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)
def test_FISTA_Norm2Sq(self):
print ("Test FISTA Norm2Sq")
ig = ImageGeometry(127,139,149)
b = ig.allocate(ImageGeometry.RANDOM)
# fill with random numbers
x_init = ig.allocate(ImageGeometry.RANDOM)
identity = Identity(ig)
#### it seems FISTA does not work with Nowm2Sq
norm2sq = LeastSquares(identity, b)
#norm2sq.L = 2 * norm2sq.c * identity.norm()**2
#norm2sq = FunctionOperatorComposition(L2NormSquared(b=b), identity)
opt = {'tol': 1e-4, 'memopt':False}
print ("initial objective", norm2sq(x_init))
alg = FISTA(x_init=x_init, f=norm2sq, g=ZeroFunction())
alg.max_iteration = 2
alg.run(20, verbose=True)
self.assertNumpyArrayAlmostEqual(alg.x.as_array(), b.as_array())
alg = FISTA(x_init=x_init, 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=True)
self.assertNumpyArrayAlmostEqual(alg.x.as_array(), b.as_array())
def test_FISTA(self):
print ("Test FISTA")
ig = ImageGeometry(127,139,149)
x_init = ImageData(geometry=ig)
b = x_init.copy()
# fill with random numbers
b.fill(numpy.random.random(x_init.shape))
x_init = ImageData(geometry=ig)
x_init.fill(numpy.random.random(x_init.shape))
identity = TomoIdentity(geometry=ig)
norm2sq = Norm2sq(identity, b)
opt = {'tol': 1e-4, 'memopt':False}
alg = FISTA(x_init=x_init, f=norm2sq, g=None, opt=opt)
alg.max_iteration = 2
alg.run(20, verbose=True)
self.assertNumpyArrayAlmostEqual(alg.x.as_array(), b.as_array())
alg.run(20, verbose=True)
self.assertNumpyArrayAlmostEqual(alg.x.as_array(), b.as_array())
# Using the test data b, different reconstruction methods can now be set up as
# demonstrated in the rest of this file. In general all methods need an initial
# guess and some algorithm options to be set:
x_init = ig.allocate(0.0)
opt = {'tol': 1e-4, 'iter': 200}
# Create least squares object instance with projector, test data and a constant
# coefficient of 0.5. Note it is least squares over all channels:
#f = Norm2Sq(Aop,b,c=0.5)
f = FunctionOperatorComposition(L2NormSquared(b=b), Aop)
# Run FISTA for least squares without regularization
FISTA_alg = FISTA()
FISTA_alg.set_up(x_init=x_init, f=f, g=ZeroFunction())
FISTA_alg.max_iteration = 2000
FISTA_alg.run(opt['iter'])
x_FISTA = FISTA_alg.get_output()
# Display reconstruction and criterion
ff0, axarrf0 = plt.subplots(1, numchannels)
for k in numpy.arange(3):
axarrf0[k].imshow(x_FISTA.as_array()[k], vmin=0, vmax=2.5)
plt.show()
plt.figure()
plt.semilogy(FISTA_alg.objective)
plt.title('Criterion vs iterations, least squares')
plt.show()
# FISTA can also solve regularised forms by specifying a second function object
# such as 1-norm regularisation with choice of regularisation parameter lam.
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)
# Set up operators: Projection and Gradient
# 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
tau = 1 / (sigma * normK**2)
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) fista1 = FISTA(x_init=x_init, f=f1, g=IndicatorBox(lower=0, upper=1))
out *= 0.5
# ADD the constraint here
out.maximum(0, out=out)
fid.proximal = KL_Prox_PosCone
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(3000, verbose=True)
# Show results
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(fista.get_output().as_array())
plt.title('Reconstruction')
plt.colorbar()
plt.show()
#%% Use FISTA algorithm to solve same smoothed TV regularised denoising proglem
# Manually set guess of Lipschitz parameter of function to step size selection.
objective_function.L = 1000000
# Set up and run FISTA algorithms
print(
"Running FISTA with smooth approximation of TV.\nThis will take some time .... "
)
fi = FISTA(x_init,
objective_function,
max_iteration=10000,
update_objective_interval=100)
fi.run(verbose=True)
## Show FISTA 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)
plt.imshow(fi.get_output().as_array())
plt.title('FISTA Reconstruction')
plt.colorbar()
def test_FISTA_cvx(self):
if False:
if not cvx_not_installable:
try:
# Problem data.
m = 30
n = 20
np.random.seed(1)
Amat = np.random.randn(m, n)
A = LinearOperatorMatrix(Amat)
bmat = np.random.randn(m)
bmat.shape = (bmat.shape[0], 1)
