Impulse Noise Restoration via CSC¶
This example demonstrates the removal of salt & pepper noise from a colour image using convolutional sparse coding, with a colour dictionary [51] and with an \(\ell_1\) data fidelity term, an \(\ell_1\) regularisation term, and an additional gradient regularization term [52]
\[\mathrm{argmin}_\mathbf{x} \; \sum_c \left\| \sum_m \mathbf{d}_{c,m} * \mathbf{x}_m -\mathbf{s}_c \right\|_1 + \lambda \sum_m \| \mathbf{x}_m \|_1 + (\mu/2) \sum_i \sum_m \| G_i \mathbf{x}_m \|_2^2\]
where \(\mathbf{d}_{c,m}\) is channel \(c\) of the \(m^{\text{th}}\) dictionary filter, \(\mathbf{x}_m\) is the coefficient map corresponding to the \(m^{\text{th}}\) dictionary filter, \(\mathbf{s}_c\) is channel \(c\) of the input image, and \(G_i\) is an operator computing the derivative along spatial index \(i\).
This example uses the GPU accelerated version of admm.cbpdn
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 plot
plot.config_notebook_plotting()
from sporco.metric import psnr
from sporco.cupy import (cupy_enabled, np2cp, cp2np, select_device_by_load,
gpu_info)
from sporco.cupy.admm import cbpdn
Boundary artifacts are handled by performing a symmetric extension on the image to be denoised and then cropping the result to the original image support. This approach is simpler than the boundary handling strategies that involve the insertion of a spatial mask into the data fidelity term, and for many problems gives results of comparable quality. The functions defined here implement symmetric extension and cropping of images.
def pad(x, n=8):
if x.ndim == 2:
return np.pad(x, n, mode='symmetric')
else:
return np.pad(x, ((n, n), (n, n), (0, 0)), mode='symmetric')
def crop(x, n=8):
return x[n:-n, n:-n]
Load a reference image and corrupt it with 33% salt and pepper noise.
(The call to np.random.seed ensures that the pseudo-random noise is
reproducible.)
img = util.ExampleImages().image('monarch.png', zoom=0.5, scaled=True,
idxexp=np.s_[:, 160:672])
np.random.seed(12345)
imgn = signal.spnoise(img, 0.33)
We use a colour dictionary. The impulse denoising problem is solved by
appending some additional filters to the learned dictionary D0,
which is one of those distributed with SPORCO. These additional
components consist of a set of three impulse filters, one per colour
channel, that will represent the low frequency image components when
used together with a gradient penalty on the coefficient maps, as
discussed below.
D0 = util.convdicts()['RGB:8x8x3x64']
Di = np.zeros(D0.shape[0:2] + (3, 3), dtype=np.float32)
np.fill_diagonal(Di[0, 0], 1.0)
D = np.concatenate((Di, D0), axis=3)
The problem is solved using class admm.cbpdn.ConvL1L1Grd,
which implements a convolutional sparse coding problem with an
\(\ell_1\) data fidelity term, an \(\ell_1\) regularisation
term, and an additional gradient regularization term
[52], as defined above. The
regularization parameters for the \(\ell_1\) and gradient terms are
lmbda and mu respectively. Setting correct weighting arrays for
these regularization terms is critical to obtaining good performance.
For the \(\ell_1\) norm, the weights on the filters that are
intended to represent low frequency components are set to zero (we only
want them penalised by the gradient term), and the weights of the
remaining filters are set to zero. For the gradient penalty, all weights
are set to zero except for those corresponding to the filters intended
to represent low frequency components, which are set to unity.
lmbda = 3e0
mu = 2e1
w1 = np.ones((1, 1, 1, 1, D.shape[-1]), dtype=np.float32)
w1[..., 0:3] = 0.0
wg = np.zeros((D.shape[-1]), dtype=np.float32)
wg[..., 0:3] = 1.0
opt = cbpdn.ConvL1L1Grd.Options({'Verbose': True, 'MaxMainIter': 200,
'RelStopTol': 5e-3, 'AuxVarObj': False,
'rho': 4e1, 'RelaxParam': 1.8,
'L1Weight': np2cp(w1),
'GradWeight': np2cp(wg)})
Initialise the admm.cbpdn.ConvL1L1Grd object and call the
solve method.
