# Create functions
f1 = alpha * MixedL21Norm()
f2 = KullbackLeibler(noisy_data)
f = BlockFunction(f1, f2)
g = ZeroFunction()
normK = operator.norm()
# Primal & dual stepsizes
sigma = 5
tau = 1/(sigma*normK**2)
# Setup and run the PDHG algorithm
pdhg = PDHG(f=f,g=g,operator=operator, tau=tau, sigma=sigma, memopt=True)
pdhg.max_iteration = 1000
pdhg.update_objective_interval = 200
pdhg.run(1000)
tindex = [0, int(phantom_2Dt.shape[0]/2), phantom_2Dt.shape[0]-1]
fig2, axes2 = plt.subplots(nrows=2, ncols=3, figsize=(5, 5))
# Ground Truth
axes2[0, 0].imshow(phantom_2Dt[tindex[0],:,:])
axes2[0, 0].set_title('Time {}'.format(tindex[0]))
axes2[0,0].set_ylabel('Ground Truth')
axes2[0, 1].imshow(phantom_2Dt[tindex[1],:,:])
g = IndicatorBox(lower=0)
sigma = 1
tau = 1 / (sigma * normK**2)
elif noise == 'gaussian':
alpha = 200
f2 = 0.5 * L2NormSquared(b=noisy_data)
g = ZeroFunction()
sigma = 10
tau = 1 / (sigma * normK**2)
f1 = alpha * L2NormSquared()
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)
plt.figure(figsize=(15, 15))
plt.subplot(3, 1, 1)
plt.imshow(data.as_array())
plt.title('Ground Truth')
plt.colorbar()
plt.subplot(3, 1, 2)
plt.imshow(noisy_data.as_array())
plt.title('Noisy Data')
plt.colorbar()
plt.subplot(3, 1, 3)
plt.imshow(pdhg.get_output().as_array())
f1 = alpha * MixedL21Norm()
f2 = beta * MixedL21Norm()
f = BlockFunction(f1, f2)
g = BlockFunction(f3, 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.subset(channel=0).as_array())
plt.title('Ground Truth')
plt.colorbar()
plt.subplot(1,4,2)
plt.imshow(noisy_data.subset(channel=0).as_array())
plt.title('Noisy Data')
plt.colorbar()
plt.subplot(1,4,3)
operator = BlockOperator(op1, op2, shape=(2, 1))
# Compute the operator norm
normK = operator.norm()
alpha_coupled = 0.05
f1 = 0.5 * L2NormSquared(b=data)
f2 = alpha_coupled * MixedL21Norm()
f = BlockFunction(f1, f2)
g = IndicatorBox(lower=0)
sigma = 1
tau = 1 / (sigma * normK**2)
pdhg = PDHG(f=f, g=g, operator=operator, tau=tau, sigma=sigma)
pdhg.max_iteration = 100
pdhg.update_objective_interval = 20
pdhg.run(1000, verbose=True, callback=show_data_4D)
#%% Let's move to 2D + energy channel reconstruction
ag2D = AcquisitionGeometry(
'cone',
'2D',
angles,
pixel_num_h=num_pixels_h,
pixel_size_h=0.25,
dist_source_center=233.0,
dist_center_detector=245.0,
channels=num_channels
###############################################################################
# Setup and run the PDHG algorithm
op1 = Gradient(ig)
op2 = Identity(ig, ag)
operator = BlockOperator(op1, op2, shape=(2, 1))
f = BlockFunction(alpha * L2NormSquared(), fidelity)
g = ZeroFunction()
normK = operator.norm()
sigma = 1
tau = 1 / (sigma * normK**2)
pdhg = PDHG(f=f, g=g, operator=operator, tau=tau, sigma=sigma, memopt=True)
pdhg.max_iteration = 2000
pdhg.update_objective_interval = 200
pdhg.run(2000, verbose=False)
###############################################################################
# Show results
plt.figure(figsize=(10, 10))
plt.subplot(2, 1, 1)
plt.imshow(pdhg.get_output().as_array())
plt.title('PDHG reconstruction')
plt.subplot(2, 1, 2)
plt.imshow(fista.get_output().as_array())
f = BlockFunction(f1, f2) g = ZeroFunction() # Compute operator Norm normK1 = operator1.norm() normK2 = operator2.norm() # Primal & dual stepsizes sigma1 = 1 tau1 = 1 / (sigma1 * normK1**2) sigma2 = 1 tau2 = 1 / (sigma2 * normK2**2) # Setup and run the PDHG algorithm pdhg1 = PDHG(f=f, g=g, operator=operator1, tau=tau1, sigma=sigma1) pdhg1.max_iteration = 2000 pdhg1.update_objective_interval = 200 pdhg1.run(1000) # Setup and run the PDHG algorithm pdhg2 = PDHG(f=f, g=g, operator=operator2, tau=tau2, sigma=sigma2) pdhg2.max_iteration = 2000 pdhg2.update_objective_interval = 200 pdhg2.run(1000) #%% tindex = [8, 16, 24] fig2, axes2 = plt.subplots(nrows=3, ncols=3, figsize=(10, 10)) # Ground Truth
#%% Use PDHG to solve non-smooth version of problem for comparison
# Set up non-smooth TV regularisation term
operator = Grad
f = alpha * MixedL21Norm()
