From d158b57e6bf7893288ef7bc0551b267c4b9f42f3 Mon Sep 17 00:00:00 2001
From: epapoutsellis <epapoutsellis@gmail.com>
Date: Thu, 9 May 2019 11:49:06 +0100
Subject: move demos
---
.../Python/demos/PDHG_TGV_Denoising_SaltPepper.py | 194 -------------------
.../Python/demos/PDHG_TV_Denoising_Gaussian.py | 204 --------------------
Wrappers/Python/demos/PDHG_TV_Denoising_Poisson.py | 213 ---------------------
.../Python/demos/PDHG_TV_Denoising_SaltPepper.py | 198 -------------------
Wrappers/Python/demos/PDHG_Tikhonov_Denoising.py | 176 -----------------
5 files changed, 985 deletions(-)
delete mode 100644 Wrappers/Python/demos/PDHG_TGV_Denoising_SaltPepper.py
delete mode 100644 Wrappers/Python/demos/PDHG_TV_Denoising_Gaussian.py
delete mode 100644 Wrappers/Python/demos/PDHG_TV_Denoising_Poisson.py
delete mode 100644 Wrappers/Python/demos/PDHG_TV_Denoising_SaltPepper.py
delete mode 100644 Wrappers/Python/demos/PDHG_Tikhonov_Denoising.py
diff --git a/Wrappers/Python/demos/PDHG_TGV_Denoising_SaltPepper.py b/Wrappers/Python/demos/PDHG_TGV_Denoising_SaltPepper.py
deleted file mode 100644
index 7b65c31..0000000
--- a/Wrappers/Python/demos/PDHG_TGV_Denoising_SaltPepper.py
+++ /dev/null
@@ -1,194 +0,0 @@
-#!/usr/bin/env python3
-# -*- coding: utf-8 -*-
-"""
-Created on Fri Feb 22 14:53:03 2019
-
-@author: evangelos
-"""
-
-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)
-
-# 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, memopt=True)
-pdhg.max_iteration = 2000
-pdhg.update_objective_interval = 50
-pdhg.run(2000)
-
-#%%
-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]))
-
-
-
-
-
diff --git a/Wrappers/Python/demos/PDHG_TV_Denoising_Gaussian.py b/Wrappers/Python/demos/PDHG_TV_Denoising_Gaussian.py
deleted file mode 100644
index afdb6a2..0000000
--- a/Wrappers/Python/demos/PDHG_TV_Denoising_Gaussian.py
+++ /dev/null
@@ -1,204 +0,0 @@
-#========================================================================
-# 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 Variation Denoising using PDHG algorithm:
-
-
-Problem: min_{x} \alpha * ||\nabla x||_{2,1} + \frac{1}{2} * || x - g ||_{2}^{2}
-
- \alpha: Regularization parameter
-
- \nabla: Gradient operator
-
- g: Noisy Data with Gaussian Noise
-
- Method = 0 ( PDHG - split ) : K = [ \nabla,
- Identity]
-
-
- Method = 1 (PDHG - explicit ): K = \nabla
-
-"""
-
-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
-from ccpi.optimisation.functions import ZeroFunction, L2NormSquared, \
- MixedL21Norm, BlockFunction
-
-# Load Data
-N = 100
-
-data = np.zeros((N,N))
-data[round(N/4):round(3*N/4),round(N/4):round(3*N/4)] = 0.5
-data[round(N/8):round(7*N/8),round(3*N/8):round(5*N/8)] = 1
-data = ImageData(data)
-ig = ImageGeometry(voxel_num_x = N, voxel_num_y = N)
-ag = ig
-
-# Create Noisy data. Add Gaussian noise
-np.random.seed(10)
-noisy_data = ImageData( data.as_array() + np.random.normal(0, 0.1, size=ig.shape) )
-
-# 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 Parameter
-alpha = 0.2
-
-method = '0'
-
-if method == '0':
-
- # Create operators
- op1 = Gradient(ig)
- op2 = Identity(ig, ag)
-
- # Create BlockOperator
- operator = BlockOperator(op1, op2, shape=(2,1) )
-
- # Create functions
- f1 = alpha * MixedL21Norm()
- f2 = 0.5 * L2NormSquared(b = noisy_data)
- f = BlockFunction(f1, f2)
-
- g = ZeroFunction()
-
-else:
-
- # Without the "Block Framework"
- operator = Gradient(ig)
- f = alpha * MixedL21Norm()
- g = 0.5 * L2NormSquared(b = noisy_data)
-
-# 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 = 3000
-pdhg.update_objective_interval = 200
