4th order diffusion added

5 files changed, 905 insertions, 516 deletions

diff --git a/Wrappers/Python/demos/demo_cpu_regularisers.py b/Wrappers/Python/demos/demo_cpu_regularisers.py
index 986e3e9..51e7fb5 100644
--- a/Wrappers/Python/demos/demo_cpu_regularisers.py
+++ b/Wrappers/Python/demos/demo_cpu_regularisers.py
@@ -12,7 +12,7 @@ import matplotlib.pyplot as plt
 import numpy as np
 import os
 import timeit
-from ccpi.filters.regularisers import ROF_TV, FGP_TV, SB_TV, FGP_dTV, TNV, NDF
+from ccpi.filters.regularisers import ROF_TV, FGP_TV, SB_TV, FGP_dTV, TNV, NDF, DIFF4th
 from qualitymetrics import rmse
 ###############################################################################
 def printParametersToString(pars):
@@ -221,9 +221,9 @@ imgplot = plt.imshow(u0,cmap="gray")
 # set parameters
 pars = {'algorithm' : NDF, \
         'input' : u0,\
-        'regularisation_parameter':0.06, \
-        'edge_parameter':0.04,\
-        'number_of_iterations' :1000 ,\
+        'regularisation_parameter':0.025, \
+        'edge_parameter':0.015,\
+        'number_of_iterations' :500 ,\
         'time_marching_parameter':0.025,\
         'penalty_type':1
         }
@@ -255,11 +255,56 @@ plt.title('{}'.format('CPU results'))
 
 
 print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-print ("_____________FGP-dTV (2D)__________________")
+print ("___Anisotropic Diffusion 4th Order (2D)____")
 print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
 
 ## plot 
 fig = plt.figure(5)
+plt.suptitle('Performance of DIFF4th regulariser using the CPU')
+a=fig.add_subplot(1,2,1)
+a.set_title('Noisy Image')
+imgplot = plt.imshow(u0,cmap="gray")
+
+# set parameters
+pars = {'algorithm' : DIFF4th, \
+        'input' : u0,\
+        'regularisation_parameter':3.5, \
+        'edge_parameter':0.02,\
+        'number_of_iterations' :500 ,\
+        'time_marching_parameter':0.005
+        }
+        
+print ("#############DIFF4th CPU################")
+start_time = timeit.default_timer()
+diff4_cpu = DIFF4th(pars['input'], 
+              pars['regularisation_parameter'],
+              pars['edge_parameter'], 
+              pars['number_of_iterations'],
+              pars['time_marching_parameter'],'cpu')
+             
+rms = rmse(Im, diff4_cpu)
+pars['rmse'] = rms
+
+txtstr = printParametersToString(pars)
+txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
+print (txtstr)
+a=fig.add_subplot(1,2,2)
+
+# these are matplotlib.patch.Patch properties
+props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
+# place a text box in upper left in axes coords
+a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
+         verticalalignment='top', bbox=props)
+imgplot = plt.imshow(diff4_cpu, cmap="gray")
+plt.title('{}'.format('CPU results'))
+
+
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+print ("_____________FGP-dTV (2D)__________________")
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+
+## plot 
+fig = plt.figure(6)
 plt.suptitle('Performance of FGP-dTV regulariser using the CPU')
 a=fig.add_subplot(1,2,1)
 a.set_title('Noisy Image')
@@ -311,7 +356,7 @@ print ("__________Total nuclear Variation__________")
 print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
 