# Set algorithm parameters: primal and dual step sizes, sigma and tau,
# standard choices based on operator's norm.
normK = operator.norm()
sigma = 1
tau = 1 / (sigma * normK**2)
# Setup and run the PDHG algorithm
print("Running PDHG with non-smooth TV.\nThis will take some time...")
pdhg = PDHG(f=f, g=f2, operator=operator, tau=tau, sigma=sigma)
pdhg.max_iteration = 10000
pdhg.update_objective_interval = 100
pdhg.run(very_verbose=True)
## Show PDHG reconstruction 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)
am_rescaled = ScaledOperator(am, (1 / am_norm))
K = am_rescaled
# In[ ]:
sigma = 1.0
tau = 1.0
pet.set_max_omp_threads(15)
# In[ ]:
pdhg = PDHG(f=F,
g=G,
operator=K,
sigma=sigma,
tau=tau,
max_iteration=1000,
update_objective_interval=10)
pdhg.run(20, very_verbose=True)
# In[ ]:
plt.figure()
plt.imshow(pdhg.get_output().as_array()[75, :, :], cmap="inferno")
plt.colorbar()
plt.show()
# # SPDHG without regularization
# In[ ]:
if noise == 's&p':
g = L1Norm(b=noisy_data)
elif noise == 'poisson':
g = KullbackLeibler(noisy_data)
elif noise == 'gaussian':
g = 0.5 * L2NormSquared(b=noisy_data)
# 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)
# Show results
plt.figure(figsize=(10, 10))
plt.subplot(1, 3, 1)
plt.imshow(data.as_array())
plt.title('Ground Truth')
plt.subplot(1, 3, 2)
plt.imshow(noisy_data.as_array())
plt.title('Noisy Data')
plt.subplot(1, 3, 3)
plt.imshow(pdhg1.get_output().as_array())
plt.title('TV Reconstruction')
# Create BlockOperator
operator = BlockOperator(op1, op2, shape=(2,1) )
# 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 = 1000
pdhg.update_objective_interval = 100
pdhg.run(1000)
# Show results
plt.figure(figsize=(20,5))
plt.subplot(1,3,1)
plt.imshow(data.as_array(),vmin=0.0,vmax=1.0)
plt.title('Ground Truth')
if colour_mode==0:
plt.gray()
plt.colorbar()
plt.subplot(1,3,2)
plt.imshow(noisy_data.as_array(),vmin=0.0,vmax=1.0)
plt.title('Noisy and Masked Data')
def main():
###########################################################################
# Parse input files
###########################################################################
if trans_pattern is None:
raise AssertionError("--trans missing")
if sino_pattern is None:
raise AssertionError("--sino missing")
trans_files = sorted(glob(trans_pattern))
sino_files = sorted(glob(sino_pattern))
attn_files = sorted(glob(attn_pattern))
rand_files = sorted(glob(rand_pattern))
num_ms = len(sino_files)
# Check some sinograms found
if num_ms == 0:
raise AssertionError("No sinograms found!")
