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authorepapoutsellis <epapoutsellis@gmail.com>2019-06-12 15:17:26 +0100
committerepapoutsellis <epapoutsellis@gmail.com>2019-06-12 15:17:26 +0100
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delete old demo
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-rw-r--r--Wrappers/Python/demos/PDHG_examples/TGV_Denoising/PDHG_TGV_Denoising_SaltPepper.py245
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diff --git a/Wrappers/Python/demos/PDHG_examples/TGV_Denoising/PDHG_TGV_Denoising_SaltPepper.py b/Wrappers/Python/demos/PDHG_examples/TGV_Denoising/PDHG_TGV_Denoising_SaltPepper.py
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--- a/Wrappers/Python/demos/PDHG_examples/TGV_Denoising/PDHG_TGV_Denoising_SaltPepper.py
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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.
-#
-#=========================================================================
-"""
-
-Total Generalised Variation (TGV) Denoising using PDHG algorithm:
-
-
-Problem: min_{x} \alpha * ||\nabla x - w||_{2,1} +
- \beta * || E w ||_{2,1} +
- \frac{1}{2} * || x - g ||_{2}^{2}
-
- \alpha: Regularization parameter
- \beta: Regularization parameter
-
- \nabla: Gradient operator
- E: Symmetrized Gradient operator
-
- g: Noisy Data with Salt & Pepper Noise
-
- Method = 0 ( PDHG - split ) : K = [ \nabla, - Identity
- ZeroOperator, E
- Identity, ZeroOperator]
-
-
- Method = 1 (PDHG - explicit ): K = [ \nabla, - Identity
- ZeroOperator, E ]
-
-"""
-
-from ccpi.framework import ImageData, ImageGeometry
-
-import numpy as np
-import numpy
-import matplotlib.pyplot as plt
-
-from ccpi.optimisation.algorithms import PDHG
-
-from ccpi.optimisation.operators import BlockOperator, Identity, \
- Gradient, SymmetrizedGradient, ZeroOperator
-from ccpi.optimisation.functions import ZeroFunction, L1Norm, \
- MixedL21Norm, BlockFunction
-
-from skimage.util import random_noise
-
-# Create phantom for TGV SaltPepper denoising
-
-N = 100
-
-data = np.zeros((N,N))
-
-x1 = np.linspace(0, int(N/2), N)
-x2 = np.linspace(int(N/2), 0., N)
-xv, yv = np.meshgrid(x1, x2)
-
-xv[int(N/4):int(3*N/4)-1, int(N/4):int(3*N/4)-1] = yv[int(N/4):int(3*N/4)-1, int(N/4):int(3*N/4)-1].T
-
-data = xv
-data = ImageData(data/data.max())
-
-ig = ImageGeometry(voxel_num_x = N, voxel_num_y = N)
-ag = ig
-
-# Create noisy data. Add Gaussian noise
-n1 = random_noise(data.as_array(), mode = 's&p', salt_vs_pepper = 0.9, amount=0.2)
-noisy_data = ImageData(n1)
-
-# Show Ground Truth and Noisy Data
-plt.figure(figsize=(15,15))
-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()
-
-# Regularisation Parameters
-alpha = 0.8
-beta = numpy.sqrt(2)* alpha
-
-method = '1'
-
-if method == '0':
-
- # Create operators
- op11 = Gradient(ig)
- op12 = Identity(op11.range_geometry())
-
- op22 = SymmetrizedGradient(op11.domain_geometry())
- op21 = ZeroOperator(ig, op22.range_geometry())
-
- op31 = Identity(ig, ag)
- op32 = ZeroOperator(op22.domain_geometry(), ag)
-
- operator = BlockOperator(op11, -1*op12, op21, op22, op31, op32, shape=(3,2) )
-
- f1 = alpha * MixedL21Norm()
- f2 = beta * MixedL21Norm()