 ## plot 
-fig = plt.figure(6)
+fig = plt.figure(7)
 plt.suptitle('Performance of TNV regulariser using the CPU')
 a=fig.add_subplot(1,2,1)
 a.set_title('Noisy Image')
@@ -355,257 +400,3 @@ a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
          verticalalignment='top', bbox=props)
 imgplot = plt.imshow(tnv_cpu[3,:,:], cmap="gray")
 plt.title('{}'.format('CPU results'))
-
-
-# Uncomment to test 3D regularisation performance 
-#%%
-"""
-slices = 20
-perc = 0.05
-
-noisyVol = np.zeros((slices,N,M),dtype='float32')
-noisyRef = np.zeros((slices,N,M),dtype='float32')
-idealVol = np.zeros((slices,N,M),dtype='float32')
-
-for i in range (slices):
-    noisyVol[i,:,:] = Im + np.random.normal(loc = 0 , scale = perc * Im , size = np.shape(Im))
-    noisyRef[i,:,:] = Im + np.random.normal(loc = 0 , scale = 0.01 * Im , size = np.shape(Im))
-    idealVol[i,:,:] = Im
-
-
-print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-print ("_______________ROF-TV (3D)_________________")
-print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-
-## plot 
-fig = plt.figure(7)
-plt.suptitle('Performance of ROF-TV regulariser using the CPU')
-a=fig.add_subplot(1,2,1)
-a.set_title('Noisy 15th slice of a volume')
-imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
-
-# set parameters
-pars = {'algorithm': ROF_TV, \
-        'input' : noisyVol,\
-        'regularisation_parameter':0.04,\
-        'number_of_iterations': 500,\
-        'time_marching_parameter': 0.0025        
-        }
-print ("#############ROF TV CPU####################")
-start_time = timeit.default_timer()
-rof_cpu3D = ROF_TV(pars['input'],
-             pars['regularisation_parameter'],
-             pars['number_of_iterations'],
-             pars['time_marching_parameter'],'cpu')
-rms = rmse(idealVol, rof_cpu3D)
-pars['rmse'] = rms
-
-txtstr = printParametersToString(pars)
-txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
-print (txtstr)
-a=fig.add_subplot(1,2,2)
-
-# these are matplotlib.patch.Patch properties
-props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
-# place a text box in upper left in axes coords
-a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
-         verticalalignment='top', bbox=props)
-imgplot = plt.imshow(rof_cpu3D[10,:,:], cmap="gray")
-plt.title('{}'.format('Recovered volume on the CPU using ROF-TV'))
-
-
-print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-print ("_______________FGP-TV (3D)__________________")
-print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-
-## plot 
-fig = plt.figure(8)
-plt.suptitle('Performance of FGP-TV regulariser using the CPU')
-a=fig.add_subplot(1,2,1)
-a.set_title('Noisy Image')
-imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
-
-# set parameters
-pars = {'algorithm' : FGP_TV, \
-        'input' : noisyVol,\
-        'regularisation_parameter':0.04, \
-        'number_of_iterations' :300 ,\
-        'tolerance_constant':0.00001,\
-        'methodTV': 0 ,\
-        'nonneg': 0 ,\
-        'printingOut': 0 
-        }
-        
-print ("#############FGP TV CPU####################")
-start_time = timeit.default_timer()
-fgp_cpu3D = FGP_TV(pars['input'], 
-              pars['regularisation_parameter'],
-              pars['number_of_iterations'],
-              pars['tolerance_constant'], 
-              pars['methodTV'],
-              pars['nonneg'],
-              pars['printingOut'],'cpu')  
-             
-             
-rms = rmse(idealVol, fgp_cpu3D)
-pars['rmse'] = rms
-
-txtstr = printParametersToString(pars)
-txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
-print (txtstr)
-a=fig.add_subplot(1,2,2)
-
-# these are matplotlib.patch.Patch properties
-props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
-# place a text box in upper left in axes coords
-a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
-         verticalalignment='top', bbox=props)
-imgplot = plt.imshow(fgp_cpu3D[10,:,:], cmap="gray")
-plt.title('{}'.format('Recovered volume on the CPU using FGP-TV'))
-
-print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-print ("_______________SB-TV (3D)_________________")
-print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-
-## plot 
-fig = plt.figure(9)
-plt.suptitle('Performance of SB-TV regulariser using the CPU')
-a=fig.add_subplot(1,2,1)
-a.set_title('Noisy Image')
-imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
-
-# set parameters
-pars = {'algorithm' : SB_TV, \
-        'input' : noisyVol,\
-        'regularisation_parameter':0.04, \
-        'number_of_iterations' :150 ,\
-        'tolerance_constant':0.00001,\
-        'methodTV': 0 ,\
-        'printingOut': 0 
-        }
-        
-print ("#############SB TV CPU####################")
-start_time = timeit.default_timer()
-sb_cpu3D = SB_TV(pars['input'], 
-              pars['regularisation_parameter'],
-              pars['number_of_iterations'],
-              pars['tolerance_constant'], 
-              pars['methodTV'],
-              pars['printingOut'],'cpu')
-             
-rms = rmse(idealVol, sb_cpu3D)
-pars['rmse'] = rms
-
-txtstr = printParametersToString(pars)
-txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
-print (txtstr)
-a=fig.add_subplot(1,2,2)
-
-# these are matplotlib.patch.Patch properties
-props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
-# place a text box in upper left in axes coords
-a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
-         verticalalignment='top', bbox=props)
-imgplot = plt.imshow(sb_cpu3D[10,:,:], cmap="gray")
-plt.title('{}'.format('Recovered volume on the CPU using SB-TV'))
-
-print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-print ("________________NDF (3D)___________________")
-print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-
-## plot 
-fig = plt.figure(10)
-plt.suptitle('Performance of NDF regulariser using the CPU')
-a=fig.add_subplot(1,2,1)
-a.set_title('Noisy volume')
-imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
-
-# set parameters
-pars = {'algorithm' : NDF, \
-        'input' : noisyVol,\
-        'regularisation_parameter':0.06, \
-        'edge_parameter':0.04,\
-        'number_of_iterations' :1000 ,\
-        'time_marching_parameter':0.025,\
-        'penalty_type':  1
-        }
-        
-print ("#############NDF CPU################")
-start_time = timeit.default_timer()
-ndf_cpu3D = NDF(pars['input'], 
-              pars['regularisation_parameter'],
-              pars['edge_parameter'], 
-              pars['number_of_iterations'],
-              pars['time_marching_parameter'], 
-              pars['penalty_type'])  
-             
-rms = rmse(idealVol, ndf_cpu3D)
-pars['rmse'] = rms
-
-txtstr = printParametersToString(pars)
-txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
-print (txtstr)
-a=fig.add_subplot(1,2,2)
-
-# these are matplotlib.patch.Patch properties
-props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
-# place a text box in upper left in axes coords
-a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
-         verticalalignment='top', bbox=props)
-imgplot = plt.imshow(ndf_cpu3D[10,:,:], cmap="gray")
-plt.title('{}'.format('Recovered volume on the CPU using NDF iterations'))
-
-print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-print ("_______________FGP-dTV (3D)__________________")
-print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-
