.12e+00 4.22e+03 1.81e-04 4.40e-03 1.99e-03 1.00e-01 1.29e-03 5.36e-02 2.18e+02
93 4.63e+01 4.11e+00 4.22e+03 1.83e-04 4.29e-03 1.92e-03 1.00e-01 1.27e-03 5.27e-02 2.18e+02
94 4.63e+01 4.11e+00 4.22e+03 1.76e-04 4.19e-03 1.89e-03 1.00e-01 1.25e-03 5.19e-02 2.18e+02
95 4.63e+01 4.11e+00 4.22e+03 1.70e-04 4.10e-03 1.85e-03 1.00e-01 1.23e-03 5.11e-02 2.18e+02
96 4.63e+01 4.10e+00 4.22e+03 1.70e-04 4.02e-03 1.79e-03 1.00e-01 1.20e-03 5.02e-02 2.18e+02
97 4.63e+01 4.10e+00 4.22e+03 1.63e-04 3.93e-03 1.75e-03 1.00e-01 1.18e-03 4.94e-02 2.18e+02
98 4.63e+01 4.10e+00 4.22e+03 1.61e-04 3.85e-03 1.72e-03 1.00e-01 1.16e-03 4.87e-02 2.18e+02
99 4.63e+01 4.10e+00 4.22e+03 1.62e-04 3.76e-03 1.68e-03 1.00e-01 1.14e-03 4.80e-02 2.18e+02
--------------------------------------------------------------------------------------------------------
Set pdcsc.ConvProdDictBPDN solver options.
lmbda = 1e-1
opt = pdcsc.ConvProdDictBPDN.Options({'Verbose': True, 'MaxMainIter': 100,
'RelStopTol': 5e-3, 'AuxVarObj': False})
Initialise and run CSC solver.
if not cupy_enabled():
print('CuPy/GPU device not available: running without GPU acceleration\n')
else:
id = select_device_by_load()
info = gpu_info()
if info:
print('Running on GPU %d (%s)\n' % (id, info[id].name))
b = pdcsc.ConvProdDictBPDN(np2cp(D), np2cp(B), np2cp(shc), lmbda, opt, dimK=0)
X = cp2np(b.solve())
print("ConvProdDictBPDN solve time: %.2fs" % b.timer.elapsed('solve'))
Running on GPU 0 (NVIDIA GeForce RTX 2080 Ti)
Itn Fnc DFid Regℓ1 r s ρ
----------------------------------------------------------------
0 4.30e+02 6.96e-01 4.30e+03 1.00e+00 1.86e-03 6.00e+00
1 3.87e+02 3.95e+00 3.83e+03 9.87e-01 4.14e-02 6.00e+00
2 3.37e+02 1.35e+01 3.24e+03 8.14e-01 2.59e-01 2.07e+01
3 2.67e+02 2.62e+01 2.41e+03 3.67e-01 3.45e-01 2.60e+01
4 2.89e+02 2.83e+01 2.60e+03 2.83e-01 2.30e-01 1.90e+01
5 2.67e+02 2.68e+01 2.40e+03 2.47e-01 1.57e-01 1.49e+01
6 2.35e+02 2.67e+01 2.08e+03 2.19e-01 1.18e-01 1.32e+01
7 2.17e+02 2.74e+01 1.89e+03 1.79e-01 8.78e-02 1.32e+01
8 2.00e+02 2.84e+01 1.71e+03 1.42e-01 7.38e-02 1.32e+01
9 1.90e+02 2.90e+01 1.61e+03 1.13e-01 6.49e-02 1.32e+01
10 1.84e+02 2.94e+01 1.55e+03 9.31e-02 5.71e-02 1.32e+01
11 1.78e+02 2.95e+01 1.48e+03 8.35e-02 5.05e-02 1.19e+01
12 1.74e+02 2.95e+01 1.44e+03 7.59e-02 4.44e-02 1.08e+01
13 1.69e+02 2.96e+01 1.39e+03 6.57e-02 3.92e-02 1.08e+01
14 1.62e+02 2.96e+01 1.33e+03 5.71e-02 3.56e-02 1.08e+01
15 1.58e+02 2.97e+01 1.29e+03 5.34e-02 3.28e-02 9.68e+00
16 1.55e+02 2.99e+01 1.25e+03 5.03e-02 2.99e-02 8.73e+00
17 1.54e+02 2.99e+01 1.24e+03 4.46e-02 2.70e-02 8.73e+00
18 1.53e+02 3.00e+01 1.23e+03 4.24e-02 2.48e-02 7.93e+00
19 1.51e+02 3.00e+01 1.21e+03 3.82e-02 2.30e-02 7.93e+00
20 1.50e+02 3.00e+01 1.20e+03 3.66e-02 2.15e-02 7.22e+00
21 1.47e+02 2.99e+01 1.18e+03 3.34e-02 2.01e-02 7.22e+00
22 1.46e+02 2.99e+01 1.16e+03 3.24e-02 1.88e-02 6.59e+00
23 1.44e+02 2.99e+01 1.14e+03 2.99e-02 1.75e-02 6.59e+00
