def test_PDHG_strongly_convex_gamma_g(self):
ig = ImageGeometry(3,3)
data = ig.allocate('random')
f = L2NormSquared(b=data)
g = L2NormSquared()
operator = IdentityOperator(ig)
# sigma, tau
sigma = 1.0
tau = 1.0
pdhg = PDHG(f=f, g=g, operator=operator, sigma = sigma, tau=tau,
max_iteration=5, gamma_g=0.5)
pdhg.run(1, verbose=0)
self.assertAlmostEquals(pdhg.theta, 1.0/ np.sqrt(1 + 2 * pdhg.gamma_g * tau))
self.assertAlmostEquals(pdhg.tau, tau * pdhg.theta)
self.assertAlmostEquals(pdhg.sigma, sigma / pdhg.theta)
pdhg.run(4, verbose=0)
self.assertNotEqual(pdhg.sigma, sigma)
self.assertNotEqual(pdhg.tau, tau)
# check negative strongly convex constant
with self.assertRaises(ValueError):
pdhg = PDHG(f=f, g=g, operator=operator, sigma = sigma, tau=tau,
max_iteration=5, gamma_g=-0.5)
# check strongly convex constant not a number
with self.assertRaises(ValueError):
pdhg = PDHG(f=f, g=g, operator=operator, sigma = sigma, tau=tau,
max_iteration=5, gamma_g="-0.5")
def test_compare_with_PDHG(self):
# Load an image from the CIL gallery.
data = dataexample.SHAPES.get()
ig = data.geometry
# Add gaussian noise
noisy_data = applynoise.gaussian(data, seed=10, var=0.005)
# TV regularisation parameter
alpha = 1
# fidelity = 0.5 * L2NormSquared(b=noisy_data)
# fidelity = L1Norm(b=noisy_data)
fidelity = KullbackLeibler(b=noisy_data, use_numba=False)
# Setup and run the PDHG algorithm
F = BlockFunction(alpha * MixedL21Norm(), fidelity)
G = ZeroFunction()
K = BlockOperator(GradientOperator(ig), IdentityOperator(ig))
# Compute operator Norm
normK = K.norm()
# Primal & dual stepsizes
sigma = 1. / normK
tau = 1. / normK
pdhg = PDHG(f=F,
g=G,
operator=K,
tau=tau,
sigma=sigma,
max_iteration=100,
update_objective_interval=10)
pdhg.run(verbose=0)
sigma = 1
tau = sigma / normK**2
admm = LADMM(f=G,
g=F,
operator=K,
tau=tau,
sigma=sigma,
max_iteration=100,
update_objective_interval=10)
admm.run(verbose=0)
from cil.utilities.quality_measures import psnr
if debug_print:
print("PSNR", psnr(admm.solution, pdhg.solution))
np.testing.assert_almost_equal(psnr(admm.solution, pdhg.solution),
84.46678222768597,
decimal=4)
def test_PDHG_strongly_convex_both_fconj_and_g(self):
ig = ImageGeometry(3,3)
data = ig.allocate('random')
f = L2NormSquared(b=data)
g = L2NormSquared()
operator = IdentityOperator(ig)
try:
pdhg = PDHG(f=f, g=g, operator=operator, max_iteration=10,
gamma_g = 0.5, gamma_fconj=0.5)
pdhg.run(verbose=0)
except ValueError as err:
print(err)
def test_PDHG_strongly_convex_gamma_fcong(self):
ig = ImageGeometry(3,3)
data = ig.allocate('random')
f = L2NormSquared(b=data)
g = L2NormSquared()
operator = IdentityOperator(ig)
# sigma, tau
sigma = 1.0
tau = 1.0
pdhg = PDHG(f=f, g=g, operator=operator, sigma = sigma, tau=tau,
max_iteration=5, gamma_fconj=0.5)
pdhg.run(1, verbose=0)
self.assertEquals(pdhg.theta, 1.0/ np.sqrt(1 + 2 * pdhg.gamma_fconj * sigma))
self.assertEquals(pdhg.tau, tau / pdhg.theta)
self.assertEquals(pdhg.sigma, sigma * pdhg.theta)
pdhg.run(4, verbose=0)
self.assertNotEqual(pdhg.sigma, sigma)
self.assertNotEqual(pdhg.tau, tau)
# check negative strongly convex constant
try:
pdhg = PDHG(f=f, g=g, operator=operator, sigma = sigma, tau=tau,
max_iteration=5, gamma_fconj=-0.5)
except ValueError as ve:
print(ve)
# check strongly convex constant not a number
try:
pdhg = PDHG(f=f, g=g, operator=operator, sigma = sigma, tau=tau,
max_iteration=5, gamma_fconj="-0.5")
except ValueError as ve:
print(ve)
def test_SPDHG_vs_PDHG_explicit(self):
data = dataexample.SIMPLE_PHANTOM_2D.get(size=(128, 128))
ig = data.geometry
ig.voxel_size_x = 0.1
ig.voxel_size_y = 0.1
detectors = ig.shape[0]
angles = np.linspace(0, np.pi, 180)
ag = AcquisitionGeometry('parallel',
'2D',
angles,
detectors,
pixel_size_h=0.1,
angle_unit='radian')
# Select device
dev = 'cpu'
Aop = AstraProjectorSimple(ig, ag, dev)
sin = Aop.direct(data)
# Create noisy data. Apply Gaussian noise
noises = ['gaussian', 'poisson']
noise = noises[1]
if noise == 'poisson':
scale = 5
noisy_data = scale * applynoise.poisson(sin / scale, seed=10)
# np.random.seed(10)
# scale = 5
# eta = 0
# noisy_data = AcquisitionData(np.random.poisson( scale * (eta + sin.as_array()))/scale, ag)
elif noise == 'gaussian':
noisy_data = noise.gaussian(sin, var=0.1, seed=10)
# np.random.seed(10)
# n1 = np.random.normal(0, 0.1, size = ag.shape)
# noisy_data = AcquisitionData(n1 + sin.as_array(), ag)
else:
raise ValueError('Unsupported Noise ', noise)
#%% 'explicit' SPDHG, scalar step-sizes
subsets = 10
size_of_subsets = int(len(angles) / subsets)
# create Gradient operator
op1 = GradientOperator(ig)
# take angles and create uniform subsets in uniform+sequential setting
list_angles = [
angles[i:i + size_of_subsets]
for i in range(0, len(angles), size_of_subsets)
]
# create acquisitioin geometries for each the interval of splitting angles
list_geoms = [
AcquisitionGeometry('parallel',
'2D',
list_angles[i],
detectors,
pixel_size_h=0.1,
angle_unit='radian')
for i in range(len(list_angles))
]
# create with operators as many as the subsets
A = BlockOperator(*[
AstraProjectorSimple(ig, list_geoms[i], dev)
for i in range(subsets)
] + [op1])
## number of subsets
#(sub2ind, ind2sub) = divide_1Darray_equally(range(len(A)), subsets)
#
## acquisisiton data
## acquisisiton data
AD_list = []
for sub_num in range(subsets):
for i in range(0, len(angles), size_of_subsets):
arr = noisy_data.as_array()[i:i + size_of_subsets, :]
AD_list.append(
AcquisitionData(arr, geometry=list_geoms[sub_num]))
g = BlockDataContainer(*AD_list)
alpha = 0.5
## block function
F = BlockFunction(*[
*[KullbackLeibler(b=g[i])
for i in range(subsets)] + [alpha * MixedL21Norm()]
])
G = IndicatorBox(lower=0)
prob = [1 / (2 * subsets)] * (len(A) - 1) + [1 / 2]
spdhg = SPDHG(f=F,
g=G,
operator=A,
max_iteration=1000,
update_objective_interval=200,
prob=prob)
spdhg.run(1000, verbose=0)
#%% 'explicit' PDHG, scalar step-sizes
op1 = GradientOperator(ig)
op2 = Aop
# Create BlockOperator
operator = BlockOperator(op1, op2, shape=(2, 1))
f2 = KullbackLeibler(b=noisy_data)
g = IndicatorBox(lower=0)
normK = operator.norm()
sigma = 1 / normK
tau = 1 / normK
f1 = alpha * MixedL21Norm()
f = BlockFunction(f1, f2)
