diff options
| -rw-r--r-- | Wrappers/Python/ccpi/plugins/regularisers.py | 7 | ||||
| -rw-r--r-- | Wrappers/Python/wip/demo_compare_RGLTK_TV_denoising.py | 163 |
2 files changed, 117 insertions, 53 deletions
diff --git a/Wrappers/Python/ccpi/plugins/regularisers.py b/Wrappers/Python/ccpi/plugins/regularisers.py index e9c88a4..46464a9 100644 --- a/Wrappers/Python/ccpi/plugins/regularisers.py +++ b/Wrappers/Python/ccpi/plugins/regularisers.py @@ -25,7 +25,6 @@ from ccpi.optimisation.ops import Operator import numpy as np - class _ROF_TV_(Operator): def __init__(self,lambdaReg,iterationsTV,tolerance,time_marchstep,device): # set parameters @@ -36,7 +35,7 @@ class _ROF_TV_(Operator): def __call__(self,x): # evaluate objective function of TV gradient EnergyValTV = TV_ENERGY(np.asarray(x.as_array(), dtype=np.float32), np.asarray(x.as_array(), dtype=np.float32), self.lambdaReg, 2) - return EnergyValTV + return 0.5*EnergyValTV[0] def prox(self,x,Lipshitz): pars = {'algorithm' : ROF_TV, \ 'input' : np.asarray(x.as_array(), dtype=np.float32),\ @@ -63,7 +62,7 @@ class _FGP_TV_(Operator): def __call__(self,x): # evaluate objective function of TV gradient EnergyValTV = TV_ENERGY(np.asarray(x.as_array(), dtype=np.float32), np.asarray(x.as_array(), dtype=np.float32), self.lambdaReg, 2) - return EnergyValTV + return 0.5*EnergyValTV[0] def prox(self,x,Lipshitz): pars = {'algorithm' : FGP_TV, \ 'input' : np.asarray(x.as_array(), dtype=np.float32),\ @@ -96,7 +95,7 @@ class _SB_TV_(Operator): def __call__(self,x): # evaluate objective function of TV gradient EnergyValTV = TV_ENERGY(np.asarray(x.as_array(), dtype=np.float32), np.asarray(x.as_array(), dtype=np.float32), self.lambdaReg, 2) - return EnergyValTV + return 0.5*EnergyValTV[0] def prox(self,x,Lipshitz): pars = {'algorithm' : SB_TV, \ 'input' : np.asarray(x.as_array(), dtype=np.float32),\ diff --git a/Wrappers/Python/wip/demo_compare_RGLTK_TV_denoising.py b/Wrappers/Python/wip/demo_compare_RGLTK_TV_denoising.py index 559679e..911cff4 100644 --- a/Wrappers/Python/wip/demo_compare_RGLTK_TV_denoising.py +++ b/Wrappers/Python/wip/demo_compare_RGLTK_TV_denoising.py @@ -1,12 +1,22 @@ +# 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 - from ccpi.optimisation.ops import LinearOperatorMatrix, Identity -from ccpi.plugins.regularisers import _ROF_TV_, _FGP_TV_ +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 @@ -16,11 +26,7 @@ use_cvxpy = True if use_cvxpy: from cvxpy import * -import numpy as np -import matplotlib.pyplot as plt - - -# 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 @@ -45,6 +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() @@ -52,9 +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) @@ -64,72 +70,118 @@ 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.imshow(xtv_denoise.value) -plt.title('CVX TV') -plt.show() -print(objectivetv_denoise.value) - - -#%% THen FBPD + # 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 f_denoise = Norm2sq(I,y,c=0.5) +#%% + +#%% 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') +plt.title('FBPD TV with objective equal to {:.2f}'.format(criterfbpdtv_denoise[-1])) 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=5000,tolerance=1e-5,time_marchstep=0.01,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()) -plt.title('ROF TV prox') +EnergytotalROF = f_denoise(xtv_rof) + g_rof(xtv_rof) +plt.title('ROF TV prox with objective equal to {:.2f}'.format(EnergytotalROF)) plt.show() -print(g_rof(xtv_rof)) +print(EnergytotalROF) #%% FISTA with FGP-TV regularisation -g_fgp = _FGP_TV_(lambdaReg = lam_tv,iterationsTV=5000,tolerance=1e-5,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()) -plt.title('FGP TV prox') +EnergytotalFGP = f_denoise(xtv_fgp) + g_fgp(xtv_fgp) +plt.title('FGP TV prox with objective equal to {:.2f}'.format(EnergytotalFGP)) plt.show() -print(g_fgp(xtv_fgp)) +print(EnergytotalFGP) + +#%% 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()) +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) dlims = (-0.2,0.2) -cols = 3 +cols = 4 rows = 2 current = 1 @@ -153,18 +205,31 @@ 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 - TV') -imgplot = plt.imshow(xtv_rof.as_array()-xtv_denoise.value,vmin=dlims[0],vmax=dlims[1]) +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('FGP - TV') -imgplot = plt.imshow(xtv_fgp.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') |