Tikhonov demos

2 files changed, 284 insertions, 0 deletions

diff --git a/Wrappers/Python/wip/Demos/PDHG_Tikhonov_Denoising.py b/Wrappers/Python/wip/Demos/PDHG_Tikhonov_Denoising.py
new file mode 100644
index 0000000..3f275e2
--- /dev/null
+++ b/Wrappers/Python/wip/Demos/PDHG_Tikhonov_Denoising.py
@@ -0,0 +1,176 @@
+# -*- 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 = '1'
+
+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]))
+
+
+
+
+
diff --git a/Wrappers/Python/wip/Demos/PDHG_Tikhonov_Tomo2D.py b/Wrappers/Python/wip/Demos/PDHG_Tikhonov_Tomo2D.py
new file mode 100644
index 0000000..5c03362
--- /dev/null
+++ b/Wrappers/Python/wip/Demos/PDHG_Tikhonov_Tomo2D.py
@@ -0,0 +1,108 @@
+# -*- 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, AcquisitionGeometry, AcquisitionData
+
+import numpy as np 
+import numpy                          
+import matplotlib.pyplot as plt
+
+from ccpi.optimisation.algorithms import PDHG
+
+from ccpi.optimisation.operators import BlockOperator, Gradient
+from ccpi.optimisation.functions import ZeroFunction, L2NormSquared, BlockFunction
+from skimage.util import random_noise
+from ccpi.astra.ops import AstraProjectorSimple
+
+# Create phantom for TV 2D tomography 
+N = 75
+x = np.zeros((N,N))
+x[round(N/4):round(3*N/4),round(N/4):round(3*N/4)] = 0.5
+x[round(N/8):round(7*N/8),round(3*N/8):round(5*N/8)] = 1
+
+data = ImageData(x)
+ig = ImageGeometry(voxel_num_x = N, voxel_num_y = N)
+
+detectors = N
+angles = np.linspace(0, np.pi, N, dtype=np.float32)
+
+ag = AcquisitionGeometry('parallel','2D',angles, detectors)
+Aop = AstraProjectorSimple(ig, ag, 'cpu')
+sin = Aop.direct(data)
+
+# Create noisy data. Apply Gaussian noise
+
+np.random.seed(10)
+noisy_data = sin + AcquisitionData(np.random.normal(0, 3, sin.shape))
+
+# Regularisation Parameter
+alpha = 500
+
+# Create operators
+op1 = Gradient(ig)
+op2 = Aop
+
+# 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()
+    
+# 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 = 5000
+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()
+
+