-## plot 
-fig = plt.figure(11)
-plt.suptitle('Performance of FGP-dTV regulariser using the CPU')
-a=fig.add_subplot(1,2,1)
-a.set_title('Noisy Image')
-imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
-
-# set parameters
-pars = {'algorithm' : FGP_dTV,\
-        'input' : noisyVol,\
-        'refdata' : noisyRef,\
-        'regularisation_parameter':0.04, \
-        'number_of_iterations' :300 ,\
-        'tolerance_constant':0.00001,\
-        'eta_const':0.2,\
-        'methodTV': 0 ,\
-        'nonneg': 0 ,\
-        'printingOut': 0 
-        }
-        
-print ("#############FGP dTV CPU####################")
-start_time = timeit.default_timer()
-fgp_dTV_cpu3D = FGP_dTV(pars['input'],
-              pars['refdata'], 
-              pars['regularisation_parameter'],
-              pars['number_of_iterations'],
-              pars['tolerance_constant'], 
-              pars['eta_const'],
-              pars['methodTV'],
-              pars['nonneg'],
-              pars['printingOut'],'cpu')
-             
-             
-rms = rmse(idealVol, fgp_dTV_cpu3D)
-pars['rmse'] = rms
-
-txtstr = printParametersToString(pars)
-txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
-print (txtstr)
-a=fig.add_subplot(1,2,2)
-
-# these are matplotlib.patch.Patch properties
-props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
-# place a text box in upper left in axes coords
-a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
-         verticalalignment='top', bbox=props)
-imgplot = plt.imshow(fgp_dTV_cpu3D[10,:,:], cmap="gray")
-plt.title('{}'.format('Recovered volume on the CPU using FGP-dTV'))
-"""
-#%%
diff --git a/Wrappers/Python/demos/demo_cpu_regularisers3D.py b/Wrappers/Python/demos/demo_cpu_regularisers3D.py
new file mode 100644
index 0000000..0f47ea9
--- /dev/null
+++ b/Wrappers/Python/demos/demo_cpu_regularisers3D.py
@@ -0,0 +1,366 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Thu Feb 22 11:39:43 2018
+
+Demonstration of 3D CPU regularisers 
+
+@authors: Daniil Kazantsev, Edoardo Pasca
+"""
+
+import matplotlib.pyplot as plt
+import numpy as np
+import os
+import timeit
+from ccpi.filters.regularisers import ROF_TV, FGP_TV, SB_TV, FGP_dTV, TNV, NDF, DIFF4th
+from qualitymetrics import rmse
+###############################################################################
+def printParametersToString(pars):
+        txt = r''
+        for key, value in pars.items():
+            if key== 'algorithm' :
+                txt += "{0} = {1}".format(key, value.__name__)
+            elif key == 'input':
+                txt += "{0} = {1}".format(key, np.shape(value))
+            elif key == 'refdata':
+                txt += "{0} = {1}".format(key, np.shape(value))
+            else:
+                txt += "{0} = {1}".format(key, value)
+            txt += '\n'
+        return txt
+###############################################################################
+#%%
+filename = os.path.join(".." , ".." , ".." , "data" ,"lena_gray_512.tif")
+
+# read image
+Im = plt.imread(filename)
+Im = np.asarray(Im, dtype='float32')
+
+Im = Im/255
+perc = 0.05
+u0 = Im + np.random.normal(loc = 0 ,
+                                  scale = perc * Im , 
+                                  size = np.shape(Im))
+u_ref = Im + np.random.normal(loc = 0 ,
+                                  scale = 0.01 * Im , 
+                                  size = np.shape(Im))
+(N,M) = np.shape(u0)
+# map the u0 u0->u0>0
+# f = np.frompyfunc(lambda x: 0 if x < 0 else x, 1,1)
+u0 = u0.astype('float32')
+u_ref = u_ref.astype('float32')
+
+# change dims to check that modules work with non-squared images
+"""
+M = M-100
+u_ref2 = np.zeros([N,M],dtype='float32')
+u_ref2[:,0:M] = u_ref[:,0:M]
+u_ref = u_ref2
+del u_ref2
+
+u02 = np.zeros([N,M],dtype='float32')
+u02[:,0:M] = u0[:,0:M]
+u0 = u02
+del u02
+
+Im2 = np.zeros([N,M],dtype='float32')
+Im2[:,0:M] = Im[:,0:M]
+Im = Im2
+del Im2
+"""
+
+# Uncomment to test 3D regularisation performance 
+#%%
+slices = 20
+
+noisyVol = np.zeros((slices,N,M),dtype='float32')
+noisyRef = np.zeros((slices,N,M),dtype='float32')
+idealVol = np.zeros((slices,N,M),dtype='float32')
+
+for i in range (slices):
+    noisyVol[i,:,:] = Im + np.random.normal(loc = 0 , scale = perc * Im , size = np.shape(Im))
+    noisyRef[i,:,:] = Im + np.random.normal(loc = 0 , scale = 0.01 * Im , size = np.shape(Im))
+    idealVol[i,:,:] = Im
+
+
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+print ("_______________ROF-TV (3D)_________________")
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+
+## plot 
+fig = plt.figure(1)
+plt.suptitle('Performance of ROF-TV regulariser using the CPU')
+a=fig.add_subplot(1,2,1)
+a.set_title('Noisy 15th slice of a volume')
+imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
+
+# set parameters
+pars = {'algorithm': ROF_TV, \
+        'input' : noisyVol,\
+        'regularisation_parameter':0.04,\
+        'number_of_iterations': 500,\
+        'time_marching_parameter': 0.0025        
+        }
+print ("#############ROF TV CPU####################")
+start_time = timeit.default_timer()
+rof_cpu3D = ROF_TV(pars['input'],
+             pars['regularisation_parameter'],
+             pars['number_of_iterations'],
+             pars['time_marching_parameter'],'cpu')
+rms = rmse(idealVol, rof_cpu3D)
+pars['rmse'] = rms
+
+txtstr = printParametersToString(pars)
+txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
+print (txtstr)
+a=fig.add_subplot(1,2,2)
+
+# these are matplotlib.patch.Patch properties
+props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
+# place a text box in upper left in axes coords
+a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
+         verticalalignment='top', bbox=props)
+imgplot = plt.imshow(rof_cpu3D[10,:,:], cmap="gray")
+plt.title('{}'.format('Recovered volume on the CPU using ROF-TV'))
+
+
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+print ("_______________FGP-TV (3D)__________________")
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+
+## plot 
+fig = plt.figure(2)
+plt.suptitle('Performance of FGP-TV regulariser using the CPU')
+a=fig.add_subplot(1,2,1)
+a.set_title('Noisy Image')
+imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
+
+# set parameters
+pars = {'algorithm' : FGP_TV, \
+        'input' : noisyVol,\
+        'regularisation_parameter':0.04, \
+        'number_of_iterations' :300 ,\
+        'tolerance_constant':0.00001,\
+        'methodTV': 0 ,\
+        'nonneg': 0 ,\
+        'printingOut': 0 
+        }
+        
+print ("#############FGP TV CPU####################")
+start_time = timeit.default_timer()
+fgp_cpu3D = FGP_TV(pars['input'], 
+              pars['regularisation_parameter'],
+              pars['number_of_iterations'],
+              pars['tolerance_constant'], 
+              pars['methodTV'],
+              pars['nonneg'],
+              pars['printingOut'],'cpu')  
+             
+             
+rms = rmse(idealVol, fgp_cpu3D)
+pars['rmse'] = rms
+
+txtstr = printParametersToString(pars)
+txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
+print (txtstr)
+a=fig.add_subplot(1,2,2)
+
+# these are matplotlib.patch.Patch properties
+props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
+# place a text box in upper left in axes coords
+a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
+         verticalalignment='top', bbox=props)