# Should have as many trans as sinos
if num_ms != len(trans_files):
raise AssertionError("#trans should match #sinos. "
"#sinos = " + str(num_ms) + ", #trans = " +
str(len(trans_files)))
# If any rand, check num == num_ms
if len(rand_files) > 0 and len(rand_files) != num_ms:
raise AssertionError("#rand should match #sinos. "
"#sinos = " + str(num_ms) + ", #rand = " +
str(len(rand_files)))
# For attn, there should be 0, 1 or num_ms images
if len(attn_files) > 1 and len(attn_files) != num_ms:
raise AssertionError("#attn should be 0, 1 or #sinos")
###########################################################################
# Read input
###########################################################################
if trans_type == "tm":
trans = [reg.AffineTransformation(file) for file in trans_files]
elif trans_type == "disp":
trans = [
reg.NiftiImageData3DDisplacement(file) for file in trans_files
]
elif trans_type == "def":
trans = [reg.NiftiImageData3DDeformation(file) for file in trans_files]
else:
raise error("Unknown transformation type")
sinos_raw = [pet.AcquisitionData(file) for file in sino_files]
attns = [pet.ImageData(file) for file in attn_files]
rands = [pet.AcquisitionData(file) for file in rand_files]
# Loop over all sinograms
sinos = [0] * num_ms
for ind in range(num_ms):
# If any sinograms contain negative values
# (shouldn't be the case), set them to 0
sino_arr = sinos_raw[ind].as_array()
if (sino_arr < 0).any():
print("Input sinogram " + str(ind) +
" contains -ve elements. Setting to 0...")
sinos[ind] = sinos_raw[ind].clone()
sino_arr[sino_arr < 0] = 0
sinos[ind].fill(sino_arr)
else:
sinos[ind] = sinos_raw[ind]
# If rebinning is desired
segs_to_combine = 1
if args['--numSegsToCombine']:
segs_to_combine = int(args['--numSegsToCombine'])
views_to_combine = 1
if args['--numViewsToCombine']:
views_to_combine = int(args['--numViewsToCombine'])
if segs_to_combine * views_to_combine > 1:
sinos[ind] = sinos[ind].rebin(segs_to_combine, views_to_combine)
# only print first time
if ind == 0:
print(f"Rebinned sino dimensions: {sinos[ind].dimensions()}")
###########################################################################
# Initialise recon image
###########################################################################
if initial_estimate:
image = pet.ImageData(initial_estimate)
else:
# Create image based on ProjData
image = sinos[0].create_uniform_image(0.0, (nxny, nxny))
# If using GPU, need to make sure that image is right size.
if use_gpu:
dim = (127, 320, 320)
spacing = (2.03125, 2.08626, 2.08626)
# elif non-default spacing desired
elif args['--dxdy']:
dim = image.dimensions()
dxdy = float(args['--dxdy'])
spacing = (image.voxel_sizes()[0], dxdy, dxdy)
if use_gpu or args['--dxdy']:
image.initialise(dim=dim, vsize=spacing)
image.fill(0.0)
###########################################################################
# Set up resamplers
###########################################################################
resamplers = [get_resampler(image, trans=tran) for tran in trans]
###########################################################################
# Resample attenuation images (if necessary)
###########################################################################
resampled_attns = None
if len(attns) > 0:
resampled_attns = [0] * num_ms
# if using GPU, dimensions of attn and recon images have to match
ref = image if use_gpu else None
for i in range(len(attns)):
# if we only have 1 attn image, then we need to resample into
# space of each gate. However, if we have num_ms attn images, then
# assume they are already in the correct position, so use None as
# transformation.
tran = trans[i] if len(attns) == 1 else None
# If only 1 attn image, then resample that. If we have num_ms attn
# images, then use each attn image of each frame.
attn = attns[0] if len(attns) == 1 else attns[i]
resam = get_resampler(attn, ref=ref, trans=tran)
resampled_attns[i] = resam.forward(attn)
###########################################################################
# Set up acquisition models
###########################################################################
print("Setting up acquisition models...")
if not use_gpu:
acq_models = num_ms * [pet.AcquisitionModelUsingRayTracingMatrix()]
else:
acq_models = num_ms * [pet.AcquisitionModelUsingNiftyPET()]
for acq_model in acq_models:
acq_model.set_use_truncation(True)
acq_model.set_cuda_verbosity(verbosity)
# If present, create ASM from ECAT8 normalisation data
asm_norm = None
if norm_file:
asm_norm = pet.AcquisitionSensitivityModel(norm_file)
# Loop over each motion state
for ind in range(num_ms):
# Create attn ASM if necessary
asm_attn = None
if resampled_attns:
asm_attn = get_asm_attn(sinos[ind], resampled_attns[i],
acq_models[ind])
# Get ASM dependent on attn and/or norm
asm = None
if asm_norm and asm_attn:
if ind == 0:
print("ASM contains norm and attenuation...")