- f3 = L1Norm(b=noisy_data)
- f = BlockFunction(f1, f2, f3)
- g = ZeroFunction()
-
-else:
-
- # Create operators
- op11 = Gradient(ig)
- op12 = Identity(op11.range_geometry())
- op22 = SymmetrizedGradient(op11.domain_geometry())
- op21 = ZeroOperator(ig, op22.range_geometry())
-
- operator = BlockOperator(op11, -1*op12, op21, op22, shape=(2,2) )
-
- f1 = alpha * MixedL21Norm()
- f2 = beta * MixedL21Norm()
-
- f = BlockFunction(f1, f2)
- g = BlockFunction(L1Norm(b=noisy_data), ZeroFunction())
-
-## Compute operator Norm
-normK = operator.norm()
-#
-# Primal & dual stepsizes
-sigma = 1
-tau = 1/(sigma*normK**2)
-
-
-# Setup and run the PDHG algorithm
-pdhg = PDHG(f=f,g=g,operator=operator, tau=tau, sigma=sigma)
-pdhg.max_iteration = 2000
-pdhg.update_objective_interval = 50
-pdhg.run(2000, verbose = False)
-
-#%%
-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(pdhg.get_output()[0].as_array())
-plt.title('TGV Reconstruction')
-plt.colorbar()
-plt.show()
-##
-plt.plot(np.linspace(0,N,N), data.as_array()[int(N/2),:], label = 'GTruth')
-plt.plot(np.linspace(0,N,N), pdhg.get_output()[0].as_array()[int(N/2),:], label = 'TV reconstruction')
-plt.legend()
-plt.title('Middle Line Profiles')
-plt.show()
-
-
-#%% Check with CVX solution
-
-from ccpi.optimisation.operators import SparseFiniteDiff
-
-try:
- from cvxpy import *
- cvx_not_installable = True
-except ImportError:
- cvx_not_installable = False
-
-if cvx_not_installable:
-
- u = Variable(ig.shape)
- w1 = Variable((N, N))
- w2 = Variable((N, N))
-
- # create TGV regulariser
- DY = SparseFiniteDiff(ig, direction=0, bnd_cond='Neumann')
- DX = SparseFiniteDiff(ig, direction=1, bnd_cond='Neumann')
-
- regulariser = alpha * sum(norm(vstack([DX.matrix() * vec(u) - vec(w1), \
- DY.matrix() * vec(u) - vec(w2)]), 2, axis = 0)) + \
- beta * sum(norm(vstack([ DX.matrix().transpose() * vec(w1), DY.matrix().transpose() * vec(w2), \
- 0.5 * ( DX.matrix().transpose() * vec(w2) + DY.matrix().transpose() * vec(w1) ), \
- 0.5 * ( DX.matrix().transpose() * vec(w2) + DY.matrix().transpose() * vec(w1) ) ]), 2, axis = 0 ) )
-
- constraints = []
- fidelity = pnorm(u - noisy_data.as_array(),1)
- solver = MOSEK
-
- # choose solver
- if 'MOSEK' in installed_solvers():
- solver = MOSEK
- else:
- solver = SCS
-
- obj = Minimize( regulariser + fidelity)
- prob = Problem(obj)
- result = prob.solve(verbose = True, solver = solver)
-
- diff_cvx = numpy.abs( pdhg.get_output()[0].as_array() - u.value )
-
- plt.figure(figsize=(15,15))
- plt.subplot(3,1,1)
- plt.imshow(pdhg.get_output()[0].as_array())
- plt.title('PDHG solution')
- plt.colorbar()
- plt.subplot(3,1,2)
- plt.imshow(u.value)
- plt.title('CVX solution')
- plt.colorbar()
- plt.subplot(3,1,3)
- plt.imshow(diff_cvx)
- plt.title('Difference')
- plt.colorbar()
- plt.show()
-
- plt.plot(np.linspace(0,N,N), pdhg.get_output()[0].as_array()[int(N/2),:], label = 'PDHG')
- plt.plot(np.linspace(0,N,N), u.value[int(N/2),:], label = 'CVX')
- plt.legend()
- plt.title('Middle Line Profiles')
- plt.show()
-
- print('Primal Objective (CVX) {} '.format(obj.value))
- print('Primal Objective (PDHG) {} '.format(pdhg.objective[-1][0]))
-
-
-
-
-