+imgplot = plt.imshow(fgp_cpu3D[10,:,:], cmap="gray")
+plt.title('{}'.format('Recovered volume on the CPU using FGP-TV'))
+
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+print ("_______________SB-TV (3D)_________________")
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+
+## plot 
+fig = plt.figure(3)
+plt.suptitle('Performance of SB-TV regulariser using the CPU')
+a=fig.add_subplot(1,2,1)
+a.set_title('Noisy Image')
+imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
+
+# set parameters
+pars = {'algorithm' : SB_TV, \
+        'input' : noisyVol,\
+        'regularisation_parameter':0.04, \
+        'number_of_iterations' :150 ,\
+        'tolerance_constant':0.00001,\
+        'methodTV': 0 ,\
+        'printingOut': 0 
+        }
+        
+print ("#############SB TV CPU####################")
+start_time = timeit.default_timer()
+sb_cpu3D = SB_TV(pars['input'], 
+              pars['regularisation_parameter'],
+              pars['number_of_iterations'],
+              pars['tolerance_constant'], 
+              pars['methodTV'],
+              pars['printingOut'],'cpu')
+             
+rms = rmse(idealVol, sb_cpu3D)
+pars['rmse'] = rms
+
+txtstr = printParametersToString(pars)
+txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
+print (txtstr)
+a=fig.add_subplot(1,2,2)
+
+# these are matplotlib.patch.Patch properties
+props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
+# place a text box in upper left in axes coords
+a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
+         verticalalignment='top', bbox=props)
+imgplot = plt.imshow(sb_cpu3D[10,:,:], cmap="gray")
+plt.title('{}'.format('Recovered volume on the CPU using SB-TV'))
+
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+print ("________________NDF (3D)___________________")
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+
+## plot 
+fig = plt.figure(4)
+plt.suptitle('Performance of NDF regulariser using the CPU')
+a=fig.add_subplot(1,2,1)
+a.set_title('Noisy volume')
+imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
+
+# set parameters
+pars = {'algorithm' : NDF, \
+        'input' : noisyVol,\
+        'regularisation_parameter':0.025, \
+        'edge_parameter':0.015,\
+        'number_of_iterations' :500 ,\
+        'time_marching_parameter':0.025,\
+        'penalty_type':  1
+        }
+        
+print ("#############NDF CPU################")
+start_time = timeit.default_timer()
+ndf_cpu3D = NDF(pars['input'], 
+              pars['regularisation_parameter'],
+              pars['edge_parameter'], 
+              pars['number_of_iterations'],
+              pars['time_marching_parameter'], 
+              pars['penalty_type'])  
+             
+rms = rmse(idealVol, ndf_cpu3D)
+pars['rmse'] = rms
+
+txtstr = printParametersToString(pars)
+txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
+print (txtstr)
+a=fig.add_subplot(1,2,2)
+
+# these are matplotlib.patch.Patch properties
+props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
+# place a text box in upper left in axes coords
+a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
+         verticalalignment='top', bbox=props)
+imgplot = plt.imshow(ndf_cpu3D[10,:,:], cmap="gray")
+plt.title('{}'.format('Recovered volume on the CPU using NDF iterations'))
+
+
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+print ("___Anisotropic Diffusion 4th Order (2D)____")
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+
+## plot 
+fig = plt.figure(5)
+plt.suptitle('Performance of Diff4th regulariser using the CPU')
+a=fig.add_subplot(1,2,1)
+a.set_title('Noisy volume')
+imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
+
+# set parameters
+pars = {'algorithm' : DIFF4th, \
+        'input' : noisyVol,\
+        'regularisation_parameter':3.5, \
+        'edge_parameter':0.02,\
+        'number_of_iterations' :300 ,\
+        'time_marching_parameter':0.005
+        }
+        
+print ("#############DIFF4th CPU################")
+start_time = timeit.default_timer()
+diff4th_cpu3D = DIFF4th(pars['input'], 
+              pars['regularisation_parameter'],
+              pars['edge_parameter'], 
+              pars['number_of_iterations'],
+              pars['time_marching_parameter'])  
+             
+rms = rmse(idealVol, diff4th_cpu3D)
+pars['rmse'] = rms
+
+txtstr = printParametersToString(pars)
+txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
+print (txtstr)
+a=fig.add_subplot(1,2,2)
+
+# these are matplotlib.patch.Patch properties
+props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
+# place a text box in upper left in axes coords
+a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
+         verticalalignment='top', bbox=props)
+imgplot = plt.imshow(diff4th_cpu3D[10,:,:], cmap="gray")
+plt.title('{}'.format('Recovered volume on the CPU using DIFF4th iterations'))
+
+
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+print ("_______________FGP-dTV (3D)__________________")
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+
+## plot 
+fig = plt.figure(6)
+plt.suptitle('Performance of FGP-dTV regulariser using the CPU')
+a=fig.add_subplot(1,2,1)
+a.set_title('Noisy Image')
+imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
+
+# set parameters
+pars = {'algorithm' : FGP_dTV,\
+        'input' : noisyVol,\
+        'refdata' : noisyRef,\
+        'regularisation_parameter':0.04, \
+        'number_of_iterations' :300 ,\
+        'tolerance_constant':0.00001,\
+        'eta_const':0.2,\
+        'methodTV': 0 ,\
+        'nonneg': 0 ,\
+        'printingOut': 0 
+        }
+        
+print ("#############FGP dTV CPU####################")
+start_time = timeit.default_timer()
+fgp_dTV_cpu3D = FGP_dTV(pars['input'],
+              pars['refdata'], 
+              pars['regularisation_parameter'],
+              pars['number_of_iterations'],
+              pars['tolerance_constant'], 
+              pars['eta_const'],
+              pars['methodTV'],
+              pars['nonneg'],
+              pars['printingOut'],'cpu')
+             
+             
+rms = rmse(idealVol, fgp_dTV_cpu3D)
+pars['rmse'] = rms
+
+txtstr = printParametersToString(pars)
+txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
+print (txtstr)
+a=fig.add_subplot(1,2,2)
+
+# these are matplotlib.patch.Patch properties
+props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
+# place a text box in upper left in axes coords
+a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
+         verticalalignment='top', bbox=props)
+imgplot = plt.imshow(fgp_dTV_cpu3D[10,:,:], cmap="gray")
+plt.title('{}'.format('Recovered volume on the CPU using FGP-dTV'))
+#%%
diff --git a/Wrappers/Python/demos/demo_cpu_vs_gpu_regularisers.py b/Wrappers/Python/demos/demo_cpu_vs_gpu_regularisers.py
index 05db23e..2910c65 100644
--- a/Wrappers/Python/demos/demo_cpu_vs_gpu_regularisers.py
+++ b/Wrappers/Python/demos/demo_cpu_vs_gpu_regularisers.py
@@ -12,7 +12,7 @@ import matplotlib.pyplot as plt
 import numpy as np
 import os
 import timeit
-from ccpi.filters.regularisers import ROF_TV, FGP_TV, SB_TV, FGP_dTV, NDF
+from ccpi.filters.regularisers import ROF_TV, FGP_TV, SB_TV, FGP_dTV, NDF, DIFF4th
 from qualitymetrics import rmse
 ###############################################################################
 def printParametersToString(pars):
@@ -207,7 +207,7 @@ plt.title('{}'.format('GPU results'))
 
