def test_radon2d_adjointness(self):
# Set image size.
m, n = 39, 23
# Define angles.
angles = np.linspace(0, np.pi, 180, False)
# Create operators.
K, Kadj, ndet = radon.radon2d(m, n, angles)
# Apply to dummy image.
f = K(np.ones((m, n)))
np.testing.assert_allclose(f.shape[0], angles.size)
# Apply to dummy data.
f = Kadj(np.ones_like(f))
np.testing.assert_allclose(f.shape, (m, n))
# Create random matrix.
x = np.random.rand(m, n)
p, q = K(x).shape
# Create second random matrix.
y = np.random.rand(p, q)
# Check adjointness up to certain relative tolerance.
np.testing.assert_allclose(np.dot(K(x).flatten(), y.flatten()),
np.dot(x.flatten(),
Kadj(y).flatten()), 1e-3)
def test_radon2d_plot(self):
img = Image.open('data/phantom.png').convert('L')
img = np.array(img)
# Set image size.
m, n = img.shape
# Define angles.
angles = np.linspace(0, np.pi, 180, False)
# Create operators.
K, Kadj, ndet = radon.radon2d(m, n, angles)
# Plot original image.
plt.imshow(img, cmap='gray')
plt.colorbar()
plt.show()
# Apply to dummy image.
f = K(img)
# Plot data.
plt.imshow(f, cmap='gray')
plt.colorbar()
plt.show()
# Apply to dummy data.
f = Kadj(f)
# Plot result of backprojection.
plt.imshow(f, cmap='gray')
plt.colorbar()
plt.show()
def test_radon2d_operators_cuda(self):
# Define image size.
image_size = (31, 23)
# Define angles.
nangles = 180
angles = np.linspace(0, np.pi, nangles, False)
# Check if GPU is available.
cuda = torch.cuda.is_available()
device = torch.device('cuda') if cuda else 'cpu'
# Create operators.
R, Radj, ndet = radon.radon2d(*image_size, angles, cuda)
data_size = (nangles, ndet)
# Create instances for use with torch.
K = radon.RadonTransform(R, Radj, data_size)
Kadj = radon.BackProjection(R, Radj, image_size)
# Create random matrix.
x = torch.randn(1, 1, *image_size).to(device)
# Create second random matrix.
y = torch.randn(1, 1, *data_size).to(device)
# Check adjointness up to certain relative tolerance.
ip1 = torch.dot(K(x).flatten(), y.flatten())
ip2 = torch.dot(x.flatten(), Kadj(y).flatten())
torch.allclose(ip1, ip2)
def test_LinearOperator_radon_gradcheck(self):
# Set image size.
image_size = (5, 4)
# Define angles.
nangles = 180
angles = np.linspace(0, np.pi, nangles, False)
# Create operators.
R, Radj, ndet = radon.radon2d(*image_size, angles)
data_size = (nangles, ndet)
# Create instances for use with torch.
K = radon.RadonTransform(R, Radj, data_size)
Kadj = radon.BackProjection(R, Radj, image_size)
# Apply to dummy input.
x = torch.randn((1, 1, *image_size),
requires_grad=True,
dtype=torch.double)
f = K(x)
# Check for simple loss.
loss = f.sum()
loss.backward()
torch.allclose(x.grad, Kadj(x.new_ones(1, 1, *data_size)))
def op_fun(x):
out = LinearOperator.apply(x, K, Kadj)
return out.sum()
# Check for anomalies.
with tag.detect_anomaly():
x = torch.randn(1,
1,
*image_size,
requires_grad=True,
dtype=torch.double)
out = op_fun(x)
out.backward()
# Check numerical gradient up to certain tolerance.
# Due to inaccuracy of adjoint this check fails.
x = torch.randn(1,
1,
*image_size,
requires_grad=True,
dtype=torch.double)
tag.gradcheck(lambda t: K(t), x)
def test_radon2d(self):
# Set image size.
m, n = 39, 23
# Define angles.
angles = np.linspace(0, np.pi, 180, False)