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 = cbpdn.ConvL1L1Grd(np2cp(D), np2cp(pad(imgn)), lmbda, mu, opt=opt, dimK=0)
X = cp2np(b.solve())
Running on GPU 1 (GeForce RTX 2080 Ti)
Itn Fnc DFid Regℓ1 Regℓ2∇ r s
----------------------------------------------------------------
0 2.21e+05 4.84e+04 5.19e+04 8.16e+02 4.42e-01 1.50e+00
1 2.24e+05 5.18e+04 5.53e+04 3.43e+02 3.67e-01 1.42e+00
2 1.97e+05 4.97e+04 4.82e+04 1.29e+02 2.80e-01 1.50e+00
3 1.70e+05 4.89e+04 3.98e+04 1.15e+02 2.10e-01 1.53e+00
4 1.50e+05 4.64e+04 3.40e+04 7.75e+01 1.61e-01 1.58e+00
5 1.30e+05 4.54e+04 2.77e+04 8.42e+01 1.20e-01 1.53e+00
6 1.15e+05 4.39e+04 2.31e+04 7.67e+01 9.33e-02 1.61e+00
7 1.05e+05 4.34e+04 1.99e+04 8.08e+01 7.15e-02 1.42e+00
8 9.27e+04 4.23e+04 1.63e+04 7.68e+01 5.59e-02 1.65e+00
9 8.76e+04 4.17e+04 1.48e+04 7.76e+01 4.47e-02 1.40e+00
10 7.90e+04 4.10e+04 1.22e+04 7.63e+01 3.64e-02 1.73e+00
11 7.38e+04 4.05e+04 1.06e+04 7.54e+01 3.03e-02 1.41e+00
12 7.01e+04 4.00e+04 9.55e+03 7.48e+01 2.61e-02 1.76e+00
13 6.57e+04 3.95e+04 8.24e+03 7.38e+01 2.27e-02 1.52e+00
14 6.27e+04 3.90e+04 7.42e+03 7.35e+01 2.01e-02 1.72e+00
15 6.00e+04 3.86e+04 6.65e+03 7.30e+01 1.80e-02 1.67e+00
16 5.76e+04 3.83e+04 5.95e+03 7.29e+01 1.63e-02 1.65e+00
17 5.59e+04 3.79e+04 5.50e+03 7.27e+01 1.50e-02 1.73e+00
18 5.46e+04 3.76e+04 5.16e+03 7.26e+01 1.39e-02 1.66e+00
19 5.35e+04 3.74e+04 4.90e+03 7.25e+01 1.28e-02 1.72e+00
20 5.25e+04 3.72e+04 4.63e+03 7.25e+01 1.19e-02 1.69e+00
21 5.14e+04 3.70e+04 4.31e+03 7.25e+01 1.11e-02 1.68e+00
22 5.05e+04 3.68e+04 4.09e+03 7.25e+01 1.03e-02 1.69e+00
23 4.99e+04 3.67e+04 3.94e+03 7.26e+01 9.69e-03 1.66e+00
24 4.94e+04 3.65e+04 3.81e+03 7.26e+01 9.12e-03 1.65e+00
25 4.90e+04 3.64e+04 3.69e+03 7.28e+01 8.59e-03 1.65e+00
26 4.85e+04 3.64e+04 3.58e+03 7.29e+01 8.11e-03 1.63e+00
27 4.81e+04 3.63e+04 3.46e+03 7.30e+01 7.66e-03 1.62e+00
28 4.77e+04 3.62e+04 3.33e+03 7.31e+01 7.23e-03 1.59e+00
29 4.73e+04 3.62e+04 3.22e+03 7.32e+01 6.84e-03 1.57e+00
30 4.69e+04 3.61e+04 3.12e+03 7.34e+01 6.49e-03 1.55e+00
31 4.66e+04 3.61e+04 3.02e+03 7.35e+01 6.16e-03 1.53e+00