 print ("--------Compare the results--------")
 tolerance = 1e-05
-diff_im = np.zeros(np.shape(rof_cpu))
+diff_im = np.zeros(np.shape(fgp_cpu))
 diff_im = abs(fgp_cpu - fgp_gpu)
 diff_im[diff_im > tolerance] = 1
 a=fig.add_subplot(1,4,4)
@@ -293,7 +293,7 @@ plt.title('{}'.format('GPU results'))
 
 print ("--------Compare the results--------")
 tolerance = 1e-05
-diff_im = np.zeros(np.shape(rof_cpu))
+diff_im = np.zeros(np.shape(sb_cpu))
 diff_im = abs(sb_cpu - sb_gpu)
 diff_im[diff_im > tolerance] = 1
 a=fig.add_subplot(1,4,4)
@@ -379,7 +379,7 @@ plt.title('{}'.format('GPU results'))
 
 print ("--------Compare the results--------")
 tolerance = 1e-05
-diff_im = np.zeros(np.shape(rof_cpu))
+diff_im = np.zeros(np.shape(ndf_cpu))
 diff_im = abs(ndf_cpu - ndf_gpu)
 diff_im[diff_im > tolerance] = 1
 a=fig.add_subplot(1,4,4)
@@ -391,13 +391,93 @@ else:
     print ("Arrays match")
 
 
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+print ("___Anisotropic Diffusion 4th Order (2D)____")
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+
+## plot 
+fig = plt.figure(5)
+plt.suptitle('Comparison of Diff4th regulariser using CPU and GPU implementations')
+a=fig.add_subplot(1,4,1)
+a.set_title('Noisy Image')
+imgplot = plt.imshow(u0,cmap="gray")
+
+# set parameters
+pars = {'algorithm' : DIFF4th, \
+        'input' : u0,\
+        'regularisation_parameter':3.5, \
+        'edge_parameter':0.02,\
+        'number_of_iterations' :500 ,\
+        'time_marching_parameter':0.005
+        }
+
+print ("#############Diff4th CPU####################")
+start_time = timeit.default_timer()
+diff4th_cpu = Diff4th(pars['input'], 
+              pars['regularisation_parameter'],
+              pars['edge_parameter'], 
+              pars['number_of_iterations'],
+              pars['time_marching_parameter'],'cpu')
+             
+rms = rmse(Im, diff4th_cpu)
+pars['rmse'] = rms
+
+txtstr = printParametersToString(pars)
+txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
+print (txtstr)
+a=fig.add_subplot(1,4,2)
+
+# these are matplotlib.patch.Patch properties
+props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
+# place a text box in upper left in axes coords
+a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
+         verticalalignment='top', bbox=props)
+imgplot = plt.imshow(diff4th_cpu, cmap="gray")
+plt.title('{}'.format('CPU results'))
+
+print ("##############Diff4th GPU##################")
+start_time = timeit.default_timer()
+diff4th_gpu = Diff4th(pars['input'], 
+              pars['regularisation_parameter'],
+              pars['edge_parameter'], 
+              pars['number_of_iterations'],
+              pars['time_marching_parameter'], 'gpu')
+             
+rms = rmse(Im, diff4th_gpu)
+pars['rmse'] = rms
+pars['algorithm'] = Diff4th
+txtstr = printParametersToString(pars)
+txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
+print (txtstr)
+a=fig.add_subplot(1,4,3)
+
+# these are matplotlib.patch.Patch properties
+props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
+# place a text box in upper left in axes coords
+a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
+         verticalalignment='top', bbox=props)
+imgplot = plt.imshow(diff4th_gpu, cmap="gray")
+plt.title('{}'.format('GPU results'))
+
+print ("--------Compare the results--------")
+tolerance = 1e-05
+diff_im = np.zeros(np.shape(diff4th_cpu))
+diff_im = abs(diff4th_cpu - diff4th_gpu)
+diff_im[diff_im > tolerance] = 1
+a=fig.add_subplot(1,4,4)
+imgplot = plt.imshow(diff_im, vmin=0, vmax=1, cmap="gray")
+plt.title('{}'.format('Pixels larger threshold difference'))
+if (diff_im.sum() > 1):
+    print ("Arrays do not match!")
+else:
+    print ("Arrays match")
 
 print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
 print ("____________FGP-dTV bench___________________")
 print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
 
