diff options
3 files changed, 211 insertions, 120 deletions
diff --git a/Wrappers/Python/demos/PDHG_examples/GatherAll/PDHG_TGV_Denoising.py b/Wrappers/Python/demos/PDHG_examples/GatherAll/PDHG_TGV_Denoising.py index e9bad7e..8453d20 100755 --- a/Wrappers/Python/demos/PDHG_examples/GatherAll/PDHG_TGV_Denoising.py +++ b/Wrappers/Python/demos/PDHG_examples/GatherAll/PDHG_TGV_Denoising.py @@ -206,4 +206,77 @@ plt.plot(np.linspace(0,ig.shape[1],ig.shape[1]), data.as_array()[int(ig.shape[0] plt.plot(np.linspace(0,ig.shape[1],ig.shape[1]), pdhg.get_output()[0].as_array()[int(ig.shape[0]/2),:], label = 'TGV reconstruction') plt.legend() plt.title('Middle Line Profiles') -plt.show()
\ No newline at end of file +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(ig.shape) + w2 = Variable(ig.shape) + + # 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 = [] + + # choose solver + if 'MOSEK' in installed_solvers(): + solver = MOSEK + else: + solver = SCS + + # fidelity + if noise == 's&p': + fidelity = pnorm( u - noisy_data.as_array(),1) + elif noise == 'poisson': + fidelity = sum(kl_div(noisy_data.as_array(), u)) + solver = SCS + elif noise == 'gaussian': + fidelity = 0.5 * sum_squares(noisy_data.as_array() - u) + + 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,ig.shape[1],ig.shape[1]), pdhg.get_output()[0].as_array()[int(ig.shape[0]/2),:], label = 'PDHG') + plt.plot(np.linspace(0,ig.shape[1],ig.shape[1]), u.value[int(ig.shape[0]/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]))
\ No newline at end of file diff --git a/Wrappers/Python/demos/PDHG_examples/GatherAll/PDHG_TV_Denoising.py b/Wrappers/Python/demos/PDHG_examples/GatherAll/PDHG_TV_Denoising.py index c472f36..74e7901 100755 --- a/Wrappers/Python/demos/PDHG_examples/GatherAll/PDHG_TV_Denoising.py +++ b/Wrappers/Python/demos/PDHG_examples/GatherAll/PDHG_TV_Denoising.py @@ -72,7 +72,7 @@ else: if len(sys.argv) > 1: which_noise = int(sys.argv[1]) else: - which_noise = 1 + which_noise = 0 print ("Applying {} noise") if len(sys.argv) > 2: @@ -83,7 +83,7 @@ print ("method ", method) loader = TestData(data_dir=os.path.join(sys.prefix, 'share','ccpi')) -data = loader.load(TestData.SHAPES) +data = loader.load(TestData.SHAPES, size=(50,50)) ig = data.geometry ag = ig @@ -211,61 +211,71 @@ else: 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])) +##%% 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 + + # fidelity + if noise == 's&p': + fidelity = pnorm( u - noisy_data.as_array(),1) + elif noise == 'poisson': + fidelity = sum(kl_div(noisy_data.as_array(), u)) + solver = SCS + elif noise == 'gaussian': + fidelity = 0.5 * sum_squares(noisy_data.as_array() - u) + + + 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,ig.shape[1],ig.shape[1]), pdhg.get_output().as_array()[int(ig.shape[0]/2),:], label = 'PDHG') + plt.plot(np.linspace(0,ig.shape[1],ig.shape[1]), u.value[int(ig.shape[0]/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_examples/GatherAll/PDHG_Tikhonov_Denoising.py b/Wrappers/Python/demos/PDHG_examples/GatherAll/PDHG_Tikhonov_Denoising.py index 8a9920c..e16c5a6 100644 --- a/Wrappers/Python/demos/PDHG_examples/GatherAll/PDHG_Tikhonov_Denoising.py +++ b/Wrappers/Python/demos/PDHG_examples/GatherAll/PDHG_Tikhonov_Denoising.py @@ -185,65 +185,73 @@ 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])) +##%% 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)) + + # choose solver + if 'MOSEK' in installed_solvers(): + solver = MOSEK + else: + solver = SCS + + # fidelity + if noise == 's&p': + fidelity = pnorm( u - noisy_data.as_array(),1) + elif noise == 'poisson': + fidelity = sum(kl_div(noisy_data.as_array(), u)) + solver = SCS + elif noise == 'gaussian': + fidelity = 0.5 * sum_squares(noisy_data.as_array() - u) + + 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,ig.shape[1],ig.shape[1]), pdhg.get_output().as_array()[int(ig.shape[0]/2),:], label = 'PDHG') + plt.plot(np.linspace(0,ig.shape[1],ig.shape[1]), u.value[int(ig.shape[0]/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])) # # # |