def test_CGLS(self):
print ("Test CGLS")
#ig = ImageGeometry(124,153,154)
ig = ImageGeometry(10,2)
numpy.random.seed(2)
x_init = ig.allocate(0.)
b = ig.allocate('random')
# b = x_init.copy()
# fill with random numbers
# b.fill(numpy.random.random(x_init.shape))
# b = ig.allocate()
# bdata = numpy.reshape(numpy.asarray([i for i in range(20)]), (2,10))
# b.fill(bdata)
identity = Identity(ig)
alg = CGLS(x_init=x_init, operator=identity, data=b)
alg.max_iteration = 200
alg.run(20, verbose=True)
self.assertNumpyArrayAlmostEqual(alg.x.as_array(), b.as_array())
alg = CGLS(x_init=x_init, operator=identity, data=b, max_iteration=200, update_objective_interval=2)
self.assertTrue(alg.max_iteration == 200)
self.assertTrue(alg.update_objective_interval==2)
alg.run(20, verbose=True)
self.assertNumpyArrayAlmostEqual(alg.x.as_array(), b.as_array())
def test_CGLS(self):
print ("Test CGLS")
ig = ImageGeometry(124,153,154)
x_init = ImageData(geometry=ig)
b = x_init.copy()
# fill with random numbers
b.fill(numpy.random.random(x_init.shape))
identity = TomoIdentity(geometry=ig)
alg = CGLS(x_init=x_init, operator=identity, data=b)
alg.max_iteration = 1
alg.run(20, verbose=True)
self.assertNumpyArrayAlmostEqual(alg.x.as_array(), b.as_array())
Aop = AstraProjectorSimple(ig, ag, dev) sin = Aop.direct(data) noisy_data = AcquisitionData(sin.as_array() + np.random.normal(0, 3, ig.shape)) # Setup and run the CGLS algorithm alpha = 50 Grad = Gradient(ig) # Form Tikhonov as a Block CGLS structure op_CGLS = BlockOperator(Aop, alpha * Grad, shape=(2, 1)) block_data = BlockDataContainer(noisy_data, Grad.range_geometry().allocate()) x_init = ig.allocate() cgls = CGLS(x_init=x_init, operator=op_CGLS, data=block_data) cgls.max_iteration = 1000 cgls.update_objective_interval = 200 cgls.run(1000, verbose=False) #Setup and run the PDHG algorithm # 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
plt.colorbar()
plt.subplot(2, 1, 2)
plt.imshow(noisy_data.as_array())
plt.title('Noisy Data')
plt.colorbar()
plt.show()
# Setup and run the regularised CGLS algorithm (Tikhonov with Gradient)
x_init = ig.allocate()
alpha = 2
op = Gradient(ig)
block_op = BlockOperator(Identity(ig), alpha * op, shape=(2, 1))
block_data = BlockDataContainer(noisy_data, op.range_geometry().allocate())
cgls = CGLS(x_init=x_init, operator=block_op, data=block_data)
cgls.max_iteration = 200
cgls.update_objective_interval = 5
cgls.run(200, verbose=True)
# Show results
plt.figure(figsize=(20, 10))
plt.subplot(3, 1, 1)
plt.imshow(data.as_array())
plt.title('Ground Truth')
plt.subplot(3, 1, 2)
plt.imshow(noisy_data.as_array())
plt.title('Noisy')
plt.subplot(3, 1, 3)
plt.imshow(cgls.get_output().as_array())
plt.title('Regularised GGLS with Gradient')
im2 = axs[1].imshow(tmp[channel, :, axis[1], :], cmap='inferno')
axs[1].set_title('coronal view')
fig.colorbar(im2, ax=axs[1])
im3 = axs[2].imshow(tmp[channel, :, :, axis[2]], cmap='inferno')
axs[2].set_title('sagittal view')
fig.colorbar(im3, ax=axs[2])
fig.suptitle(title + ': Channel {}'.format(channel), fontsize=20)
plt.show()
#%% CGLS reconstruction on the 4D volume = 3D + channels
x_init = A3D_chan.volume_geometry.allocate()
cgls = CGLS(x_init=x_init, operator=A3D_chan, data=data)
cgls.max_iteration = 100
cgls.update_objective_interval = 10
cgls.run(50, verbose=True, callback=show_data_4D)
show_4D_channel_slice(cgls.get_output(), 5, 'CGLS reconstruction')
show_4D_channel_slice(cgls.get_output(), 10, 'CGLS reconstruction')
show_4D_channel_slice(cgls.get_output(), 15, 'CGLS reconstruction')
#%% TV reconstuction channel-wise.