 ## plot 
-fig = plt.figure(5)
+fig = plt.figure(6)
 plt.suptitle('Comparison of FGP-dTV regulariser using CPU and GPU implementations')
 a=fig.add_subplot(1,4,1)
 a.set_title('Noisy Image')
@@ -475,7 +555,7 @@ plt.title('{}'.format('GPU results'))
 
 print ("--------Compare the results--------")
 tolerance = 1e-05
-diff_im = np.zeros(np.shape(rof_cpu))
+diff_im = np.zeros(np.shape(fgp_dtv_cpu))
 diff_im = abs(fgp_dtv_cpu - fgp_dtv_gpu)
 diff_im[diff_im > tolerance] = 1
 a=fig.add_subplot(1,4,4)
diff --git a/Wrappers/Python/demos/demo_gpu_regularisers.py b/Wrappers/Python/demos/demo_gpu_regularisers.py
index f3ed50c..8432696 100644
--- a/Wrappers/Python/demos/demo_gpu_regularisers.py
+++ b/Wrappers/Python/demos/demo_gpu_regularisers.py
@@ -12,7 +12,7 @@ import matplotlib.pyplot as plt
 import numpy as np
 import os
 import timeit
-from ccpi.filters.regularisers import ROF_TV, FGP_TV, SB_TV, FGP_dTV, NDF
+from ccpi.filters.regularisers import ROF_TV, FGP_TV, SB_TV, FGP_dTV, NDF, DIFF4th
 from qualitymetrics import rmse
 ###############################################################################
 def printParametersToString(pars):
@@ -219,9 +219,9 @@ imgplot = plt.imshow(u0,cmap="gray")
 # set parameters
 pars = {'algorithm' : NDF, \
         'input' : u0,\
-        'regularisation_parameter':0.06, \
-        'edge_parameter':0.04,\
-        'number_of_iterations' :1000 ,\
+        'regularisation_parameter':0.025, \
+        'edge_parameter':0.015,\
+        'number_of_iterations' :500 ,\
         'time_marching_parameter':0.025,\
         'penalty_type':  1
         }
@@ -253,246 +253,34 @@ plt.title('{}'.format('GPU results'))
 
 
 print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-print ("____________FGP-dTV bench___________________")
+print ("___Anisotropic Diffusion 4th Order (2D)____")
 print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
 
 ## plot 
 fig = plt.figure(5)
-plt.suptitle('Performance of the FGP-dTV regulariser using the GPU')
+plt.suptitle('Performance of DIFF4th regulariser using the GPU')
 a=fig.add_subplot(1,2,1)
 a.set_title('Noisy Image')
 imgplot = plt.imshow(u0,cmap="gray")
 