# A = Identity()
# Change n to equal to m.
#b = DataContainer(bmat)
vg = VectorGeometry(m)
b = vg.allocate('random')
# Regularization parameter
lam = 10
opt = {'memopt': True}
# Create object instances with the test data A and b.
f = LeastSquares(A, b, c=0.5)
g0 = ZeroFunction()
# Initial guess
#x_init = DataContainer(np.zeros((n, 1)))
x_init = vg.allocate()
f.gradient(x_init, out = x_init)
# Run FISTA for least squares plus zero function.
#x_fista0, it0, timing0, criter0 = FISTA(x_init, f, g0, opt=opt)
fa = FISTA(x_init=x_init, f=f, g=g0)
fa.max_iteration = 10
fa.run(10)
# Print solution and final objective/criterion value for comparison
print("FISTA least squares plus zero function solution and objective value:")
print(fa.get_output())
print(fa.get_last_objective())
# Compare to CVXPY
# Construct the problem.
x0 = Variable(n)
objective0 = Minimize(0.5*sum_squares(Amat*x0 - bmat.T[0]))
prob0 = Problem(objective0)
# The optimal objective is returned by prob.solve().
result0 = prob0.solve(verbose=False, solver=SCS, eps=1e-9)
# The optimal solution for x is stored in x.value and optimal objective value
# is in result as well as in objective.value
print("CVXPY least squares plus zero function solution and objective value:")
print(x0.value)
print(objective0.value)
self.assertNumpyArrayAlmostEqual(
numpy.squeeze(x_fista0.array), x0.value, 6)
except SolverError as se:
print (str(se))
self.assertTrue(True)
else:
self.assertTrue(cvx_not_installable)
def stest_FISTA_Norm1_cvx(self):
if not cvx_not_installable:
try:
opt = {'memopt': True}
# Problem data.
m = 30
n = 20
np.random.seed(1)
Amat = np.random.randn(m, n)
A = LinearOperatorMatrix(Amat)
bmat = np.random.randn(m)
#bmat.shape = (bmat.shape[0], 1)
# A = Identity()
# Change n to equal to m.
vgb = VectorGeometry(m)
vgx = VectorGeometry(n)
b = vgb.allocate()
b.fill(bmat)
#b = DataContainer(bmat)
# Regularization parameter
lam = 10
opt = {'memopt': True}
# Create object instances with the test data A and b.
f = LeastSquares(A, b, c=0.5)
g0 = ZeroFunction()
# Initial guess
#x_init = DataContainer(np.zeros((n, 1)))
x_init = vgx.allocate()
# Create 1-norm object instance
g1 = lam * L1Norm()
g1(x_init)
g1.prox(x_init, 0.02)
# Combine with least squares and solve using generic FISTA implementation
#x_fista1, it1, timing1, criter1 = FISTA(x_init, f, g1, opt=opt)
fa = FISTA(x_init=x_init, f=f, g=g1)
fa.max_iteration = 10
fa.run(10)
# Print for comparison
print("FISTA least squares plus 1-norm solution and objective value:")
print(fa.get_output())
print(fa.get_last_objective())
# Compare to CVXPY
# Construct the problem.
x1 = Variable(n)
objective1 = Minimize(
0.5*sum_squares(Amat*x1 - bmat.T[0]) + lam*norm(x1, 1))
prob1 = Problem(objective1)
# The optimal objective is returned by prob.solve().
result1 = prob1.solve(verbose=False, solver=SCS, eps=1e-9)
# The optimal solution for x is stored in x.value and optimal objective value
# is in result as well as in objective.value
print("CVXPY least squares plus 1-norm solution and objective value:")
print(x1.value)
print(objective1.value)
self.assertNumpyArrayAlmostEqual(
numpy.squeeze(x_fista1.array), x1.value, 6)
except SolverError as se:
print (str(se))
self.assertTrue(True)
else:
self.assertTrue(cvx_not_installable)
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)
fista.max_iteration = 500
fista.update_objective_interval = 100
fista.run(500, verbose=True)
#%% Show results
plt.figure(figsize=(10, 10))
plt.suptitle('Reconstructions ', fontsize=16)
plt.subplot(2, 2, 1)
plt.imshow(cgls.get_output().as_array())
plt.colorbar()
plt.title('CGLS reconstruction')
plt.subplot(2, 2, 2)
plt.imshow(fista.get_output().as_array())
plt.colorbar()
plt.title('FISTA reconstruction')