-pdhg.run(3000, verbose=False)
-
-# 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(pdhg.get_output().as_array())
-plt.title('TV 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().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:
-
- ##Construct problem
- u = Variable(ig.shape)
-
- DY = SparseFiniteDiff(ig, direction=0, bnd_cond='Neumann')
- DX = SparseFiniteDiff(ig, direction=1, bnd_cond='Neumann')
-
- # Define Total Variation as a regulariser
- regulariser = alpha * sum(norm(vstack([DX.matrix() * vec(u), DY.matrix() * vec(u)]), 2, axis = 0))
- fidelity = 0.5 * sum_squares(u - noisy_data.as_array())
-
- # 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 = MOSEK)
-
- diff_cvx = numpy.abs( pdhg.get_output().as_array() - u.value )
-
- plt.figure(figsize=(15,15))
- plt.subplot(3,1,1)
- plt.imshow(pdhg.get_output().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().as_array()[int(N/2),:], label = 'PDHG')
- plt.plot(np.linspace(0,N,N), u.value[int(N/2),:], label = 'CVX')
- plt.plot(np.linspace(0,N,N), data.as_array()[int(N/2),:], label = 'Truth')
-
- 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]))
-
diff --git a/Wrappers/Python/demos/PDHG_TV_Denoising_Poisson.py b/Wrappers/Python/demos/PDHG_TV_Denoising_Poisson.py
deleted file mode 100644
index 0db8c29..0000000
--- a/Wrappers/Python/demos/PDHG_TV_Denoising_Poisson.py
+++ /dev/null
@@ -1,213 +0,0 @@
-#========================================================================
-# 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 Variation Denoising using PDHG algorithm:
-
-Problem: min_x, x>0 \alpha * ||\nabla x||_{1} + \int x - g * log(x)
-
- \alpha: Regularization parameter
-
- \nabla: Gradient operator
-
- g: Noisy Data with Poisson Noise
-
-
- Method = 0 ( PDHG - split ) : K = [ \nabla,
- Identity]
-
-
- Method = 1 (PDHG - explicit ): K = \nabla
-
-"""
-
-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
-from ccpi.optimisation.functions import ZeroFunction, KullbackLeibler, \
- MixedL21Norm, BlockFunction
-
-from skimage.util import random_noise
-
-# Create phantom for TV Poisson denoising
-N = 100
-
-data = np.zeros((N,N))
-data[round(N/4):round(3*N/4),round(N/4):round(3*N/4)] = 0.5
-data[round(N/8):round(7*N/8),round(3*N/8):round(5*N/8)] = 1
-data = ImageData(data)
-ig = ImageGeometry(voxel_num_x = N, voxel_num_y = N)
-ag = ig
-
-# Create noisy data. Apply Poisson noise
-n1 = random_noise(data.as_array(), mode = 'poisson', seed = 10)
-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 Parameter
-alpha = 2
-
-method = '0'
-
-if method == '0':
-
- # Create operators
- op1 = Gradient(ig)
- op2 = Identity(ig, ag)
-
- # Create BlockOperator
- operator = BlockOperator(op1, op2, shape=(2,1) )
-
- # Create functions
-
- f1 = alpha * MixedL21Norm()
- f2 = KullbackLeibler(noisy_data)
- f = BlockFunction(f1, f2)
-
- g = ZeroFunction()
-
-else:
-
- # Without the "Block Framework"
- operator = Gradient(ig)
- f = alpha * MixedL21Norm()
- g = KullbackLeibler(noisy_data)
-
-
-# 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 = 3000
-pdhg.update_objective_interval = 200
-pdhg.run(3000, 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().as_array())
-plt.title('TV 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().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:
-
- ##Construct problem
- u1 = Variable(ig.shape)
- q = Variable()
-
- DY = SparseFiniteDiff(ig, direction=0, bnd_cond='Neumann')
- DX = SparseFiniteDiff(ig, direction=1, bnd_cond='Neumann')
-
- # Define Total Variation as a regulariser
