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_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)
# Set regularisation parameter.
alpha = 0.02
# Create functions to be blocked with operators
f1 = alpha * MixedL21Norm()
f2 = 0.5 * L2NormSquared(b=blurredimage)
# Create BlockOperator
operator = BlockOperator(op1, op2, shape=(2,1) )
# 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)
def test_PDHG_vs_PDHG_explicit_axpby(self):
data = dataexample.SIMPLE_PHANTOM_2D.get(size=(128, 128))
if debug_print:
print("test_PDHG_vs_PDHG_explicit_axpby here")
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')
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':
np.random.seed(10)
scale = 5
eta = 0
noisy_data = AcquisitionData(
np.random.poisson(scale * (eta + sin.as_array())) / scale,
geometry=ag)
elif noise == 'gaussian':
np.random.seed(10)
n1 = np.random.normal(0, 0.1, size=ag.shape)
noisy_data = AcquisitionData(n1 + sin.as_array(), geometry=ag)
else:
raise ValueError('Unsupported Noise ', noise)
alpha = 0.5
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
algos = []
algos.append(
PDHG(f=f,
g=g,
operator=operator,
tau=tau,
sigma=sigma,
max_iteration=1000,
update_objective_interval=200,
use_axpby=True))
algos[0].run(1000, verbose=0)
algos.append(
PDHG(f=f,
g=g,
operator=operator,
tau=tau,
sigma=sigma,
max_iteration=1000,
update_objective_interval=200,
use_axpby=False))
algos[1].run(1000, verbose=0)
from cil.utilities.quality_measures import mae, mse, psnr
qm = (mae(algos[0].get_output(), algos[1].get_output()),
mse(algos[0].get_output(), algos[1].get_output()),
psnr(algos[0].get_output(), algos[1].get_output()))
if debug_print:
print("Quality measures", qm)
np.testing.assert_array_less(qm[0], 0.005)
np.testing.assert_array_less(qm[1], 3e-05)
update_objective_interval=2)
#%%
algo.update_objective_interval = 2
algo.run(10, verbose=1)
plotter2D(algo.solution, cmap='gist_earth')
# %%
from cil.optimisation.algorithms import PDHG
from cil.optimisation.functions import MixedL21Norm, BlockFunction, L2NormSquared, IndicatorBox
from cil.optimisation.operators import GradientOperator, BlockOperator
nabla = GradientOperator(ig_cs, backend='c')
F = BlockFunction(0.5 * L2NormSquared(b=ldata), alpha * MixedL21Norm())
BK = BlockOperator(K, nabla)
normK = BK.norm()
pdhg = PDHG(f=F,
g=IndicatorBox(lower=0.),
operator=BK,
max_iteration=1000,
update_objective_interval=100)
#%%
# pdhg.run(1000, verbose=2)
#%%
plotter2D(pdhg.solution, cmap='gist_earth')
# %%
class AcquisitionGeometrySubsetGenerator(object):