def test_FISTA_Denoising(self):
if debug_print:
print("FISTA Denoising Poisson Noise Tikhonov")
# adapted from demo FISTA_Tikhonov_Poisson_Denoising.py in CIL-Demos repository
data = dataexample.SHAPES.get()
ig = data.geometry
ag = ig
N = 300
# Create Noisy data with Poisson noise
scale = 5
noisy_data = applynoise.poisson(data / scale, seed=10) * scale
# Regularisation Parameter
alpha = 10
# Setup and run the FISTA algorithm
operator = GradientOperator(ig)
fid = KullbackLeibler(b=noisy_data)
reg = OperatorCompositionFunction(alpha * L2NormSquared(), operator)
initial = ig.allocate()
fista = FISTA(initial=initial, f=reg, g=fid)
fista.max_iteration = 3000
fista.update_objective_interval = 500
fista.run(verbose=0)
rmse = (fista.get_output() - data).norm() / data.as_array().size
if debug_print:
print("RMSE", rmse)
self.assertLess(rmse, 4.2e-4)
def test_FISTA_Norm2Sq(self):
print("Test FISTA Norm2Sq")
ig = ImageGeometry(127, 139, 149)
b = ig.allocate(ImageGeometry.RANDOM)
# fill with random numbers
initial = ig.allocate(ImageGeometry.RANDOM)
identity = IdentityOperator(ig)
#### it seems FISTA does not work with Nowm2Sq
norm2sq = LeastSquares(identity, b)
#norm2sq.L = 2 * norm2sq.c * identity.norm()**2
#norm2sq = OperatorCompositionFunction(L2NormSquared(b=b), identity)
opt = {'tol': 1e-4, 'memopt': False}
if debug_print:
print("initial objective", norm2sq(initial))
alg = FISTA(initial=initial, f=norm2sq, g=ZeroFunction())
alg.max_iteration = 2
alg.run(20, verbose=0)
self.assertNumpyArrayAlmostEqual(alg.x.as_array(), b.as_array())
alg = FISTA(initial=initial,
f=norm2sq,
g=ZeroFunction(),
max_iteration=2,
update_objective_interval=3)
self.assertTrue(alg.max_iteration == 2)
self.assertTrue(alg.update_objective_interval == 3)
alg.run(20, verbose=0)
self.assertNumpyArrayAlmostEqual(alg.x.as_array(), b.as_array())
title="FBP reconstruction",
fix_range=(-0.02, 0.07))
#%% Setup least sqaures and force pre-calculation of Lipschitz constant
Projector = ProjectionOperator(ig, ag)
LS = LeastSquares(A=Projector, b=aq_data)
print("Lipschitz constant =", LS.L)
#%% Setup FISTA to solve for least squares
fista = FISTA(x_init=ig.allocate(0),
f=LS,
g=ZeroFunction(),
max_iteration=1000)
fista.update_objective_interval = 10
#%% Run FISTA
fista.run(300)
LS_reco = fista.get_output()
show2D(LS_reco,
slice_list=[('vertical', 204 // bins), ('horizontal_y', 570 // bins)],
title="LS reconstruction",
fix_range=(-0.02, 0.07))
#%%
plt.figure()
plt.semilogy(fista.objective)
plt.title('FISTA LS criterion')
plt.show()
#%% Setup total-variation (TV) with a non-negativity (NN) contraint
alpha = 1
TV = alpha * FGP_TV(isotropic=True, device='gpu')
f.L = 1071.1967
else:
f.L = 24.4184
alpha_rgl = 0.003
alpha = alpha_rgl * ig_cs.voxel_size_x
g = alpha * TotalVariation(lower=0.)
g = FGP_TV(alpha, 100, 1e-5, 1, 1, 0, 'gpu')
algo = FISTA(initial=K.domain.allocate(0),
f=f,
g=g,
max_iteration=10000,
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.),