diff options
| -rw-r--r-- | Wrappers/Python/wip/demo_compare_RGLTK_TV_denoising.py | 133 |
1 files changed, 83 insertions, 50 deletions
diff --git a/Wrappers/Python/wip/demo_compare_RGLTK_TV_denoising.py b/Wrappers/Python/wip/demo_compare_RGLTK_TV_denoising.py index fd992de..911cff4 100644 --- a/Wrappers/Python/wip/demo_compare_RGLTK_TV_denoising.py +++ b/Wrappers/Python/wip/demo_compare_RGLTK_TV_denoising.py @@ -1,4 +1,10 @@ +# This demo illustrates how the CCPi Regularisation Toolkit can be used +# as TV denoising for use with the FISTA algorithm of the modular +# optimisation framework and compares with the FBPD TV implementation as well +# as CVXPY. + +# All own imports from ccpi.framework import ImageData, ImageGeometry, AcquisitionGeometry, DataContainer from ccpi.optimisation.algs import FISTA, FBPD, CGLS from ccpi.optimisation.funcs import Norm2sq, ZeroFun, Norm1, TV2D @@ -6,12 +12,15 @@ from ccpi.optimisation.ops import LinearOperatorMatrix, Identity from ccpi.plugins.regularisers import _ROF_TV_, _FGP_TV_, _SB_TV_ +# All external imports import numpy as np import matplotlib.pyplot as plt + #%% # Requires CVXPY, see http://www.cvxpy.org/ # CVXPY can be installed in anaconda using # conda install -c cvxgrp cvxpy libgcc + # Whether to use or omit CVXPY use_cvxpy = True if use_cvxpy: @@ -19,8 +28,6 @@ if use_cvxpy: #%% -# Now try 1-norm and TV denoising with FBPD, first 1-norm. - # Set up phantom size NxN by creating ImageGeometry, initialising the # ImageData object with this geometry and empty array and finally put some # data into its array, and display as image. @@ -44,6 +51,7 @@ y = I.direct(Phantom) np.random.seed(0) y.array = y.array + 0.1*np.random.randn(N, N) +# Display noisy image plt.imshow(y.array) plt.title('Noisy image') plt.show() @@ -51,9 +59,8 @@ plt.show() #%% TV parameter lam_tv = 1.0 -#%% Do CVX as high quality ground truth +#%% Do CVX as high quality ground truth for comparison. if use_cvxpy: - # Compare to CVXPY # Construct the problem. xtv_denoise = Variable(N,N) @@ -63,17 +70,15 @@ if use_cvxpy: # The optimal objective is returned by prob.solve(). resulttv_denoise = probtv_denoise.solve(verbose=False,solver=SCS,eps=1e-12) - # The optimal solution for x is stored in x.value and optimal objective value - # is in result as well as in objective.value - print("CVXPY least squares plus TV solution and objective value:") - # print(xtv_denoise.value) - # print(objectivetv_denoise.value) + # The optimal solution for x is stored in x.value and optimal objective + # value is in result as well as in objective.value -plt.figure() -plt.imshow(xtv_denoise.value) -plt.title('CVX TV with objective equal to {:.2f}'.format(objectivetv_denoise.value)) -plt.show() -print(objectivetv_denoise.value) + # Display + plt.figure() + plt.imshow(xtv_denoise.value) + plt.title('CVX TV with objective equal to {:.2f}'.format(objectivetv_denoise.value)) + plt.show() + print(objectivetv_denoise.value) #%% # Data fidelity term @@ -81,19 +86,22 @@ f_denoise = Norm2sq(I,y,c=0.5) #%% -#%% THen FBPD +#%% Then run FBPD algorithm for TV denoising + # Initial guess x_init_denoise = ImageData(np.zeros((N,N))) +# Set up TV function gtv = TV2D(lam_tv) -gtv(gtv.op.direct(x_init_denoise)) -opt_tv = {'tol': 1e-4, 'iter': 10000} +# Evalutate TV of noisy image. +gtv(gtv.op.direct(y)) +# Specify FBPD options and run FBPD. +opt_tv = {'tol': 1e-4, 'iter': 10000} x_fbpdtv_denoise, itfbpdtv_denoise, timingfbpdtv_denoise, criterfbpdtv_denoise = FBPD(x_init_denoise, None, f_denoise, gtv,opt=opt_tv) - -print("CVXPY least squares plus TV solution and objective value:") +print("FBPD least squares plus TV solution and objective value:") plt.figure() plt.imshow(x_fbpdtv_denoise.as_array()) plt.title('FBPD TV with objective equal to {:.2f}'.format(criterfbpdtv_denoise[-1])) @@ -101,16 +109,24 @@ plt.show() print(criterfbpdtv_denoise[-1]) -#%% -plt.loglog([0,opt_tv['iter']], [objectivetv_denoise.value,objectivetv_denoise.value], label='CVX