 # set parameters
-pars = {'algorithm' : FGP_dTV, \
+pars = {'algorithm' : DIFF4th, \
         'input' : u0,\
-        'refdata' : u_ref,\
-        'regularisation_parameter':0.04, \
-        'number_of_iterations' :2000 ,\
-        'tolerance_constant':1e-06,\
-        'eta_const':0.2,\
-        'methodTV': 0 ,\
-        'nonneg': 0 ,\
-        'printingOut': 0 
-        }
-
-print ("##############FGP dTV GPU##################")
-start_time = timeit.default_timer()
-fgp_dtv_gpu = FGP_dTV(pars['input'], 
-              pars['refdata'], 
-              pars['regularisation_parameter'],
-              pars['number_of_iterations'],
-              pars['tolerance_constant'], 
-              pars['eta_const'], 
-              pars['methodTV'],
-              pars['nonneg'],
-              pars['printingOut'],'gpu')
-                                   
-rms = rmse(Im, fgp_dtv_gpu)
-pars['rmse'] = rms
-pars['algorithm'] = FGP_dTV
-txtstr = printParametersToString(pars)
-txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
-print (txtstr)
-a=fig.add_subplot(1,2,2)
-
-# these are matplotlib.patch.Patch properties
-props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
-# place a text box in upper left in axes coords
-a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
-         verticalalignment='top', bbox=props)
-imgplot = plt.imshow(fgp_dtv_gpu, cmap="gray")
-plt.title('{}'.format('GPU results'))
-
-
-# Uncomment to test 3D regularisation performance 
-#%%
-"""
-N = 512
-slices = 20
-
-filename = os.path.join(".." , ".." , ".." , "data" ,"lena_gray_512.tif")
-Im = plt.imread(filename)
-Im = np.asarray(Im, dtype='float32')
-
-Im = Im/255
-perc = 0.05
-
-noisyVol = np.zeros((slices,N,N),dtype='float32')
-noisyRef = np.zeros((slices,N,N),dtype='float32')
-idealVol = np.zeros((slices,N,N),dtype='float32')
-
-for i in range (slices):
-    noisyVol[i,:,:] = Im + np.random.normal(loc = 0 , scale = perc * Im , size = np.shape(Im))
-    noisyRef[i,:,:] = Im + np.random.normal(loc = 0 , scale = 0.01 * Im , size = np.shape(Im))
-    idealVol[i,:,:] = Im
-
-print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-print ("_______________ROF-TV (3D)_________________")
-print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-
-## plot 
-fig = plt.figure(6)
-plt.suptitle('Performance of ROF-TV regulariser using the GPU')
-a=fig.add_subplot(1,2,1)
-a.set_title('Noisy 15th slice of a volume')
-imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
-
-# set parameters
-pars = {'algorithm': ROF_TV, \
-        'input' : noisyVol,\
-        'regularisation_parameter':0.04,\
-        'number_of_iterations': 500,\
-        'time_marching_parameter': 0.0025        
+        'regularisation_parameter':3.5, \
+        'edge_parameter':0.02,\
+        'number_of_iterations' :500 ,\
+        'time_marching_parameter':0.005
         }
-print ("#############ROF TV GPU####################")
+        
+print ("#############DIFF4th CPU################")
 start_time = timeit.default_timer()
-rof_gpu3D = ROF_TV(pars['input'],
-             pars['regularisation_parameter'],
-             pars['number_of_iterations'],
-             pars['time_marching_parameter'],'gpu')
-rms = rmse(idealVol, rof_gpu3D)
-pars['rmse'] = rms
-
-txtstr = printParametersToString(pars)
-txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
-print (txtstr)
-a=fig.add_subplot(1,2,2)
-
-# these are matplotlib.patch.Patch properties
-props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
-# place a text box in upper left in axes coords
-a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
-         verticalalignment='top', bbox=props)
-imgplot = plt.imshow(rof_gpu3D[10,:,:], cmap="gray")
-plt.title('{}'.format('Recovered volume on the GPU using ROF-TV'))
-
-print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-print ("_______________FGP-TV (3D)__________________")
-print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-
-## plot 
-fig = plt.figure(7)
-plt.suptitle('Performance of FGP-TV regulariser using the GPU')
-a=fig.add_subplot(1,2,1)
-a.set_title('Noisy Image')
-imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
-
-# set parameters
-pars = {'algorithm' : FGP_TV, \
-        'input' : noisyVol,\
-        'regularisation_parameter':0.04, \
-        'number_of_iterations' :300 ,\
-        'tolerance_constant':0.00001,\
-        'methodTV': 0 ,\
-        'nonneg': 0 ,\
-        'printingOut': 0 
-        }
-
-print ("#############FGP TV GPU####################")
-start_time = timeit.default_timer()
-fgp_gpu3D = FGP_TV(pars['input'], 
-              pars['regularisation_parameter'],
-              pars['number_of_iterations'],
-              pars['tolerance_constant'], 
-              pars['methodTV'],
-              pars['nonneg'],
-              pars['printingOut'],'gpu')
-
-rms = rmse(idealVol, fgp_gpu3D)
-pars['rmse'] = rms
-
-txtstr = printParametersToString(pars)
-txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
-print (txtstr)
-a=fig.add_subplot(1,2,2)
-
-# these are matplotlib.patch.Patch properties
-props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
-# place a text box in upper left in axes coords
-a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
-         verticalalignment='top', bbox=props)
-imgplot = plt.imshow(fgp_gpu3D[10,:,:], cmap="gray")
-plt.title('{}'.format('Recovered volume on the GPU using FGP-TV'))
-
-print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-print ("_______________SB-TV (3D)__________________")
-print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-
-## plot 
-fig = plt.figure(8)
-plt.suptitle('Performance of SB-TV regulariser using the GPU')
-a=fig.add_subplot(1,2,1)
-a.set_title('Noisy Image')
-imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
-
-# set parameters
-pars = {'algorithm' : SB_TV, \
-        'input' : noisyVol,\
-        'regularisation_parameter':0.04, \
-        'number_of_iterations' :100 ,\
-        'tolerance_constant':1e-05,\
-        'methodTV': 0 ,\
-        'printingOut': 0 
-        }
-
-print ("#############SB TV GPU####################")
-start_time = timeit.default_timer()
-sb_gpu3D = SB_TV(pars['input'], 
-              pars['regularisation_parameter'],
-              pars['number_of_iterations'],
-              pars['tolerance_constant'], 
-              pars['methodTV'],
-              pars['printingOut'],'gpu')
-
-rms = rmse(idealVol, sb_gpu3D)
-pars['rmse'] = rms
-
-txtstr = printParametersToString(pars)
-txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
-print (txtstr)
-a=fig.add_subplot(1,2,2)
-
-# these are matplotlib.patch.Patch properties
-props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
-# place a text box in upper left in axes coords
-a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
-         verticalalignment='top', bbox=props)
-imgplot = plt.imshow(sb_gpu3D[10,:,:], cmap="gray")
-plt.title('{}'.format('Recovered volume on the GPU using SB-TV'))
-
-
-print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-print ("_______________NDF-TV (3D)_________________")
-print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-
-## plot 
-fig = plt.figure(9)
-plt.suptitle('Performance of NDF regulariser using the GPU')
-a=fig.add_subplot(1,2,1)
-a.set_title('Noisy Image')
-imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
-
-# set parameters
-pars = {'algorithm' : NDF, \
-        'input' : noisyVol,\
-        'regularisation_parameter':0.06, \
-        'edge_parameter':0.04,\
-        'number_of_iterations' :1000 ,\
-        'time_marching_parameter':0.025,\
-        'penalty_type':  1
-        }
-
-print ("#############NDF GPU####################")
-start_time = timeit.default_timer()
-ndf_gpu3D = NDF(pars['input'], 
+diff4_gpu = DIFF4th(pars['input'], 
               pars['regularisation_parameter'],
               pars['edge_parameter'], 
               pars['number_of_iterations'],
-              pars['time_marching_parameter'], 
-              pars['penalty_type'],'gpu')
-
-rms = rmse(idealVol, ndf_gpu3D)
+              pars['time_marching_parameter'],'gpu')
+             
+rms = rmse(Im, diff4_gpu)
 pars['rmse'] = rms
 
 txtstr = printParametersToString(pars)
@@ -505,49 +293,48 @@ props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
 # place a text box in upper left in axes coords
 a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
          verticalalignment='top', bbox=props)
-imgplot = plt.imshow(ndf_gpu3D[10,:,:], cmap="gray")
-plt.title('{}'.format('Recovered volume on the GPU using NDF'))
-
+imgplot = plt.imshow(diff4_gpu, cmap="gray")
+plt.title('{}'.format('GPU results'))
 
 print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
-print ("_______________FGP-dTV (3D)________________")
+print ("____________FGP-dTV bench___________________")
 print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
 
 ## plot 
-fig = plt.figure(10)
-plt.suptitle('Performance of FGP-dTV regulariser using the GPU')
+fig = plt.figure(6)
+plt.suptitle('Performance of the FGP-dTV regulariser using the GPU')
 a=fig.add_subplot(1,2,1)
 a.set_title('Noisy Image')
-imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
+imgplot = plt.imshow(u0,cmap="gray")
 
 # set parameters
 pars = {'algorithm' : FGP_dTV, \
-        'input' : noisyVol,\
-        'refdata' : noisyRef,\
+        'input' : u0,\
+        'refdata' : u_ref,\
         'regularisation_parameter':0.04, \
-        'number_of_iterations' :300 ,\
-        'tolerance_constant':0.00001,\
+        'number_of_iterations' :2000 ,\
+        'tolerance_constant':1e-06,\
         'eta_const':0.2,\
         'methodTV': 0 ,\
         'nonneg': 0 ,\
         'printingOut': 0 
         }
 