asm = pet.AcquisitionSensitivityModel(asm_norm, asm_attn)
elif asm_norm:
if ind == 0:
print("ASM contains norm...")
asm = asm_norm
elif asm_attn:
if ind == 0:
print("ASM contains attenuation...")
asm = asm_attn
if asm:
acq_models[ind].set_acquisition_sensitivity(asm)
if len(rands) > 0:
acq_models[ind].set_background_term(rands[ind])
# Set up
acq_models[ind].set_up(sinos[ind], image)
###########################################################################
# Set up reconstructor
###########################################################################
print("Setting up reconstructor...")
# Create composition operators containing acquisition models and resamplers
C = [
CompositionOperator(am, res, preallocate=True)
for am, res in zip(*(acq_models, resamplers))
]
# Configure the PDHG algorithm
if args['--normK'] and not args['--onlyNormK']:
normK = float(args['--normK'])
else:
kl = [KullbackLeibler(b=sino, eta=(sino * 0 + 1e-5)) for sino in sinos]
f = BlockFunction(*kl)
K = BlockOperator(*C)
# Calculate normK
print("Calculating norm of the block operator...")
normK = K.norm(iterations=10)
print("Norm of the BlockOperator ", normK)
if args['--onlyNormK']:
exit(0)
# Optionally rescale sinograms and BlockOperator using normK
scale_factor = 1. / normK if args['--normaliseDataAndBlock'] else 1.0
kl = [
KullbackLeibler(b=sino * scale_factor, eta=(sino * 0 + 1e-5))
for sino in sinos
]
f = BlockFunction(*kl)
K = BlockOperator(*C) * scale_factor
# If preconditioned
if precond:
def get_nonzero_recip(data):
"""Get the reciprocal of a datacontainer. Voxels where input == 0
will have their reciprocal set to 1 (instead of infinity)"""
inv_np = data.as_array()
inv_np[inv_np == 0] = 1
inv_np = 1. / inv_np
data.fill(inv_np)
tau = K.adjoint(K.range_geometry().allocate(1))
get_nonzero_recip(tau)
tmp_sigma = K.direct(K.domain_geometry().allocate(1))
sigma = 0. * tmp_sigma
get_nonzero_recip(sigma[0])
def precond_proximal(self, x, tau, out=None):
"""Modify proximal method to work with preconditioned tau"""
pars = {
'algorithm':
FGP_TV,
'input':
np.asarray(x.as_array() / tau.as_array(), dtype=np.float32),
'regularization_parameter':
self.lambdaReg,
'number_of_iterations':
self.iterationsTV,
'tolerance_constant':
self.tolerance,
'methodTV':
self.methodTV,
'nonneg':
self.nonnegativity,
'printingOut':
self.printing
}
res, info = regularisers.FGP_TV(pars['input'],
pars['regularization_parameter'],
pars['number_of_iterations'],
pars['tolerance_constant'],
pars['methodTV'], pars['nonneg'],
self.device)
if out is not None:
out.fill(res)
else:
out = x.copy()
out.fill(res)
out *= tau
return out
FGP_TV.proximal = precond_proximal
print("Will run proximal with preconditioned tau...")
