fix TGV tomo2D example

1 files changed, 200 insertions, 0 deletions

diff --git a/Wrappers/Python/wip/pdhg_TGV_tomography2D.py b/Wrappers/Python/wip/pdhg_TGV_tomography2D.py
new file mode 100644
index 0000000..ee3b089
--- /dev/null
+++ b/Wrappers/Python/wip/pdhg_TGV_tomography2D.py
@@ -0,0 +1,200 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Fri Feb 22 14:53:03 2019
+
+@author: evangelos
+"""
+
+from ccpi.framework import ImageData, ImageGeometry, AcquisitionGeometry
+
+import numpy as np 
+import numpy                          
+import matplotlib.pyplot as plt
+
+from ccpi.optimisation.algorithms import PDHG, PDHG_old
+
+from ccpi.optimisation.operators import BlockOperator, Identity, \
+                        Gradient, SymmetrizedGradient, ZeroOperator
+from ccpi.optimisation.functions import ZeroFunction, L2NormSquared, \
+                      MixedL21Norm, BlockFunction
+
+from skimage.util import random_noise
+
+from timeit import default_timer as timer
+from ccpi.astra.ops import AstraProjectorSimple
+
+#def dt(steps):
+#    return steps[-1] - steps[-2]
+
+# Create phantom for TGV Gaussian 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())
+
+plt.imshow(data.as_array())
+plt.show()
+
+ig = ImageGeometry(voxel_num_x = N, voxel_num_y = N)
+
+detectors = N
+angles = np.linspace(0,np.pi,N)
+
+ag = AcquisitionGeometry('parallel','2D',angles, detectors)
+Aop = AstraProjectorSimple(ig, ag, 'cpu')
+sin = Aop.direct(data)
+
+plt.imshow(sin.as_array())
+plt.title('Sinogram')
+plt.colorbar()
+plt.show()
+
+# Add Gaussian noise to the sinogram data
+np.random.seed(10)
+n1 = np.random.random(sin.shape)
+
+noisy_data = sin + ImageData(5*n1)
+
+plt.imshow(noisy_data.as_array())
+plt.title('Noisy Sinogram')
+plt.colorbar()
+plt.show()
+
+#%%
+
+alpha, beta = 20, 50
+
+
+# Create operators
+op11 = Gradient(ig)
+op12 = Identity(op11.range_geometry())
+
+op22 = SymmetrizedGradient(op11.domain_geometry())    
+op21 = ZeroOperator(ig, op22.range_geometry())
+    
+op31 = Aop
+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 = 0.5 * L2NormSquared(b = noisy_data)    
+f = BlockFunction(f1, f2, f3)         
+g = ZeroFunction()
+             
+## Compute operator Norm
+normK = operator.norm()
+#
+## Primal & dual stepsizes
+sigma = 1
+tau = 1/(sigma*normK**2)
+##
+opt = {'niter':5000}
+opt1 = {'niter':5000, 'memopt': True}
+#
+t1 = timer()
+res, time, primal, dual, pdgap = PDHG_old(f, g, operator, tau = tau, sigma = sigma, opt = opt) 
+t2 = timer()
+#
+plt.imshow(res[0].as_array())
+plt.show()
+
+
+#t3 = timer()
+#res1, time1, primal1, dual1, pdgap1 = PDHG_old(f, g, operator, tau = tau, sigma = sigma, opt = opt1) 
+#t4 = timer()
+#
+#plt.figure(figsize=(15,15))
+#plt.subplot(3,1,1)
+#plt.imshow(res[0].as_array())
+#plt.title('no memopt')
+#plt.colorbar()
+#plt.subplot(3,1,2)
+#plt.imshow(res1[0].as_array())
+#plt.title('memopt')
+#plt.colorbar()
+#plt.subplot(3,1,3)
+#plt.imshow((res1[0] - res[0]).abs().as_array())
+#plt.title('diff')
+#plt.colorbar()
+#plt.show()
+#
+#print("NoMemopt/Memopt is {}/{}".format(t2-t1, t4-t3))
+    
+
+#%% 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 = 0.5 * sum_squares(u - noisy_data.as_array())    
+#    solver = MOSEK
+#
+#    obj =  Minimize( regulariser +  fidelity)
+#    prob = Problem(obj)
+#    result = prob.solve(verbose = True, solver = solver)
+#    
+#    diff_cvx = numpy.abs( res[0].as_array() - u.value )   
+#    
+#    # Show result
+#    plt.figure(figsize=(15,15))
+#    plt.subplot(3,1,1)
+#    plt.imshow(res[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), res[0].as_array()[int(N/2),:], label = 'PDHG')
+#    plt.plot(np.linspace(0,N,N), u.value[int(N/2),:], label = 'CVX')
+#    plt.legend()   
+#    
+#    print('Primal Objective (CVX) {} '.format(obj.value))
+#    print('Primal Objective (PDHG) {} '.format(primal[-1])) 
+#    print('Min/Max of absolute difference {}/{}'.format(diff_cvx.min(), diff_cvx.max()))
+    
+    
+