- regulariser = alpha * sum(norm(vstack([DX.matrix() * vec(u1), DY.matrix() * vec(u1)]), 2, axis = 0))
-
- fidelity = sum( u1 - multiply(noisy_data.as_array(), log(u1)) )
- constraints = [q>= fidelity, u1>=0]
-
- solver = ECOS
- obj = Minimize( regulariser + q)
- prob = Problem(obj, constraints)
- result = prob.solve(verbose = True, solver = solver)
-
-
- diff_cvx = numpy.abs( pdhg.get_output().as_array() - u1.value )
-
- plt.figure(figsize=(15,15))
- plt.subplot(3,1,1)
- plt.imshow(pdhg.get_output().as_array())
- plt.title('PDHG solution')
- plt.colorbar()
- plt.subplot(3,1,2)
- plt.imshow(u1.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().as_array()[int(N/2),:], label = 'PDHG')
- plt.plot(np.linspace(0,N,N), u1.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]))
-
-
-
-
-
diff --git a/Wrappers/Python/demos/PDHG_TV_Denoising_SaltPepper.py b/Wrappers/Python/demos/PDHG_TV_Denoising_SaltPepper.py
deleted file mode 100644
index f5d4ce4..0000000
--- a/Wrappers/Python/demos/PDHG_TV_Denoising_SaltPepper.py
+++ /dev/null
@@ -1,198 +0,0 @@
-# -*- coding: utf-8 -*-
-# This work is part of the Core Imaging Library developed by
-# Visual Analytics and Imaging System Group of the Science Technology
-# Facilities Council, STFC
-
-# Copyright 2018-2019 Evangelos Papoutsellis and Edoardo Pasca
-
-# 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
-
-# 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 Variation Denoising using PDHG algorithm:
-
- min_{x} max_{y} < K x, y > + g(x) - f^{*}(y)
-
-
-Problem: min_x, x>0 \alpha * ||\nabla x||_{1} + ||x-g||_{1}
-
- \nabla: Gradient operator
- g: Noisy Data with Salt & Pepper Noise
- \alpha: Regularization parameter
-
- Method = 0: K = [ \nabla,
- Identity]
-
- Method = 1: K = \nabla
-
-
-"""
-
-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
-from ccpi.optimisation.functions import ZeroFunction, L1Norm, \
- MixedL21Norm, BlockFunction
-
-from skimage.util import random_noise
-
-# Create phantom for TV Salt & Pepper denoising
-N = 100
-
-data = np.zeros((N,N))
-data[round(N/4):round(3*N/4),round(N/4):round(3*N/4)] = 0.5
-data[round(N/8):round(7*N/8),round(3*N/8):round(5*N/8)] = 1
-data = ImageData(data)
-ig = ImageGeometry(voxel_num_x = N, voxel_num_y = N)
-ag = ig
-
-# Create noisy data. Apply Salt & Pepper noise
-n1 = random_noise(data.as_array(), mode = 's&p', salt_vs_pepper = 0.9, amount=0.2)
-noisy_data = ImageData(n1)
-
-# Regularisation Parameter
-alpha = 2
-
-method = '0'
-
-if method == '0':
-
- # Create operators
- op1 = Gradient(ig)
- op2 = Identity(ig, ag)
-
- # Create BlockOperator
- operator = BlockOperator(op1, op2, shape=(2,1) )
-
- # Create functions
-
- f1 = alpha * MixedL21Norm()
- f2 = L1Norm(b = noisy_data)
- f = BlockFunction(f1, f2)
-
- g = ZeroFunction()
-
-else:
-
- # Without the "Block Framework"
- operator = Gradient(ig)
- f = alpha * MixedL21Norm()
- g = L1Norm(b = noisy_data)
-
-
-# Compute operator Norm
-normK = operator.norm()
-
-# Primal & dual stepsizes
-sigma = 1
-tau = 1/(sigma*normK**2)
-opt = {'niter':2000, 'memopt': True}
-
-# Setup and run the PDHG algorithm
-pdhg = PDHG(f=f,g=g,operator=operator, tau=tau, sigma=sigma, memopt=True)
-pdhg.max_iteration = 2000
-pdhg.update_objective_interval = 50
-pdhg.run(2000)
-
-
-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().as_array())
-plt.title('TV 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().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:
-
- ##Construct problem
- u = Variable(ig.shape)
-
- DY = SparseFiniteDiff(ig, direction=0, bnd_cond='Neumann')
- DX = SparseFiniteDiff(ig, direction=1, bnd_cond='Neumann')
-