# Setup and run the PDHG algorithm
pdhg = PDHG(f=f, g=g, operator=operator, tau=tau, sigma=sigma)
pdhg.max_iteration = 1000
pdhg.update_objective_interval = 200
pdhg.run(1000, verbose=0)
#%% show diff between PDHG and SPDHG
# plt.imshow(spdhg.get_output().as_array() -pdhg.get_output().as_array())
# plt.colorbar()
# plt.show()
from cil.utilities.quality_measures import mae, mse, psnr
qm = (mae(spdhg.get_output(),
pdhg.get_output()), mse(spdhg.get_output(),
pdhg.get_output()),
psnr(spdhg.get_output(), pdhg.get_output()))
if debug_print:
print("Quality measures", qm)
np.testing.assert_almost_equal(mae(spdhg.get_output(),
pdhg.get_output()),
0.00150,
decimal=3)
np.testing.assert_almost_equal(mse(spdhg.get_output(),
pdhg.get_output()),
1.68590e-05,
decimal=3)
def test_SPDHG_vs_PDHG_implicit(self):
data = dataexample.SIMPLE_PHANTOM_2D.get(size=(128, 128))
ig = data.geometry
ig.voxel_size_x = 0.1
ig.voxel_size_y = 0.1
detectors = ig.shape[0]
angles = np.linspace(0, np.pi, 90)
ag = AcquisitionGeometry('parallel',
'2D',
angles,
detectors,
pixel_size_h=0.1,
angle_unit='radian')
# Select device
dev = 'cpu'
Aop = AstraProjectorSimple(ig, ag, dev)
sin = Aop.direct(data)
# Create noisy data. Apply Gaussian noise
noises = ['gaussian', 'poisson']
noise = noises[1]
noisy_data = ag.allocate()
if noise == 'poisson':
np.random.seed(10)
scale = 20
eta = 0
noisy_data.fill(
np.random.poisson(scale * (eta + sin.as_array())) / scale)
elif noise == 'gaussian':
np.random.seed(10)
n1 = np.random.normal(0, 0.1, size=ag.shape)
noisy_data.fill(n1 + sin.as_array())
else:
raise ValueError('Unsupported Noise ', noise)
# Create BlockOperator
operator = Aop
f = KullbackLeibler(b=noisy_data)
alpha = 0.005
g = alpha * TotalVariation(50, 1e-4, lower=0)
normK = operator.norm()
#% 'implicit' PDHG, preconditioned step-sizes
tau_tmp = 1.
sigma_tmp = 1.
tau = sigma_tmp / operator.adjoint(
tau_tmp * operator.range_geometry().allocate(1.))
sigma = tau_tmp / operator.direct(
sigma_tmp * operator.domain_geometry().allocate(1.))
# initial = operator.domain_geometry().allocate()
# # Setup and run the PDHG algorithm
pdhg = PDHG(f=f,
g=g,
operator=operator,
tau=tau,
sigma=sigma,
max_iteration=1000,
update_objective_interval=500)
pdhg.run(verbose=0)
subsets = 10
size_of_subsets = int(len(angles) / subsets)
# take angles and create uniform subsets in uniform+sequential setting
list_angles = [
angles[i:i + size_of_subsets]
for i in range(0, len(angles), size_of_subsets)
]
# create acquisitioin geometries for each the interval of splitting angles
list_geoms = [
AcquisitionGeometry('parallel',
'2D',
list_angles[i],
detectors,
pixel_size_h=0.1,
angle_unit='radian')
for i in range(len(list_angles))
]
# create with operators as many as the subsets
A = BlockOperator(*[
AstraProjectorSimple(ig, list_geoms[i], dev)
for i in range(subsets)
])
## number of subsets
#(sub2ind, ind2sub) = divide_1Darray_equally(range(len(A)), subsets)
#
## acquisisiton data
AD_list = []
for sub_num in range(subsets):
for i in range(0, len(angles), size_of_subsets):
arr = noisy_data.as_array()[i:i + size_of_subsets, :]
AD_list.append(