32 4.63e+04 3.61e+04 2.92e+03 7.37e+01 5.86e-03 1.51e+00
33 4.60e+04 3.60e+04 2.84e+03 7.38e+01 5.57e-03 1.48e+00
34 4.58e+04 3.60e+04 2.77e+03 7.39e+01 5.32e-03 1.45e+00
35 4.56e+04 3.60e+04 2.71e+03 7.41e+01 5.09e-03 1.42e+00
36 4.54e+04 3.60e+04 2.65e+03 7.42e+01 4.87e-03 1.39e+00
37 4.52e+04 3.60e+04 2.59e+03 7.43e+01 4.66e-03 1.36e+00
38 4.50e+04 3.60e+04 2.53e+03 7.45e+01 4.46e-03 1.32e+00
39 4.48e+04 3.60e+04 2.46e+03 7.46e+01 4.26e-03 1.29e+00
40 4.46e+04 3.59e+04 2.40e+03 7.47e+01 4.08e-03 1.26e+00
41 4.45e+04 3.59e+04 2.35e+03 7.48e+01 3.91e-03 1.22e+00
42 4.43e+04 3.59e+04 2.30e+03 7.50e+01 3.75e-03 1.19e+00
43 4.42e+04 3.59e+04 2.25e+03 7.51e+01 3.60e-03 1.16e+00
44 4.41e+04 3.59e+04 2.21e+03 7.52e+01 3.46e-03 1.12e+00
45 4.40e+04 3.59e+04 2.17e+03 7.54e+01 3.33e-03 1.08e+00
46 4.38e+04 3.59e+04 2.13e+03 7.55e+01 3.21e-03 1.05e+00
47 4.37e+04 3.59e+04 2.10e+03 7.56e+01 3.09e-03 1.02e+00
48 4.36e+04 3.59e+04 2.06e+03 7.57e+01 2.98e-03 9.83e-01
49 4.35e+04 3.59e+04 2.02e+03 7.58e+01 2.87e-03 9.51e-01
50 4.34e+04 3.59e+04 1.99e+03 7.59e+01 2.77e-03 9.19e-01
51 4.33e+04 3.59e+04 1.96e+03 7.60e+01 2.67e-03 8.89e-01
52 4.32e+04 3.59e+04 1.92e+03 7.61e+01 2.58e-03 8.63e-01
53 4.31e+04 3.59e+04 1.90e+03 7.62e+01 2.49e-03 8.41e-01
54 4.31e+04 3.59e+04 1.87e+03 7.63e+01 2.41e-03 8.20e-01
55 4.30e+04 3.59e+04 1.84e+03 7.64e+01 2.33e-03 7.98e-01
56 4.29e+04 3.59e+04 1.82e+03 7.64e+01 2.26e-03 7.74e-01
57 4.29e+04 3.59e+04 1.80e+03 7.65e+01 2.19e-03 7.48e-01
58 4.28e+04 3.59e+04 1.77e+03 7.66e+01 2.12e-03 7.23e-01
59 4.27e+04 3.59e+04 1.75e+03 7.66e+01 2.06e-03 6.99e-01
60 4.27e+04 3.59e+04 1.73e+03 7.67e+01 2.00e-03 6.77e-01
61 4.26e+04 3.59e+04 1.71e+03 7.67e+01 1.94e-03 6.57e-01
62 4.26e+04 3.59e+04 1.69e+03 7.68e+01 1.88e-03 6.37e-01
63 4.25e+04 3.59e+04 1.68e+03 7.68e+01 1.82e-03 6.18e-01
64 4.24e+04 3.59e+04 1.66e+03 7.68e+01 1.77e-03 5.99e-01
65 4.24e+04 3.59e+04 1.64e+03 7.69e+01 1.72e-03 5.82e-01
66 4.23e+04 3.59e+04 1.62e+03 7.69e+01 1.67e-03 5.66e-01
67 4.23e+04 3.59e+04 1.61e+03 7.69e+01 1.63e-03 5.50e-01
68 4.23e+04 3.59e+04 1.59e+03 7.70e+01 1.58e-03 5.37e-01
69 4.22e+04 3.59e+04 1.58e+03 7.70e+01 1.54e-03 5.24e-01