# Create operators.
K, Kadj, ndet = radon.radon2d(m, n, angles)
# Apply to dummy image.
f = K(np.ones((m, n)))
np.testing.assert_allclose(f.shape[0], angles.size)
# Apply to dummy data.
f = Kadj(np.ones_like(f))
np.testing.assert_allclose(f.shape, (m, n))
def test_LinearOperator_radon_cuda(self):
# Set image size.
image_size = 5, 4
# Define angles.
nangles = 180
angles = np.linspace(0, np.pi, nangles, False)
# Check if GPU is available.
cuda = torch.cuda.is_available()
device = torch.device('cuda' if cuda else 'cpu')
# Create operators.
R, Radj, ndet = radon.radon2d(*image_size, angles, cuda)
data_size = (nangles, ndet)
# Create instances for use with torch.
K = radon.RadonTransform(R, Radj, data_size)
Kadj = radon.BackProjection(R, Radj, image_size)
# Apply to dummy input.
x = torch.randn((1, 1, *image_size),
requires_grad=True,
dtype=torch.double,
device=device)
f = K(x)
# Check for simple loss.
loss = f.sum()
loss.backward()
torch.allclose(x.grad, Kadj(x.new_ones(1, 1, *data_size)))
def op_fun(x):
out = LinearOperator.apply(x, K, Kadj)
return out.sum()
# Check for anomalies.
with tag.detect_anomaly():
x = torch.randn(1,
1,
*image_size,
requires_grad=True,
dtype=torch.double,
device=device)
out = op_fun(x)
out.backward()
def setup_reconstruction_problem(image_size: tuple):
"""Set up reconstruction problem using Radon transform."""
# Define angles.
nangles = 180
angles = np.linspace(0, np.pi, nangles, False)
# Define Radon transform and adjoint.
R, Radj, ndet = radon.radon2d(*image_size, angles)
data_size = (nangles, ndet)
# Create instances for use with torch.
K = radon.RadonTransform(R, Radj, data_size)
Kadj = radon.BackProjection(R, Radj, image_size)
# Create data fidelity and its gradient.
G, gradG = functionals.OpSqNormDataTerm(K, Kadj)
return K, Kadj, G, gradG, data_size
def setup_reconstruction_problem(f: np.array, sigma: float):
"""Set up reconstruction problem using Radon transform."""
m, n = f.shape
# Define angles.
nangles = 180
angles = np.linspace(0, np.pi, nangles, False)
# Define Radon transform and adjoint.
K, Kadj, ndet = radon.radon2d(m, n, angles)
# Generate data and add noise.
y = K(f)
# Add noise.
ydelta = y + sigma**2 * y.var() * y.max() * np.random.randn(*y.shape)
# Define data fidelity and its gradient.
G, gradG = functionals.OpSqNormDataTerm(K, Kadj, ydelta)
return ydelta, G, gradG
def landweber():
"""Compute a solution by Landweber iteration."""
# Load phantom image.
f = np.asarray(Image.open('data/phantom.png').convert('L'),
dtype=np.double)
f = f / np.max(f)
m, n = f.shape
# Define angles.
angles = np.linspace(0, np.pi, 180, False)
# Define Radon transform and adjoint.
K, Kadj, ndet = radon.radon2d(m, n, angles)
# Generate data and add noise.
y = K(f)
ydelta = y + 5 * np.random.randn(*y.shape)
# Show image.
plt.figure()
plt.imshow(ydelta, cmap='gray')
plt.colorbar()
plt.show()
# Initialise solution.
x = np.zeros_like(f)
# Define stepsize parameter.
omega = 2e-5
# Run Landweber iteration.
nliter = 30
for i in range(nliter):
x = x - omega * Kadj(K(x) - ydelta)
plt.figure()
plt.imshow(x, cmap='gray')
plt.colorbar()
plt.show()