# If not preconditioned
else:
sigma = float(args['--sigma'])
# If we need to calculate default tau
if args['--tau']:
tau = float(args['--tau'])
else:
tau = 1 / (sigma * normK**2)
if regularisation == 'none':
G = IndicatorBox(lower=0)
elif regularisation == 'FGP_TV':
r_iterations = float(args['--reg_iters'])
r_tolerance = 1e-7
r_iso = 0
r_nonneg = 1
r_printing = 0
device = 'gpu' if use_gpu else 'cpu'
G = FGP_TV(r_alpha, r_iterations, r_tolerance, r_iso, r_nonneg,
r_printing, device)
else:
raise error("Unknown regularisation")
if precond:
def PDHG_new_update(self):
"""Modify the PDHG update to allow preconditioning"""
# save previous iteration
self.x_old.fill(self.x)
self.y_old.fill(self.y)
# Gradient ascent for the dual variable
self.operator.direct(self.xbar, out=self.y_tmp)
self.y_tmp *= self.sigma
self.y_tmp += self.y_old
self.f.proximal_conjugate(self.y_tmp, self.sigma, out=self.y)
# Gradient descent for the primal variable
self.operator.adjoint(self.y, out=self.x_tmp)
self.x_tmp *= -1 * self.tau
self.x_tmp += self.x_old
self.g.proximal(self.x_tmp, self.tau, out=self.x)
# Update
self.x.subtract(self.x_old, out=self.xbar)
self.xbar *= self.theta
self.xbar += self.x
PDHG.update = PDHG_new_update
# Get filename
outp_file = outp_prefix
if descriptive_fname:
if len(attn_files) > 0:
outp_file += "_wAC"
if norm_file:
outp_file += "_wNorm"
if use_gpu:
outp_file += "_wGPU"
outp_file += "_Reg-" + regularisation
if regularisation == 'FGP_TV':
outp_file += "-alpha" + str(r_alpha)
outp_file += "-riters" + str(r_iterations)
if args['--normK']:
outp_file += '_userNormK' + str(normK)
else:
outp_file += '_calcNormK' + str(normK)
if args['--normaliseDataAndBlock']:
outp_file += '_wDataScale'
else:
outp_file += '_noDataScale'
if not precond:
outp_file += "_sigma" + str(sigma)
outp_file += "_tau" + str(tau)
else:
outp_file += "_wPrecond"
outp_file += "_nGates" + str(len(sino_files))
if resamplers is None:
outp_file += "_noMotion"
pdhg = PDHG(f=f,
g=G,
operator=K,
sigma=sigma,
tau=tau,
max_iteration=num_iters,
update_objective_interval=update_obj_fn_interval,
x_init=image,
log_file=outp_file + ".log")
def callback_save(iteration, objective_value, solution):
"""Callback function to save images"""
if (iteration + 1) % save_interval == 0:
out = solution if not nifti else reg.NiftiImageData(solution)
out.write(outp_file + "_iters" + str(iteration + 1))
pdhg.run(iterations=num_iters,
callback=callback_save,
verbose=True,
very_verbose=True)
if visualisations:
# show reconstructed image
out = pdhg.get_output()
out_arr = out.as_array()
z = out_arr.shape[0] // 2
show_2D_array('Reconstructed image', out.as_array()[z, :, :])
pylab.show()
else:
operator = Gradient(ig)
f = alpha * MixedL21Norm()
g = f2
# 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.subset(channel=0).as_array())
plt.title('Ground Truth')
plt.colorbar()
plt.subplot(1, 4, 2)
plt.imshow(noisy_data.subset(channel=0).as_array())
plt.title('Noisy Data')
plt.colorbar()
plt.subplot(1, 4, 3)
###############################################################################
# Setup and run the PDHG algorithm
print("Running PDHG reconstruction")
operator = Aop
f = L2NormSquared(b=sinogram)
g = ZeroFunction()
## Compute operator Norm
normK = operator.norm()
## Primal & dual stepsizes
sigma = 0.02
tau = 1 / (sigma * normK**2)
pdhg = PDHG()
pdhg.set_up(f=f, g=g, operator=operator, tau=tau, sigma=sigma)
pdhg.max_iteration = 1000
pdhg.update_objective_interval = 100
pdhg.run(1000, verbose=True)
#%%
###############################################################################
# Setup and run the FISTA algorithm
print("Running FISTA reconstruction")
fidelity = FunctionOperatorComposition(L2NormSquared(b=sinogram), Aop)
regularizer = ZeroFunction()
fista = FISTA()
fista.set_up(x_init=x_init, f=fidelity, g=regularizer)
f = BlockFunction(f1, f2)
g = BlockFunction(f3, ZeroFunction())
# Compute operator Norm
normK = operator.norm()