70 4.22e+04 3.59e+04 1.56e+03 7.70e+01 1.49e-03 5.11e-01
71 4.21e+04 3.59e+04 1.55e+03 7.71e+01 1.45e-03 4.98e-01
72 4.21e+04 3.59e+04 1.54e+03 7.71e+01 1.42e-03 4.85e-01
73 4.21e+04 3.59e+04 1.53e+03 7.71e+01 1.38e-03 4.73e-01
74 4.20e+04 3.59e+04 1.52e+03 7.71e+01 1.34e-03 4.60e-01
75 4.20e+04 3.59e+04 1.51e+03 7.72e+01 1.31e-03 4.48e-01
76 4.20e+04 3.59e+04 1.49e+03 7.72e+01 1.27e-03 4.37e-01
77 4.19e+04 3.59e+04 1.48e+03 7.72e+01 1.24e-03 4.26e-01
78 4.19e+04 3.59e+04 1.47e+03 7.72e+01 1.21e-03 4.15e-01
79 4.19e+04 3.59e+04 1.46e+03 7.73e+01 1.18e-03 4.05e-01
80 4.18e+04 3.59e+04 1.45e+03 7.73e+01 1.15e-03 3.94e-01
81 4.18e+04 3.59e+04 1.44e+03 7.73e+01 1.12e-03 3.84e-01
82 4.18e+04 3.59e+04 1.43e+03 7.73e+01 1.09e-03 3.74e-01
83 4.17e+04 3.59e+04 1.42e+03 7.74e+01 1.06e-03 3.64e-01
84 4.17e+04 3.59e+04 1.41e+03 7.74e+01 1.04e-03 3.55e-01
85 4.17e+04 3.59e+04 1.41e+03 7.74e+01 1.01e-03 3.46e-01
86 4.17e+04 3.59e+04 1.40e+03 7.74e+01 9.88e-04 3.38e-01
87 4.16e+04 3.59e+04 1.39e+03 7.74e+01 9.64e-04 3.30e-01
88 4.16e+04 3.59e+04 1.38e+03 7.74e+01 9.41e-04 3.23e-01
89 4.16e+04 3.59e+04 1.38e+03 7.75e+01 9.19e-04 3.15e-01
90 4.16e+04 3.59e+04 1.37e+03 7.75e+01 8.97e-04 3.08e-01
91 4.16e+04 3.59e+04 1.36e+03 7.75e+01 8.76e-04 3.01e-01
92 4.15e+04 3.59e+04 1.36e+03 7.75e+01 8.56e-04 2.94e-01
93 4.15e+04 3.59e+04 1.35e+03 7.75e+01 8.36e-04 2.87e-01
94 4.15e+04 3.59e+04 1.34e+03 7.75e+01 8.17e-04 2.80e-01
95 4.15e+04 3.59e+04 1.34e+03 7.75e+01 7.98e-04 2.73e-01
96 4.15e+04 3.59e+04 1.33e+03 7.76e+01 7.80e-04 2.67e-01
97 4.14e+04 3.59e+04 1.32e+03 7.76e+01 7.63e-04 2.60e-01
98 4.14e+04 3.59e+04 1.32e+03 7.76e+01 7.46e-04 2.53e-01
99 4.14e+04 3.59e+04 1.31e+03 7.76e+01 7.29e-04 2.47e-01
100 4.14e+04 3.59e+04 1.31e+03 7.76e+01 7.13e-04 2.41e-01
101 4.14e+04 3.59e+04 1.30e+03 7.77e+01 6.97e-04 2.35e-01
102 4.14e+04 3.59e+04 1.30e+03 7.77e+01 6.81e-04 2.30e-01
103 4.14e+04 3.59e+04 1.29e+03 7.77e+01 6.66e-04 2.24e-01
104 4.13e+04 3.59e+04 1.29e+03 7.77e+01 6.52e-04 2.19e-01
105 4.13e+04 3.59e+04 1.28e+03 7.77e+01 6.38e-04 2.14e-01
106 4.13e+04 3.59e+04 1.28e+03 7.77e+01 6.24e-04 2.10e-01