AcquisitionData(arr, geometry=list_geoms[sub_num]))
g = BlockDataContainer(*AD_list)
## block function
F = BlockFunction(*[KullbackLeibler(b=g[i]) for i in range(subsets)])
G = alpha * TotalVariation(50, 1e-4, lower=0)
prob = [1 / len(A)] * len(A)
spdhg = SPDHG(f=F,
g=G,
operator=A,
max_iteration=1000,
update_objective_interval=200,
prob=prob)
spdhg.run(1000, verbose=0)
from cil.utilities.quality_measures import mae, mse, psnr
qm = (mae(spdhg.get_output(),
pdhg.get_output()), mse(spdhg.get_output(),
pdhg.get_output()),
psnr(spdhg.get_output(), pdhg.get_output()))
if debug_print:
print("Quality measures", qm)
np.testing.assert_almost_equal(mae(spdhg.get_output(),
pdhg.get_output()),
0.000335,
decimal=3)
np.testing.assert_almost_equal(mse(spdhg.get_output(),
pdhg.get_output()),
5.51141e-06,
decimal=3)
def test_PDHG_Denoising(self):
print("PDHG Denoising with 3 noises")
# adapted from demo PDHG_TV_Color_Denoising.py in CIL-Demos repository
data = dataexample.PEPPERS.get(size=(256, 256))
ig = data.geometry
ag = ig
which_noise = 0
# Create noisy data.
noises = ['gaussian', 'poisson', 's&p']
dnoise = noises[which_noise]
def setup(data, dnoise):
if dnoise == 's&p':
n1 = applynoise.saltnpepper(data,
salt_vs_pepper=0.9,
amount=0.2,
seed=10)
elif dnoise == 'poisson':
scale = 5
n1 = applynoise.poisson(data.as_array() / scale,
seed=10) * scale
elif dnoise == 'gaussian':
n1 = applynoise.gaussian(data.as_array(), seed=10)
else:
raise ValueError('Unsupported Noise ', noise)
noisy_data = ig.allocate()
noisy_data.fill(n1)
# Regularisation Parameter depending on the noise distribution
if dnoise == 's&p':
alpha = 0.8
elif dnoise == 'poisson':
alpha = 1
elif dnoise == 'gaussian':
alpha = .3
# fidelity
if dnoise == 's&p':
g = L1Norm(b=noisy_data)
elif dnoise == 'poisson':
g = KullbackLeibler(b=noisy_data)
elif dnoise == 'gaussian':
g = 0.5 * L2NormSquared(b=noisy_data)
return noisy_data, alpha, g
noisy_data, alpha, g = setup(data, dnoise)
operator = GradientOperator(
ig, correlation=GradientOperator.CORRELATION_SPACE)
f1 = alpha * MixedL21Norm()
# Compute operator Norm
normK = operator.norm()
# Primal & dual stepsizes
sigma = 1
tau = 1 / (sigma * normK**2)
# Setup and run the PDHG algorithm
pdhg1 = PDHG(f=f1, g=g, operator=operator, tau=tau, sigma=sigma)
pdhg1.max_iteration = 2000
pdhg1.update_objective_interval = 200
pdhg1.run(1000, verbose=0)
rmse = (pdhg1.get_output() - data).norm() / data.as_array().size
if debug_print:
print("RMSE", rmse)
self.assertLess(rmse, 2e-4)
which_noise = 1
noise = noises[which_noise]
noisy_data, alpha, g = setup(data, noise)
operator = GradientOperator(
ig, correlation=GradientOperator.CORRELATION_SPACE)
f1 = alpha * MixedL21Norm()
# Compute operator Norm
normK = operator.norm()
# Primal & dual stepsizes
sigma = 1
tau = 1 / (sigma * normK**2)
# Setup and run the PDHG algorithm
pdhg1 = PDHG(f=f1,
g=g,
operator=operator,
tau=tau,
sigma=sigma,
max_iteration=2000,
update_objective_interval=200)
pdhg1.run(1000, verbose=0)
rmse = (pdhg1.get_output() - data).norm() / data.as_array().size
if debug_print:
print("RMSE", rmse)