TV') +# Also plot history of criterion vs. CVX +if use_cvxpy: + plt.loglog([0,opt_tv['iter']], [objectivetv_denoise.value,objectivetv_denoise.value], label='CVX TV') plt.loglog(criterfbpdtv_denoise, label='FBPD TV') +plt.legend() plt.show() #%% FISTA with ROF-TV regularisation -g_rof = _ROF_TV_(lambdaReg = lam_tv,iterationsTV=2000,tolerance=0,time_marchstep=0.0009,device='cpu') +g_rof = _ROF_TV_(lambdaReg = lam_tv, + iterationsTV=2000, + tolerance=0, + time_marchstep=0.0009, + device='cpu') +# Evaluating the proximal operator corresponds to denoising. xtv_rof = g_rof.prox(y,1.0) +# Display denoised image and final criterion value. print("CCPi-RGL TV ROF:") plt.figure() plt.imshow(xtv_rof.as_array()) @@ -120,10 +136,18 @@ plt.show() print(EnergytotalROF) #%% FISTA with FGP-TV regularisation -g_fgp = _FGP_TV_(lambdaReg = lam_tv,iterationsTV=5000,tolerance=0,methodTV=0,nonnegativity=0,printing=0,device='cpu') - +g_fgp = _FGP_TV_(lambdaReg = lam_tv, + iterationsTV=5000, + tolerance=0, + methodTV=0, + nonnegativity=0, + printing=0, + device='cpu') + +# Evaluating the proximal operator corresponds to denoising. xtv_fgp = g_fgp.prox(y,1.0) +# Display denoised image and final criterion value. print("CCPi-RGL TV FGP:") plt.figure() plt.imshow(xtv_fgp.as_array()) @@ -131,11 +155,19 @@ EnergytotalFGP = f_denoise(xtv_fgp) + g_fgp(xtv_fgp) plt.title('FGP TV prox with objective equal to {:.2f}'.format(EnergytotalFGP)) plt.show() print(EnergytotalFGP) -#%% Split-Bregman-TV regularisation -g_sb = _SB_TV_(lambdaReg = lam_tv,iterationsTV=1000,tolerance=0,methodTV=0,printing=0,device='cpu') +#%% Split-Bregman-TV regularisation +g_sb = _SB_TV_(lambdaReg = lam_tv, + iterationsTV=1000, + tolerance=0, + methodTV=0, + printing=0, + device='cpu') + +# Evaluating the proximal operator corresponds to denoising. xtv_sb = g_sb.prox(y,1.0) +# Display denoised image and final criterion value. print("CCPi-RGL TV SB:") plt.figure() plt.imshow(xtv_sb.as_array()) @@ -143,8 +175,8 @@ EnergytotalSB = f_denoise(xtv_sb) + g_fgp(xtv_sb) plt.title('SB TV prox with objective equal to {:.2f}'.format(EnergytotalSB)) plt.show() print(EnergytotalSB) -#%% +#%% # Compare all reconstruction clims = (-0.2,1.2) @@ -177,26 +209,27 @@ a.set_title('SB') imgplot = plt.imshow(xtv_sb.as_array(),vmin=clims[0],vmax=clims[1]) plt.axis('off') -current = current + 1 -a=fig.add_subplot(rows,cols,current) -a.set_title('FBPD - CVX') -imgplot = plt.imshow(x_fbpdtv_denoise.as_array()-xtv_denoise.value,vmin=dlims[0],vmax=dlims[1]) -plt.axis('off') - -current = current + 1 -a=fig.add_subplot(rows,cols,current) -a.set_title('ROF - CVX') -imgplot = plt.imshow(xtv_rof.as_array()-xtv_denoise.value,vmin=dlims[0],vmax=dlims[1]) -plt.axis('off') - -current = current + 1 -a=fig.add_subplot(rows,cols,current) -a.set_title('FGP - CVX') -imgplot = plt.imshow(xtv_fgp.as_array()-xtv_denoise.value,vmin=dlims[0],vmax=dlims[1]) -plt.axis('off') - -current = current + 1 -a=fig.add_subplot(rows,cols,current) -a.set_title('SB - CVX') -imgplot = plt.imshow(xtv_sb.as_array()-xtv_denoise.value,vmin=dlims[0],vmax=dlims[1]) -plt.axis('off') +if use_cvxpy: + current = current + 1 + a=fig.add_subplot(rows,cols,current) + a.set_title('FBPD - CVX') + imgplot = plt.imshow(x_fbpdtv_denoise.as_array()-xtv_denoise.value,vmin=dlims[0],vmax=dlims[1]) + plt.axis('off') + + current = current + 1 + a=fig.add_subplot(rows,cols,current) + a.set_title('ROF - CVX') + imgplot = plt.imshow(xtv_rof.as_array()-xtv_denoise.value,vmin=dlims[0],vmax=dlims[1]) + plt.axis('off') + + current = current + 1 + a=fig.add_subplot(rows,cols,current) + a.set_title('FGP - CVX') + imgplot = plt.imshow(xtv_fgp.as_array()-xtv_denoise.value,vmin=dlims[0],vmax=dlims[1]) + plt.axis('off') + + current = current + 1 + a=fig.add_subplot(rows,cols,current) + a.set_title('SB - CVX') + imgplot = plt.imshow(xtv_sb.as_array()-xtv_denoise.value,vmin=dlims[0],vmax=dlims[1]) + plt.axis('off') |