107 4.13e+04 3.59e+04 1.27e+03 7.77e+01 6.10e-04 2.06e-01
108 4.13e+04 3.59e+04 1.27e+03 7.78e+01 5.97e-04 2.02e-01
109 4.13e+04 3.59e+04 1.27e+03 7.78e+01 5.85e-04 1.98e-01
110 4.13e+04 3.59e+04 1.26e+03 7.78e+01 5.72e-04 1.94e-01
111 4.12e+04 3.59e+04 1.26e+03 7.78e+01 5.60e-04 1.90e-01
112 4.12e+04 3.59e+04 1.25e+03 7.78e+01 5.49e-04 1.86e-01
113 4.12e+04 3.59e+04 1.25e+03 7.78e+01 5.37e-04 1.82e-01
114 4.12e+04 3.59e+04 1.25e+03 7.78e+01 5.26e-04 1.79e-01
115 4.12e+04 3.59e+04 1.24e+03 7.78e+01 5.15e-04 1.75e-01
116 4.12e+04 3.59e+04 1.24e+03 7.78e+01 5.04e-04 1.71e-01
117 4.12e+04 3.59e+04 1.24e+03 7.79e+01 4.94e-04 1.68e-01
118 4.12e+04 3.59e+04 1.23e+03 7.79e+01 4.83e-04 1.64e-01
119 4.12e+04 3.59e+04 1.23e+03 7.79e+01 4.73e-04 1.61e-01
120 4.12e+04 3.59e+04 1.23e+03 7.79e+01 4.64e-04 1.57e-01
121 4.11e+04 3.59e+04 1.22e+03 7.79e+01 4.54e-04 1.54e-01
122 4.11e+04 3.59e+04 1.22e+03 7.79e+01 4.45e-04 1.50e-01
123 4.11e+04 3.59e+04 1.22e+03 7.79e+01 4.36e-04 1.47e-01
124 4.11e+04 3.59e+04 1.21e+03 7.79e+01 4.28e-04 1.43e-01
125 4.11e+04 3.59e+04 1.21e+03 7.79e+01 4.20e-04 1.40e-01
126 4.11e+04 3.59e+04 1.21e+03 7.79e+01 4.11e-04 1.37e-01
127 4.11e+04 3.59e+04 1.20e+03 7.79e+01 4.03e-04 1.34e-01
128 4.11e+04 3.59e+04 1.20e+03 7.79e+01 3.95e-04 1.31e-01
129 4.11e+04 3.59e+04 1.20e+03 7.80e+01 3.87e-04 1.29e-01
130 4.11e+04 3.59e+04 1.20e+03 7.80e+01 3.80e-04 1.26e-01
131 4.11e+04 3.59e+04 1.19e+03 7.80e+01 3.72e-04 1.24e-01
132 4.11e+04 3.59e+04 1.19e+03 7.80e+01 3.65e-04 1.21e-01
133 4.10e+04 3.59e+04 1.19e+03 7.80e+01 3.58e-04 1.19e-01
134 4.10e+04 3.59e+04 1.19e+03 7.80e+01 3.51e-04 1.16e-01
135 4.10e+04 3.59e+04 1.19e+03 7.80e+01 3.44e-04 1.14e-01
136 4.10e+04 3.59e+04 1.18e+03 7.80e+01 3.38e-04 1.12e-01
137 4.10e+04 3.59e+04 1.18e+03 7.80e+01 3.32e-04 1.10e-01
138 4.10e+04 3.59e+04 1.18e+03 7.80e+01 3.25e-04 1.08e-01
139 4.10e+04 3.59e+04 1.18e+03 7.80e+01 3.19e-04 1.06e-01
140 4.10e+04 3.59e+04 1.17e+03 7.81e+01 3.13e-04 1.04e-01
141 4.10e+04 3.59e+04 1.17e+03 7.81e+01 3.07e-04 1.02e-01
142 4.10e+04 3.59e+04 1.17e+03 7.81e+01 3.02e-04 1.00e-01
