def test_FISTA_Denoising(self):
print ("FISTA Denoising Poisson Noise Tikhonov")
# adapted from demo FISTA_Tikhonov_Poisson_Denoising.py in CIL-Demos repository
#loader = TestData(data_dir=os.path.join(sys.prefix, 'share','ccpi'))
loader = TestData()
data = loader.load(TestData.SHAPES)
ig = data.geometry
ag = ig
N=300
# Create Noisy data with Poisson noise
scale = 5
n1 = TestData.random_noise( data.as_array()/scale, mode = 'poisson', seed = 10)*scale
noisy_data = ImageData(n1)
# Regularisation Parameter
alpha = 10
# Setup and run the FISTA algorithm
operator = Gradient(ig)
fid = KullbackLeibler(b=noisy_data)
reg = FunctionOperatorComposition(alpha * L2NormSquared(), operator)
x_init = ig.allocate()
fista = FISTA(x_init=x_init , f=reg, g=fid)
fista.max_iteration = 3000
fista.update_objective_interval = 500
fista.run(verbose=True)
rmse = (fista.get_output() - data).norm() / data.as_array().size
print ("RMSE", rmse)
self.assertLess(rmse, 4.2e-4)
x_init = A3D.volume_geometry.allocate()
# Allocate space for the channel-wise reconstruction
fista_sol_TV_channel_wise = A3D_chan.volume_geometry.allocate()
for i in range(ag.channels):
# Setup L2NormSquarred fidelity term, for each channel
f = FunctionOperatorComposition(
0.5 * L2NormSquared(b=data.subset(channel=i)), A3D)
# Run FISTA
fista = FISTA(x_init=x_init, f=f, g=g)
fista.max_iteration = 100
fista.update_objective_interval = 50
fista.run(400, verbose=True, callback=show_data_3D)
np.copyto(fista_sol_TV_channel_wise.array[i], fista.get_output().array)
#%% show reconstruction
show_4D_channel_slice(fista_sol_TV_channel_wise, 5,
'FISTA TV channel-wise reconstruction')
show_4D_channel_slice(fista_sol_TV_channel_wise, 10,
'FISTA TV channel-wise reconstruction')
show_4D_channel_slice(fista_sol_TV_channel_wise, 15,
'FISTA TV channel-wise reconstruction')
#%% Coupling Total variation reconstruction in 4D volume. For this case there is no GPU implementation
# But we can use another algorithm called PDHG ( primal - dual hybrid gradient)
plt.show()
plt.figure()
plt.semilogy(CGLS_alg.objective)
plt.title('CGLS criterion')
plt.show()
# Create least squares object instance with projector and data.
print ("Create least squares object instance with projector and data.")
f = Norm2Sq(Cop,padded_data,c=0.5)
# Run FISTA for least squares without constraints
FISTA_alg = FISTA()
FISTA_alg.set_up(x_init=x_init, f=f)
FISTA_alg.max_iteration = 2000
FISTA_alg.update_objective_interval = 10
FISTA_alg.run(opt['iter'])
x_FISTA = FISTA_alg.get_output()
# Display ortho slices of reconstruction
# Display all reconstructions and decay of objective function
fig = plt.figure()
current = 1
a=fig.add_subplot(rows,cols,current)
a.set_title('horizontal_x')
imgplot = plt.imshow(x_FISTA.subset(horizontal_x=hx).as_array(),vmin=v1,vmax=v2)
current = current + 1
a=fig.add_subplot(rows,cols,current)
noisy_data = ImageData(n1)
# Regularisation Parameter
alpha = 5
###############################################################################
# Setup and run the FISTA algorithm
operator = Gradient(ig)
fidelity = L1Norm(b=noisy_data)
regulariser = FunctionOperatorComposition(alpha * L2NormSquared(), operator)
x_init = ig.allocate()
opt = {'memopt': True}
fista = FISTA(x_init=x_init, f=regulariser, g=fidelity, opt=opt)
fista.max_iteration = 2000
fista.update_objective_interval = 50
fista.run(2000, verbose=False)
###############################################################################
###############################################################################
# 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
Aop = AstraProjectorSimple(ig, ag, dev) sin = Aop.direct(data) eta = 0 noisy_data = AcquisitionData(sin.as_array() + np.random.normal(0, 1, ag.shape)) back_proj = Aop.adjoint(noisy_data) # Define Least Squares f = FunctionOperatorComposition(L2NormSquared(b=noisy_data), Aop) # Allocate solution x_init = ig.allocate() # Run FISTA for least squares fista = FISTA(x_init=x_init, f=f, g=ZeroFunction()) fista.max_iteration = 10 fista.update_objective_interval = 2 fista.run(100, verbose=True) # Run FISTA for least squares with lower/upper bound fista0 = FISTA(x_init=x_init, f=f, g=IndicatorBox(lower=0, upper=1)) fista0.max_iteration = 10 fista0.update_objective_interval = 2 fista0.run(100, verbose=True) # Run FISTA for Regularised least squares, with Squared norm of Gradient alpha = 20 Grad = Gradient(ig) block_op = BlockOperator(Aop, alpha * Grad, shape=(2, 1)) block_data = BlockDataContainer(noisy_data, Grad.range_geometry().allocate()) f1 = FunctionOperatorComposition(L2NormSquared(b=block_data), block_op)