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author | epapoutsellis <epapoutsellis@gmail.com> | 2019-06-12 15:17:26 +0100 |
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committer | epapoutsellis <epapoutsellis@gmail.com> | 2019-06-12 15:17:26 +0100 |
commit | 144c23b09281a4bdd767ea89db70d028cda05b40 (patch) | |
tree | 6a099209b98caffbfe7b22008a9cc779510cc60b /Wrappers | |
parent | 095e9923b3fbc7a4ead3159510f3c6dea8959198 (diff) | |
download | framework-144c23b09281a4bdd767ea89db70d028cda05b40.tar.gz framework-144c23b09281a4bdd767ea89db70d028cda05b40.tar.bz2 framework-144c23b09281a4bdd767ea89db70d028cda05b40.tar.xz framework-144c23b09281a4bdd767ea89db70d028cda05b40.zip |
delete old demo
Diffstat (limited to 'Wrappers')
-rw-r--r-- | Wrappers/Python/demos/PDHG_examples/TGV_Denoising/PDHG_TGV_Denoising_SaltPepper.py | 245 |
1 files changed, 0 insertions, 245 deletions
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 deleted file mode 100644 index 15c0a05..0000000 --- a/Wrappers/Python/demos/PDHG_examples/TGV_Denoising/PDHG_TGV_Denoising_SaltPepper.py +++ /dev/null @@ -1,245 +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 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])) - - - - - |