143 4.10e+04 3.59e+04 1.17e+03 7.81e+01 2.96e-04 9.79e-02
144 4.10e+04 3.59e+04 1.17e+03 7.81e+01 2.91e-04 9.58e-02
145 4.10e+04 3.59e+04 1.17e+03 7.81e+01 2.85e-04 9.37e-02
146 4.10e+04 3.59e+04 1.16e+03 7.81e+01 2.80e-04 9.16e-02
147 4.10e+04 3.59e+04 1.16e+03 7.81e+01 2.75e-04 8.97e-02
148 4.10e+04 3.59e+04 1.16e+03 7.81e+01 2.70e-04 8.78e-02
149 4.10e+04 3.59e+04 1.16e+03 7.81e+01 2.65e-04 8.61e-02
150 4.09e+04 3.59e+04 1.16e+03 7.81e+01 2.60e-04 8.45e-02
151 4.09e+04 3.59e+04 1.16e+03 7.81e+01 2.55e-04 8.29e-02
152 4.09e+04 3.59e+04 1.15e+03 7.81e+01 2.51e-04 8.13e-02
153 4.09e+04 3.59e+04 1.15e+03 7.81e+01 2.46e-04 7.98e-02
154 4.09e+04 3.59e+04 1.15e+03 7.82e+01 2.42e-04 7.84e-02
155 4.09e+04 3.59e+04 1.15e+03 7.82e+01 2.38e-04 7.69e-02
156 4.09e+04 3.59e+04 1.15e+03 7.82e+01 2.33e-04 7.56e-02
157 4.09e+04 3.59e+04 1.15e+03 7.82e+01 2.29e-04 7.42e-02
158 4.09e+04 3.59e+04 1.15e+03 7.82e+01 2.25e-04 7.30e-02
159 4.09e+04 3.59e+04 1.14e+03 7.82e+01 2.21e-04 7.18e-02
160 4.09e+04 3.59e+04 1.14e+03 7.82e+01 2.17e-04 7.06e-02
161 4.09e+04 3.59e+04 1.14e+03 7.82e+01 2.13e-04 6.95e-02
162 4.09e+04 3.59e+04 1.14e+03 7.82e+01 2.09e-04 6.83e-02
163 4.09e+04 3.59e+04 1.14e+03 7.82e+01 2.06e-04 6.70e-02
164 4.09e+04 3.59e+04 1.14e+03 7.82e+01 2.02e-04 6.57e-02
165 4.09e+04 3.59e+04 1.14e+03 7.82e+01 1.99e-04 6.43e-02
166 4.09e+04 3.59e+04 1.14e+03 7.82e+01 1.95e-04 6.30e-02
167 4.09e+04 3.59e+04 1.13e+03 7.82e+01 1.92e-04 6.16e-02
168 4.09e+04 3.59e+04 1.13e+03 7.82e+01 1.89e-04 6.02e-02
169 4.09e+04 3.59e+04 1.13e+03 7.82e+01 1.85e-04 5.89e-02
170 4.09e+04 3.59e+04 1.13e+03 7.82e+01 1.82e-04 5.77e-02
171 4.09e+04 3.59e+04 1.13e+03 7.82e+01 1.79e-04 5.66e-02
172 4.09e+04 3.59e+04 1.13e+03 7.82e+01 1.76e-04 5.57e-02
173 4.09e+04 3.59e+04 1.13e+03 7.82e+01 1.73e-04 5.48e-02
174 4.09e+04 3.59e+04 1.13e+03 7.83e+01 1.70e-04 5.41e-02
175 4.09e+04 3.59e+04 1.13e+03 7.83e+01 1.67e-04 5.34e-02
176 4.08e+04 3.59e+04 1.12e+03 7.83e+01 1.64e-04 5.27e-02
177 4.08e+04 3.59e+04 1.12e+03 7.83e+01 1.61e-04 5.20e-02
178 4.08e+04 3.59e+04 1.12e+03 7.83e+01 1.59e-04 5.12e-02
179 4.08e+04 3.59e+04 1.12e+03 7.83e+01 1.56e-04 5.03e-02
