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(self):
print("Test FISTA")
ig = ImageGeometry(127, 139, 149)
initial = ig.allocate()
b = initial.copy()
# fill with random numbers
b.fill(numpy.random.random(initial.shape))
initial = ig.allocate(ImageGeometry.RANDOM)
identity = IdentityOperator(ig)
#### it seems FISTA does not work with Nowm2Sq
# norm2sq = Norm2Sq(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=2)
self.assertTrue(alg.max_iteration == 2)
self.assertTrue(alg.update_objective_interval == 2)
alg.run(20, verbose=0)
self.assertNumpyArrayAlmostEqual(alg.x.as_array(), b.as_array())
def test_Norm2sq_as_OperatorCompositionFunction(self):
print('Test for OperatorCompositionFunction')
M, N = 50, 50
ig = ImageGeometry(voxel_num_x=M, voxel_num_y=N)
#numpy.random.seed(1)
b = ig.allocate('random', seed=1)
print('Check call with IdentityOperator operator... OK\n')
operator = 3 * IdentityOperator(ig)
u = ig.allocate('random', seed=50)
f = 0.5 * L2NormSquared(b=b)
func1 = OperatorCompositionFunction(f, operator)
func2 = LeastSquares(operator, b, 0.5)
print("f.L {}".format(f.L))
print("0.5*f.L {}".format((0.5 * f).L))
print("type func1 {}".format(type(func1)))
print("func1.L {}".format(func1.L))
print("func2.L {}".format(func2.L))
print("operator.norm() {}".format(operator.norm()))
numpy.testing.assert_almost_equal(func1(u), func2(u))
print('Check gradient with IdentityOperator operator... OK\n')
tmp1 = ig.allocate()
tmp2 = ig.allocate()
res_gradient1 = func1.gradient(u)
res_gradient2 = func2.gradient(u)
func1.gradient(u, out=tmp1)
func2.gradient(u, out=tmp2)
self.assertNumpyArrayAlmostEqual(res_gradient1.as_array(),
res_gradient2.as_array())
self.assertNumpyArrayAlmostEqual(tmp1.as_array(), tmp2.as_array())
print('Check call with MatrixOperator... OK\n')
mat = np.random.randn(M, N)
operator = MatrixOperator(mat)
vg = VectorGeometry(N)
b = vg.allocate('random')
u = vg.allocate('random')
func1 = OperatorCompositionFunction(0.5 * L2NormSquared(b=b), operator)
func2 = LeastSquares(operator, b, 0.5)
self.assertNumpyArrayAlmostEqual(func1(u), func2(u))
numpy.testing.assert_almost_equal(func1.L, func2.L)
def test_exception_initial_GD(self):
print("Test FISTA")
ig = ImageGeometry(127, 139, 149)
initial = ig.allocate()
b = initial.copy()
# fill with random numbers
b.fill(numpy.random.random(initial.shape))
initial = ig.allocate(ImageGeometry.RANDOM)
identity = IdentityOperator(ig)
norm2sq = OperatorCompositionFunction(L2NormSquared(b=b), identity)
opt = {'tol': 1e-4, 'memopt': False}
print("initial objective", norm2sq(initial))
try:
alg = GD(initial=initial,
objective_function=norm2sq,
x_init=initial)
assert False
except ValueError as ve:
assert True