# Basically for every energy - channel we apply TV reconstruction with the same parameter
# which is not the best
# Setup Astra Projector for the 3D volume
A3D = A3D_chan.A3D
plt.title('Simulated data')
plt.show()
plt.imshow(z.array)
plt.title('Backprojected data')
plt.colorbar()
plt.show()
# 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()
opt = {'tol': 1e-4, 'iter': 100}
# First a CGLS reconstruction can be done:
CGLS_alg = CGLS(x_init=x_init, operator=Aop, data=b)
CGLS_alg.max_iteration = 2000
CGLS_alg.run(opt['iter'])
x_CGLS = CGLS_alg.get_output()
plt.figure()
plt.imshow(x_CGLS.array)
plt.title('CGLS')
plt.show()
plt.figure()
plt.semilogy(CGLS_alg.objective)
plt.title('CGLS criterion')
plt.show()
# Test backprojection and projection
z1 = Cop.adjoint(padded_data)
z2 = Cop.direct(z1)
plt.imshow(z1.subset(horizontal_x=68).array)
plt.show()
# Set initial guess for reconstruction algorithms.
print ("Initial guess")
x_init = ImageData(geometry=ig)
# Set tolerance and number of iterations for reconstruction algorithms.
opt = {'tol': 1e-4, 'iter': 100}
# First a CGLS reconstruction can be done:
CGLS_alg = CGLS()
CGLS_alg.set_up(x_init, Cop, padded_data)
CGLS_alg.max_iteration = 2000
CGLS_alg.update_objective_interval = 10
CGLS_alg.run(opt['iter'])
x_CGLS = CGLS_alg.get_output()
# Fix color and slices for display
v1 = -0.01
v2 = 0.13
hx=80
hy=80
v=68
# Display ortho slices of reconstruction
# Show Ground Truth and Noisy Data
plt.figure(figsize=(10, 10))
plt.subplot(2, 1, 1)
plt.imshow(data.as_array())
plt.title('Ground Truth')
plt.colorbar()
plt.subplot(2, 1, 2)
plt.imshow(noisy_data.as_array())
plt.title('Noisy Data')
plt.colorbar()
plt.show()
# Setup and run the simple CGLS algorithm
x_init = ig.allocate()
cgls1 = CGLS(x_init=x_init, operator=Aop, data=noisy_data)
cgls1.max_iteration = 20
cgls1.update_objective_interval = 5
cgls1.run(20, verbose=True)
# Setup and run the regularised CGLS algorithm (Tikhonov with Identity)
x_init = ig.allocate()
alpha1 = 50
op1 = Identity(ig)
block_op1 = BlockOperator(Aop, alpha1 * op1, shape=(2, 1))
block_data1 = BlockDataContainer(noisy_data, op1.range_geometry().allocate())
cgls2 = CGLS(x_init=x_init, operator=block_op1, data=block_data1)
cgls2.max_iteration = 200
# Create the algorithm object from the configuration structure
alg_id = astra.algorithm.create(cgls_astra)
astra.algorithm.run(alg_id, 500)
recon_cgls_astra = ImageData(astra.data2d.get(rec_id))
#%%
###############################################################################
#
# Setup and run the simple CGLS algorithm
print("Running CGLS reconstruction")
x_init = ig.allocate()
cgls = CGLS()
cgls.set_up(x_init=x_init, operator=Aop, data=sinogram)
cgls.max_iteration = 500
cgls.update_objective_interval = 100
cgls.run(500, verbose=True)
#%%
###############################################################################
# Setup and run the PDHG algorithm
print("Running PDHG reconstruction")
operator = Aop
f = L2NormSquared(b=sinogram)
g = ZeroFunction()
# Show Ground Truth and Noisy Data
plt.figure(figsize=(10, 10))
plt.subplot(2, 1, 1)
plt.imshow(data.as_array())
plt.title('Ground Truth')
plt.colorbar()
plt.subplot(2, 1, 2)
plt.imshow(projection_data.as_array())
plt.title('Projection Data')
plt.colorbar()
plt.show()
# Setup and run the CGLS algorithm
x_init = ig.allocate()
cgls = CGLS(x_init=x_init, operator=Aop, data=projection_data)
cgls.max_iteration = 5000
cgls.update_objective_interval = 100
cgls.run(1000, verbose=True)
plt.figure(figsize=(5, 5))
plt.imshow(cgls.get_output().as_array())
plt.title('CGLS reconstruction')
plt.colorbar()
plt.show()
#%%
# Check with CVX solution
print('If N > {} : CVX solution will take some time '.format(128))