180 4.08e+04 3.59e+04 1.12e+03 7.83e+01 1.53e-04 4.93e-02
181 4.08e+04 3.59e+04 1.12e+03 7.83e+01 1.51e-04 4.82e-02
182 4.08e+04 3.59e+04 1.12e+03 7.83e+01 1.49e-04 4.71e-02
183 4.08e+04 3.59e+04 1.12e+03 7.83e+01 1.46e-04 4.60e-02
184 4.08e+04 3.59e+04 1.12e+03 7.83e+01 1.44e-04 4.50e-02
185 4.08e+04 3.59e+04 1.12e+03 7.83e+01 1.42e-04 4.40e-02
186 4.08e+04 3.59e+04 1.12e+03 7.83e+01 1.39e-04 4.31e-02
187 4.08e+04 3.59e+04 1.12e+03 7.83e+01 1.37e-04 4.23e-02
188 4.08e+04 3.59e+04 1.11e+03 7.83e+01 1.35e-04 4.16e-02
189 4.08e+04 3.59e+04 1.11e+03 7.83e+01 1.32e-04 4.09e-02
190 4.08e+04 3.59e+04 1.11e+03 7.83e+01 1.30e-04 4.03e-02
191 4.08e+04 3.59e+04 1.11e+03 7.83e+01 1.28e-04 3.97e-02
192 4.08e+04 3.59e+04 1.11e+03 7.83e+01 1.26e-04 3.90e-02
193 4.08e+04 3.59e+04 1.11e+03 7.83e+01 1.24e-04 3.83e-02
194 4.08e+04 3.59e+04 1.11e+03 7.83e+01 1.22e-04 3.77e-02
195 4.08e+04 3.59e+04 1.11e+03 7.83e+01 1.20e-04 3.70e-02
196 4.08e+04 3.59e+04 1.11e+03 7.83e+01 1.18e-04 3.65e-02
197 4.08e+04 3.59e+04 1.11e+03 7.83e+01 1.16e-04 3.59e-02
198 4.08e+04 3.59e+04 1.11e+03 7.83e+01 1.14e-04 3.55e-02
199 4.08e+04 3.59e+04 1.11e+03 7.83e+01 1.12e-04 3.50e-02
----------------------------------------------------------------
The denoised estimate of the image is just the reconstruction from all coefficient maps.
imgdp = cp2np(b.reconstruct().squeeze())
imgd = crop(imgdp)
Display solve time and denoising performance.
print("ConvL1L1Grd solve time: %5.2f s" % b.timer.elapsed('solve'))
print("Noisy image PSNR: %5.2f dB" % psnr(img, imgn))
print("Denoised image PSNR: %5.2f dB" % psnr(img, imgd))
ConvL1L1Grd solve time: 8.58 s
Noisy image PSNR: 10.37 dB
Denoised image PSNR: 27.54 dB
Display the reference, noisy, and denoised images.
fig, ax = plot.subplots(nrows=1, ncols=3, figsize=(21, 7))
fig.suptitle('ConvL1L1Grd Results')
plot.imview(img, ax=ax[0], title='Reference', fig=fig)
plot.imview(imgn, ax=ax[1], title='Noisy', fig=fig)
plot.imview(imgd, ax=ax[2], title='CSC Result', fig=fig)
fig.show()
Display the low frequency image component.
plot.imview(X[..., 0, 0:3].squeeze(), title='Low frequency component')
