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#========================================================================
# Copyright 2019 Science Technology Facilities Council
# Copyright 2019 University of Manchester
#
# This work is part of the Core Imaging Library developed by Science Technology
# Facilities Council and University of Manchester
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0.txt
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
#=========================================================================
"""
Compare solutions of PDHG & "Block CGLS" algorithms for
Problem: min_x alpha * ||\grad x ||^{2}_{2} + || A x - g ||_{2}^{2}
A: Projection operator
g: Sinogram
"""
from ccpi.framework import AcquisitionGeometry, BlockDataContainer, AcquisitionData
import numpy as np
import numpy
import matplotlib.pyplot as plt
from ccpi.optimisation.algorithms import PDHG, CGLS
from ccpi.optimisation.operators import BlockOperator, Gradient
from ccpi.optimisation.functions import ZeroFunction, BlockFunction, L2NormSquared
from ccpi.astra.ops import AstraProjectorSimple
from ccpi.framework import TestData
import os, sys
loader = TestData(data_dir=os.path.join(sys.prefix, 'share','ccpi'))
# Create Ground truth phantom and Sinogram
N = 150
M = 150
data = loader.load(TestData.SIMPLE_PHANTOM_2D, size=(N,M), scale=(0,1))
ig = data.geometry
detectors = N
angles = np.linspace(0, np.pi, N, dtype=np.float32)
ag = AcquisitionGeometry('parallel','2D', angles, detectors)
device = input('Available device: GPU==1 / CPU==0 ')
if device=='1':
dev = 'gpu'
else:
dev = 'cpu'
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
normK = op_PDHG.norm()
## Primal & dual stepsizes
sigma = 10
tau = 1/(sigma*normK**2)
pdhg = PDHG(f=f,g=g,operator=op_PDHG, tau=tau, sigma=sigma)
pdhg.max_iteration = 1000
pdhg.update_objective_interval = 200
pdhg.run(1000, verbose=False)
# Show results
plt.figure(figsize=(10,10))
plt.subplot(2,1,1)
plt.imshow(cgls.get_output().as_array())
plt.title('CGLS reconstruction')
plt.subplot(2,1,2)
plt.imshow(pdhg.get_output().as_array())
plt.title('PDHG reconstruction')
plt.show()
diff1 = pdhg.get_output() - cgls.get_output()
plt.imshow(diff1.abs().as_array())
plt.title('Diff PDHG vs CGLS')
plt.colorbar()
plt.show()
plt.plot(np.linspace(0,N,M), pdhg.get_output().as_array()[int(N/2),:], label = 'PDHG')
plt.plot(np.linspace(0,N,M), cgls.get_output().as_array()[int(N/2),:], label = 'CGLS')
plt.legend()
plt.title('Middle Line Profiles')
plt.show()
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