# Primal & dual stepsizes
#sigma = 1/normK
#tau = 1/normK
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 = 5000
pdhg.update_objective_interval = 500
pdhg.run(5000)
# 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.show()
# Regularisation Parameter
alpha = 0.05
# Setup and run the PDHG algorithm
operator = Gradient(ig)
f = alpha * MixedL21Norm()
g = 0.5 * L2NormSquared(b=noisy_data)
normK = operator.norm()
sigma = 1
tau = 1 / (sigma * normK**2)
pdhg = PDHG(f=f, g=g, operator=operator, tau=tau, sigma=sigma, memopt=True)
pdhg.max_iteration = 1000
pdhg.update_objective_interval = 200
pdhg.run(1000, verbose=True)
# Show results
fig, axes = plt.subplots(nrows=2, ncols=3, figsize=(10, 8))
fig.suptitle('TV Reconstruction', fontsize=20)
plt.subplot(2, 3, 1)
plt.imshow(noisy_data.as_array()[sliceSel, :, :], vmin=0, vmax=1)
plt.axis('off')
plt.title('Axial View')
plt.subplot(2, 3, 2)
plt.imshow(noisy_data.as_array()[:, sliceSel, :], vmin=0, vmax=1)
# Create BlockOperator
op_PDHG = BlockOperator(Grad, Aop, shape=(2, 1))
# Create functions
f1 = 0.5 * alpha**2 * L2NormSquared()
f2 = 0.5 * L2NormSquared(b=noisy_data)
f = BlockFunction(f1, f2)
g = ZeroFunction()
## Compute operator Norm
normK = op_PDHG.norm()
## Primal & dual stepsizes
sigma = 10
tau = 1 / (sigma * normK**2)
pdhg = PDHG(f=f, g=g, operator=op_PDHG, tau=tau, sigma=sigma)
pdhg.max_iteration = 1000
pdhg.update_objective_interval = 200
pdhg.run(1000, verbose=False)
# Show results
plt.figure(figsize=(10, 10))
plt.subplot(2, 1, 1)
plt.imshow(cgls.get_output().as_array())
plt.title('CGLS reconstruction')
plt.subplot(2, 1, 2)
plt.imshow(pdhg.get_output().as_array())
plt.title('PDHG reconstruction')
def test_PDHG_Denoising(self):
print ("PDHG Denoising with 3 noises")
# adapted from demo PDHG_TV_Color_Denoising.py in CIL-Demos repository
# loader = TestData(data_dir=os.path.join(os.environ['SIRF_INSTALL_PATH'], 'share','ccpi'))
# loader = TestData(data_dir=os.path.join(sys.prefix, 'share','ccpi'))
loader = TestData()
data = loader.load(TestData.PEPPERS, size=(256,256))
ig = data.geometry
ag = ig
which_noise = 0
# Create noisy data.
noises = ['gaussian', 'poisson', 's&p']
noise = noises[which_noise]
def setup(data, noise):
if noise == 's&p':
n1 = TestData.random_noise(data.as_array(), mode = noise, salt_vs_pepper = 0.9, amount=0.2, seed=10)
elif noise == 'poisson':
scale = 5
n1 = TestData.random_noise( data.as_array()/scale, mode = noise, seed = 10)*scale
elif noise == 'gaussian':
n1 = TestData.random_noise(data.as_array(), mode = noise, seed = 10)
else:
raise ValueError('Unsupported Noise ', noise)
noisy_data = ig.allocate()
noisy_data.fill(n1)
# Regularisation Parameter depending on the noise distribution
if noise == 's&p':
alpha = 0.8
elif noise == 'poisson':
alpha = 1
elif noise == 'gaussian':
alpha = .3
# fidelity
if noise == 's&p':
g = L1Norm(b=noisy_data)
elif noise == 'poisson':
g = KullbackLeibler(b=noisy_data)
elif noise == 'gaussian':
g = 0.5 * L2NormSquared(b=noisy_data)
return noisy_data, alpha, g
noisy_data, alpha, g = setup(data, noise)
operator = Gradient(ig, correlation=Gradient.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, very_verbose=True)
rmse = (pdhg1.get_output() - data).norm() / data.as_array().size
print ("RMSE", rmse)
self.assertLess(rmse, 2e-4)
which_noise = 1
noise = noises[which_noise]
noisy_data, alpha, g = setup(data, noise)
operator = Gradient(ig, correlation=Gradient.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)
rmse = (pdhg1.get_output() - data).norm() / data.as_array().size
print ("RMSE", rmse)
self.assertLess(rmse, 2e-4)
which_noise = 2
noise = noises[which_noise]
noisy_data, alpha, g = setup(data, noise)
operator = Gradient(ig, correlation=Gradient.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)
rmse = (pdhg1.get_output() - data).norm() / data.as_array().size
print ("RMSE", rmse)
self.assertLess(rmse, 2e-4)