24 1.42e+02 2.99e+01 1.12e+03 2.77e-02 1.64e-02 6.59e+00
25 1.41e+02 2.99e+01 1.11e+03 2.57e-02 1.55e-02 6.59e+00
26 1.39e+02 2.99e+01 1.09e+03 2.53e-02 1.47e-02 5.99e+00
27 1.38e+02 3.00e+01 1.08e+03 2.37e-02 1.40e-02 5.99e+00
28 1.37e+02 3.00e+01 1.07e+03 2.23e-02 1.33e-02 5.99e+00
29 1.36e+02 3.00e+01 1.06e+03 2.10e-02 1.27e-02 5.99e+00
30 1.36e+02 3.00e+01 1.05e+03 2.09e-02 1.21e-02 5.45e+00
31 1.35e+02 3.01e+01 1.05e+03 1.98e-02 1.16e-02 5.45e+00
32 1.34e+02 3.01e+01 1.04e+03 1.88e-02 1.10e-02 5.45e+00
33 1.34e+02 3.01e+01 1.04e+03 1.79e-02 1.06e-02 5.45e+00
34 1.33e+02 3.01e+01 1.03e+03 1.71e-02 1.01e-02 5.45e+00
35 1.32e+02 3.01e+01 1.02e+03 1.63e-02 9.72e-03 5.45e+00
36 1.31e+02 3.01e+01 1.01e+03 1.55e-02 9.36e-03 5.45e+00
37 1.30e+02 3.01e+01 1.00e+03 1.57e-02 9.04e-03 4.96e+00
38 1.30e+02 3.01e+01 9.95e+02 1.50e-02 8.70e-03 4.96e+00
39 1.29e+02 3.02e+01 9.89e+02 1.44e-02 8.35e-03 4.96e+00
40 1.29e+02 3.02e+01 9.85e+02 1.39e-02 8.01e-03 4.96e+00
41 1.28e+02 3.02e+01 9.80e+02 1.33e-02 7.69e-03 4.96e+00
42 1.28e+02 3.03e+01 9.76e+02 1.28e-02 7.43e-03 4.96e+00
43 1.27e+02 3.03e+01 9.71e+02 1.24e-02 7.19e-03 4.96e+00
44 1.27e+02 3.03e+01 9.66e+02 1.19e-02 6.99e-03 4.96e+00
45 1.26e+02 3.03e+01 9.61e+02 1.15e-02 6.79e-03 4.96e+00
46 1.26e+02 3.04e+01 9.56e+02 1.11e-02 6.60e-03 4.96e+00
47 1.25e+02 3.04e+01 9.51e+02 1.08e-02 6.42e-03 4.96e+00
48 1.25e+02 3.04e+01 9.46e+02 1.04e-02 6.25e-03 4.96e+00
49 1.24e+02 3.04e+01 9.41e+02 1.01e-02 6.10e-03 4.96e+00
50 1.24e+02 3.04e+01 9.36e+02 1.03e-02 5.92e-03 4.52e+00
51 1.24e+02 3.05e+01 9.33e+02 1.00e-02 5.77e-03 4.52e+00
52 1.23e+02 3.05e+01 9.30e+02 9.74e-03 5.60e-03 4.52e+00
53 1.23e+02 3.05e+01 9.27e+02 9.48e-03 5.43e-03 4.52e+00
54 1.23e+02 3.05e+01 9.24e+02 9.22e-03 5.28e-03 4.52e+00
55 1.23e+02 3.05e+01 9.21e+02 8.96e-03 5.13e-03 4.52e+00
56 1.22e+02 3.06e+01 9.18e+02 8.72e-03 5.00e-03 4.52e+00
57 1.22e+02 3.06e+01 9.15e+02 8.48e-03 4.87e-03 4.52e+00
58 1.22e+02 3.06e+01 9.12e+02 8.25e-03 4.77e-03 4.52e+00
59 1.22e+02 3.06e+01 9.09e+02 8.04e-03 4.64e-03 4.52e+00
60 1.21e+02 3.06e+01 9.06e+02 7.83e-03 4.52e-03 4.52e+00
61 1.21e+02 3.06e+01 9.03e+02 7.63e-03 4.41e-03 4.52e+00
62 1.21e+02 3.06e+01 9.00e+02 7.44e-03 4.30e-03 4.52e+00
63 1.20e+02 3.07e+01 8.97e+02 7.26e-03 4.20e-03 4.52e+00
64 1.20e+02 3.07e+01 8.94e+02 7.08e-03 4.09e-03 4.52e+00
65 1.20e+02 3.07e+01 8.91e+02 6.89e-03 4.00e-03 4.52e+00
66 1.19e+02 3.07e+01 8.88e+02 6.73e-03 3.91e-03 4.52e+00
67 1.19e+02 3.07e+01 8.84e+02 6.56e-03 3.82e-03 4.52e+00
68 1.19e+02 3.07e+01 8.81e+02 6.40e-03 3.73e-03 4.52e+00
69 1.19e+02 3.07e+01 8.78e+02 6.25e-03 3.65e-03 4.52e+00
70 1.18e+02 3.08e+01 8.75e+02 6.10e-03 3.58e-03 4.52e+00
71 1.18e+02 3.08e+01 8.73e+02 5.96e-03 3.50e-03 4.52e+00
72 1.18e+02 3.08e+01 8.71e+02 5.82e-03 3.43e-03 4.52e+00
73 1.18e+02 3.08e+01 8.69e+02 5.69e-03 3.35e-03 4.52e+00
74 1.17e+02 3.08e+01 8.67e+02 5.56e-03 3.27e-03 4.52e+00