self.assertLess(rmse, 2e-4)
which_noise = 2
noise = noises[which_noise]
noisy_data, alpha, g = setup(data, noise)
operator = GradientOperator(
ig, correlation=GradientOperator.CORRELATION_SPACE)
f1 = alpha * MixedL21Norm()
# Compute operator Norm
normK = operator.norm()
# Primal & dual stepsizes
sigma = 1
tau = 1 / (sigma * normK**2)
# Setup and run the PDHG algorithm
pdhg1 = PDHG(f=f1, g=g, operator=operator, tau=tau, sigma=sigma)
pdhg1.max_iteration = 2000
pdhg1.update_objective_interval = 200
pdhg1.run(1000, verbose=0)
rmse = (pdhg1.get_output() - data).norm() / data.as_array().size
if debug_print:
print("RMSE", rmse)
self.assertLess(rmse, 2e-4)
# Create functions
f = BlockFunction(f1, f2)
g = ZeroFunction()
# Compute operator Norm
normK = operator.norm()
# Primal & dual stepsizes
sigma = 1
tau = 1/(sigma*normK**2)
# Setup and run the PDHG algorithm
pdhg = PDHG(f=f,g=g,operator=operator, tau=tau, sigma=sigma)
pdhg.max_iteration = 10000
pdhg.update_objective_interval = 1
pdhg.run(200,very_verbose=True)
# Show results
plt.figure(figsize=(20,5))
plt.subplot(1,3,1)
plt.imshow(data_gray.as_array(),vmin=0.0,vmax=1.0)
plt.title('Ground Truth')
plt.gray()
plt.colorbar()
plt.subplot(1,3,2)
plt.imshow(blurredimage.as_array(),vmin=0.0,vmax=1.0)
plt.title('Noisy and Masked Data')
plt.gray()
plt.colorbar()
plt.subplot(1,3,3)
plt.imshow(pdhg.get_output().as_array(),vmin=0.0,vmax=1.0)
# Create functions
f = BlockFunction(alpha * MixedL21Norm(), f2)
g = ZeroFunction()
# Compute operator Norm
normK = operator.norm()
# Primal & dual stepsizes
sigma = 1
tau = 1 / (sigma * normK**2)
# Setup and run the PDHG algorithm
pdhg = PDHG(f=f, g=g, operator=operator, tau=tau, sigma=sigma)
pdhg.max_iteration = 2000
pdhg.update_objective_interval = 100
pdhg.run(2000)
# Show results
plt.figure(figsize=(20, 5))
plt.subplot(1, 4, 1)
plt.imshow(data.as_array())
plt.title('Ground Truth')
plt.colorbar()
plt.subplot(1, 4, 2)
plt.imshow(noisy_data.as_array())
plt.title('Noisy Data')
plt.colorbar()
plt.subplot(1, 4, 3)
plt.imshow(pdhg.get_output().as_array())
plt.title('TV Reconstruction')
plt.colorbar()
from cil.optimisation.functions import MixedL21Norm, BlockFunction, L2NormSquared, IndicatorBox
from cil.optimisation.operators import GradientOperator, BlockOperator
nabla = GradientOperator(ig_cs, backend='c')
F = BlockFunction(L2NormSquared(b=ldata), alpha * MixedL21Norm())
BK = BlockOperator(K, nabla)
# normK = BK.norm()
normK = 191.54791313753265
pdhg = PDHG(f=F,
g=IndicatorBox(lower=0.),
operator=BK,
max_iteration=1000,
update_objective_interval=100)
#%%
pdhg.run(100, verbose=2, print_interval=10)
#%%
plotter2D(pdhg.solution, cmap='gist_earth')
# %%
subsets = AcquisitionGeometrySubsetGenerator.generate_subset(
ag_shift, num_subsets=8, method='stagger')
print(subsets[0])
#%%
from cil.optimisation.algorithms import SPDHG
from cil.optimisation.functions import ZeroFunction
from cil.optimisation.functions import MixedL21Norm, BlockFunction, L2NormSquared, IndicatorBox
from cil.optimisation.operators import GradientOperator, BlockOperator
# fractionate the data