def rec_error(beta):
"""
cross-validation
"""
res, energies = fista_tv(y1, beta, 400, H)
yres = H * res[-1].ravel()[:, np.newaxis]
return (((yres - y2)**2).mean()), res[-1], energies
from reconstruction.util import generate_synthetic_data
from time import time
import matplotlib.pyplot as plt
# Synthetic data
l = 256
x = generate_synthetic_data(l)
# Projection operator and projections data, with noise
H = build_projection_operator(l, l / 3)
y = H * x.ravel()[:, np.newaxis]
y += 2 * np.random.randn(*y.shape)
# Reconstruction
t1 = time()
res, energies = fista_tv(y, 50, 100, H)
t2 = time()
print "reconstruction done in %f s" % (t2 - t1)
# Fraction of errors of segmented image wrt ground truth
err = [np.abs(x - (resi > 0.5)).mean() for resi in res]
# Display results
plt.figure()
plt.subplot(221)
plt.imshow(x, cmap='gray', interpolation='nearest', vmin=0, vmax=1)
plt.title('original data (256x256)')
plt.axis('off')
plt.subplot(222)
plt.imshow(res[-1], cmap='gray', interpolation='nearest', vmin=0, vmax=1)
plt.title('reconstruction after 100 iterations')
from time import time
import matplotlib.pyplot as plt
# Synthetic data
l = 256
x = generate_synthetic_data(l)
# Projection operator and projections data, with noise
H = build_projection_operator(l, l / 3)
y = H * x.ravel()[:, np.newaxis]
y += 2 * np.random.randn(*y.shape)
# Reconstruction
t1 = time()
res, energies = fista_tv(y, 50, 100, H)
t2 = time()
print "reconstruction done in %f s" % (t2 - t1)
# Fraction of errors of segmented image wrt ground truth
err = [np.abs(x - (resi > 0.5)).mean() for resi in res]
# Display results
plt.figure()
plt.subplot(221)
plt.imshow(x, cmap="gray", interpolation="nearest", vmin=0, vmax=1)
plt.title("original data (256x256)")
plt.axis("off")
plt.subplot(222)
plt.imshow(res[-1], cmap="gray", interpolation="nearest", vmin=0, vmax=1)
plt.title("reconstruction after 100 iterations")
plt.subplot(2, 3, 1)
plt.imshow(x,
cmap=plt.cm.gnuplot2,
interpolation='nearest',
vmin=-.1,
vmax=1.2)
plt.title('original data (256x256)')
plt.axis('off')
for idx, (val_min, val_max, name) in enumerate([
(None, None, 'TV'),
(0, 1, 'TV + interval'),
]):
# Reconstruction
t1 = time()
res, energies = fista_tv(y, 50, 100, H, val_min=val_min, val_max=val_max)
t2 = time()
# Fraction of errors of segmented image wrt ground truth
err = np.abs(x - (res[-1] > 0.5)).mean()
print "%s: reconstruction done in %f s, %.3f%% segmentation error" % (
name, t2 - t1, 100 * err)
plt.subplot(2, 3, 2 + idx)
plt.imshow(res[-1],
cmap=plt.cm.gnuplot2,
interpolation='nearest',
vmin=-.1,
vmax=1.2)
plt.title('reconstruction with %s' % name)
plt.axis('off')
# Projection operator and projections data, with noise
H = build_projection_operator(l, l / 32)
y = H * x.ravel()[:, np.newaxis]
y += 5 * np.random.randn(*y.shape)
# Display original data
plt.figure(figsize=(12, 5))
plt.subplot(2, 3, 1)
plt.imshow(x, cmap=plt.cm.gnuplot2, interpolation="nearest", vmin=-0.1, vmax=1.2)
plt.title("original data (256x256)")
plt.axis("off")
for idx, (val_min, val_max, name) in enumerate([(None, None, "TV"), (0, 1, "TV + interval")]):
# Reconstruction
t1 = time()
res, energies = fista_tv(y, 50, 100, H, val_min=val_min, val_max=val_max)
t2 = time()
# Fraction of errors of segmented image wrt ground truth
err = np.abs(x - (res[-1] > 0.5)).mean()
print "%s: reconstruction done in %f s, %.3f%% segmentation error" % (name, t2 - t1, 100 * err)
plt.subplot(2, 3, 2 + idx)
plt.imshow(res[-1], cmap=plt.cm.gnuplot2, interpolation="nearest", vmin=-0.1, vmax=1.2)
plt.title("reconstruction with %s" % name)
plt.axis("off")
ax = plt.subplot(2, 3, 5 + idx)
ax.yaxis.set_scale("log")
plt.hist(res[-1].ravel(), bins=20, normed=True)
plt.yticks(())
plt.title("Histogram of pixel intensity")