75 1.17e+02 3.08e+01 8.65e+02 5.44e-03 3.21e-03 4.52e+00
76 1.17e+02 3.08e+01 8.63e+02 5.32e-03 3.14e-03 4.52e+00
77 1.17e+02 3.09e+01 8.61e+02 5.20e-03 3.08e-03 4.52e+00
78 1.17e+02 3.09e+01 8.59e+02 5.09e-03 3.02e-03 4.52e+00
79 1.17e+02 3.09e+01 8.57e+02 4.98e-03 2.96e-03 4.52e+00
----------------------------------------------------------------
ConvProdDictBPDN solve time: 11.11s
Compute partial and full reconstructions from sparse representation \(X\) with respect to convolutional dictionary \(D\) and standard dictionary \(B\). The partial reconstructions are \(DX\) and \(XB\), and the full reconstruction is \(DXB\).
DX = fft.fftconv(D[..., np.newaxis, np.newaxis, :], X, axes=(0, 1))
XB = linalg.dot(B, X, axis=2)
shr = cp2np(b.reconstruct().squeeze())
imgr = slc + shr
print("Reconstruction PSNR: %.2fdB\n" % metric.psnr(img, imgr))
Reconstruction PSNR: 34.93dB
Display original and reconstructed images.
gamma = lambda x, g: np.sign(x) * (np.abs(x)**g)
fig, ax = plot.subplots(nrows=2, ncols=2, figsize=(14, 14))
plot.imview(img, title='Original image', ax=ax[0, 0], fig=fig)
plot.imview(slc, title='Lowpass component', ax=ax[0, 1], fig=fig)
plot.imview(imgr, title='Reconstructed image', ax=ax[1, 0], fig=fig)
plot.imview(gamma(shr, 0.6), title='Reconstructed highpass component',
ax=ax[1, 1], fig=fig)
fig.show()
Display sparse representation components as sums of absolute values of coefficient maps for \(X\), \(DX\), and \(XB\).
fig, ax = plot.subplots(nrows=2, ncols=2, figsize=(14, 14))
plot.imview(gamma(np.sum(abs(X[..., 0:3, :, :]), axis=b.cri.axisM).squeeze(),
0.5), title='X (false colour, bands 0, 1, 2)', ax=ax[0, 0],
fig=fig)
plot.imview(gamma(np.sum(abs(X[..., 3:6, :, :]), axis=b.cri.axisM).squeeze(),
0.5), title='X (false colour, bands 3, 4, 5)', ax=ax[0, 1],
fig=fig)
plot.imview(gamma(np.sum(abs(DX[..., 0:3, :, :]), axis=b.cri.axisM).squeeze(),
0.5), title='DX (false colour, bands 0, 1, 2)', ax=ax[1, 0],
fig=fig)
plot.imview(gamma(np.sum(abs(DX[..., 3:6, :, :]), axis=b.cri.axisM).squeeze(),
0.5), title='DX (false colour, bands 3, 4, 5)', ax=ax[1, 1],
fig=fig)
fig.show()
plot.imview(gamma(np.sum(abs(XB), axis=b.cri.axisM).squeeze(), 0.5),
title='XB', fgsz=(6.4, 6.4))
Get iterations statistics from solver object and plot functional value, ADMM primary and dual residuals, and automatically adjusted ADMM penalty parameter against the iteration number.
its = b.getitstat()
ObjFun = [float(x) for x in its.ObjFun]
PrimalRsdl = [float(x) for x in its.PrimalRsdl]
DualRsdl = [float(x) for x in its.DualRsdl]
fig, ax = plot.subplots(nrows=1, ncols=3, figsize=(20, 5))
plot.plot(ObjFun, xlbl='Iterations', ylbl='Functional', ax=ax[0], fig=fig)
plot.plot(np.vstack((PrimalRsdl, DualRsdl)).T,
ptyp='semilogy', xlbl='Iterations', ylbl='Residual',
lgnd=['Primal', 'Dual'], ax=ax[1], fig=fig)
plot.plot(its.Rho, xlbl='Iterations', ylbl='Penalty Parameter', ax=ax[2],
fig=fig)
fig.show()