- # Define Total Variation as a regulariser
- regulariser = alpha * sum(norm(vstack([DX.matrix() * vec(u), DY.matrix() * vec(u)]), 2, axis = 0))
- fidelity = pnorm( u - noisy_data.as_array(),1)
-
- # 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().as_array() - u.value )
-
- plt.figure(figsize=(15,15))
- plt.subplot(3,1,1)
- plt.imshow(pdhg.get_output().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().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]))
-
-
-
-
-
diff --git a/Wrappers/Python/demos/PDHG_Tikhonov_Denoising.py b/Wrappers/Python/demos/PDHG_Tikhonov_Denoising.py
deleted file mode 100644
index 041d4ee..0000000
--- a/Wrappers/Python/demos/PDHG_Tikhonov_Denoising.py
+++ /dev/null
@@ -1,176 +0,0 @@
-# -*- coding: utf-8 -*-
-# This work is part of the Core Imaging Library developed by
-# Visual Analytics and Imaging System Group of the Science Technology
-# Facilities Council, STFC
-
-# Copyright 2018-2019 Evangelos Papoutsellis and Edoardo Pasca
-
-# 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
-
-# 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.
-
-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
-from ccpi.optimisation.functions import ZeroFunction, L2NormSquared, BlockFunction
-
-from skimage.util import random_noise
-
-# Create phantom for TV Salt & Pepper denoising
-N = 100
-
-data = np.zeros((N,N))
-data[round(N/4):round(3*N/4),round(N/4):round(3*N/4)] = 0.5
-data[round(N/8):round(7*N/8),round(3*N/8):round(5*N/8)] = 1
-data = ImageData(data)
-ig = ImageGeometry(voxel_num_x = N, voxel_num_y = N)
-ag = ig
-
-# Create noisy data. Apply Salt & Pepper noise
-n1 = random_noise(data.as_array(), mode = 'gaussian', mean=0, var = 0.05, seed=10)
-noisy_data = ImageData(n1)
-
-# Regularisation Parameter
-alpha = 4
-
-method = '0'
-
-if method == '0':
-
- # Create operators
- op1 = Gradient(ig)
- op2 = Identity(ig, ag)
-
- # Create BlockOperator
- operator = BlockOperator(op1, op2, shape=(2,1) )
-
- # Create functions
-
- f1 = alpha * L2NormSquared()
- f2 = 0.5 * L2NormSquared(b = noisy_data)
- f = BlockFunction(f1, f2)
- g = ZeroFunction()
-
-else:
-
- # Without the "Block Framework"
- operator = Gradient(ig)
- f = alpha * L2NormSquared()
- g = 0.5 * L2NormSquared(b = noisy_data)
-
-
-# Compute operator Norm
-normK = operator.norm()
-
-# Primal & dual stepsizes
-sigma = 1
-tau = 1/(sigma*normK**2)
-opt = {'niter':2000, 'memopt': True}
-
-# Setup and run the PDHG algorithm
-pdhg = PDHG(f=f,g=g,operator=operator, tau=tau, sigma=sigma, memopt=True)
-pdhg.max_iteration = 2000
-pdhg.update_objective_interval = 50
-pdhg.run(2000)
-
-
-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().as_array())
-plt.title('Tikhonov 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().as_array()[int(N/2),:], label = 'Tikhonov 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:
-
- ##Construct problem
- u = Variable(ig.shape)
-
- DY = SparseFiniteDiff(ig, direction=0, bnd_cond='Neumann')
- DX = SparseFiniteDiff(ig, direction=1, bnd_cond='Neumann')
-
- # Define Total Variation as a regulariser
-
- regulariser = alpha * sum_squares(norm(vstack([DX.matrix() * vec(u), DY.matrix() * vec(u)]), 2, axis = 0))
- fidelity = 0.5 * sum_squares(u - noisy_data.as_array())
-
- # 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().as_array() - u.value )
-
- plt.figure(figsize=(15,15))
- plt.subplot(3,1,1)
- plt.imshow(pdhg.get_output().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().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]))
-
-
-
-
-
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