-print ("#############FGP TV GPU####################")
+print ("##############FGP dTV GPU##################")
 start_time = timeit.default_timer()
-fgp_dTV_gpu3D = FGP_dTV(pars['input'],
+fgp_dtv_gpu = FGP_dTV(pars['input'], 
               pars['refdata'], 
               pars['regularisation_parameter'],
               pars['number_of_iterations'],
               pars['tolerance_constant'], 
-              pars['eta_const'],
+              pars['eta_const'], 
               pars['methodTV'],
               pars['nonneg'],
               pars['printingOut'],'gpu')
-
-rms = rmse(idealVol, fgp_dTV_gpu3D)
+                                   
+rms = rmse(Im, fgp_dtv_gpu)
 pars['rmse'] = rms
-
+pars['algorithm'] = FGP_dTV
 txtstr = printParametersToString(pars)
 txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
 print (txtstr)
@@ -558,7 +345,5 @@ props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
 # place a text box in upper left in axes coords
 a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
          verticalalignment='top', bbox=props)
-imgplot = plt.imshow(fgp_dTV_gpu3D[10,:,:], cmap="gray")
-plt.title('{}'.format('Recovered volume on the GPU using FGP-dTV'))
-"""
-#%%
+imgplot = plt.imshow(fgp_dtv_gpu, cmap="gray")
+plt.title('{}'.format('GPU results'))
diff --git a/Wrappers/Python/demos/demo_gpu_regularisers3D.py b/Wrappers/Python/demos/demo_gpu_regularisers3D.py
new file mode 100644
index 0000000..022df95
--- /dev/null
+++ b/Wrappers/Python/demos/demo_gpu_regularisers3D.py
@@ -0,0 +1,367 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Thu Feb 22 11:39:43 2018
+
+Demonstration of GPU regularisers
+
+@authors: Daniil Kazantsev, Edoardo Pasca
+"""
+
+import matplotlib.pyplot as plt
+import numpy as np
+import os
+import timeit
+from ccpi.filters.regularisers import ROF_TV, FGP_TV, SB_TV, FGP_dTV, NDF, DIFF4th
+from qualitymetrics import rmse
+###############################################################################
+def printParametersToString(pars):
+        txt = r''
+        for key, value in pars.items():
+            if key== 'algorithm' :
+                txt += "{0} = {1}".format(key, value.__name__)
+            elif key == 'input':
+                txt += "{0} = {1}".format(key, np.shape(value))
+            elif key == 'refdata':
+                txt += "{0} = {1}".format(key, np.shape(value))
+            else:
+                txt += "{0} = {1}".format(key, value)
+            txt += '\n'
+        return txt
+###############################################################################
+#%%
+filename = os.path.join(".." , ".." , ".." , "data" ,"lena_gray_512.tif")
+
+# read image
+Im = plt.imread(filename)                     
+Im = np.asarray(Im, dtype='float32')
+
+Im = Im/255
+perc = 0.05
+u0 = Im + np.random.normal(loc = 0 ,
+                                  scale = perc * Im , 
+                                  size = np.shape(Im))
+u_ref = Im + np.random.normal(loc = 0 ,
+                                  scale = 0.01 * Im , 
+                                  size = np.shape(Im))
+(N,M) = np.shape(u0)
+# map the u0 u0->u0>0
+# f = np.frompyfunc(lambda x: 0 if x < 0 else x, 1,1)
+u0 = u0.astype('float32')
+u_ref = u_ref.astype('float32')
+"""
+M = M-100
+u_ref2 = np.zeros([N,M],dtype='float32')
+u_ref2[:,0:M] = u_ref[:,0:M]
+u_ref = u_ref2
+del u_ref2
+
+u02 = np.zeros([N,M],dtype='float32')
+u02[:,0:M] = u0[:,0:M]
+u0 = u02
+del u02
+
+Im2 = np.zeros([N,M],dtype='float32')
+Im2[:,0:M] = Im[:,0:M]
+Im = Im2
+del Im2
+"""
+
+#%%
+slices = 20
+
+filename = os.path.join(".." , ".." , ".." , "data" ,"lena_gray_512.tif")
+Im = plt.imread(filename)
+Im = np.asarray(Im, dtype='float32')
+
+Im = Im/255
+perc = 0.05
+
+noisyVol = np.zeros((slices,N,N),dtype='float32')
+noisyRef = np.zeros((slices,N,N),dtype='float32')
+idealVol = np.zeros((slices,N,N),dtype='float32')
+
+for i in range (slices):
+    noisyVol[i,:,:] = Im + np.random.normal(loc = 0 , scale = perc * Im , size = np.shape(Im))
+    noisyRef[i,:,:] = Im + np.random.normal(loc = 0 , scale = 0.01 * Im , size = np.shape(Im))
+    idealVol[i,:,:] = Im
+
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+print ("_______________ROF-TV (3D)_________________")
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+
+## plot 
+fig = plt.figure(1)
+plt.suptitle('Performance of ROF-TV regulariser using the GPU')
+a=fig.add_subplot(1,2,1)
+a.set_title('Noisy 15th slice of a volume')
+imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
+
+# set parameters
+pars = {'algorithm': ROF_TV, \
+        'input' : noisyVol,\
+        'regularisation_parameter':0.04,\
+        'number_of_iterations': 500,\
+        'time_marching_parameter': 0.0025        
+        }
+print ("#############ROF TV GPU####################")
+start_time = timeit.default_timer()
+rof_gpu3D = ROF_TV(pars['input'],
+             pars['regularisation_parameter'],
+             pars['number_of_iterations'],
+             pars['time_marching_parameter'],'gpu')
+rms = rmse(idealVol, rof_gpu3D)
+pars['rmse'] = rms
+
+txtstr = printParametersToString(pars)
+txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
+print (txtstr)
+a=fig.add_subplot(1,2,2)
+
+# these are matplotlib.patch.Patch properties
+props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
+# place a text box in upper left in axes coords
+a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
+         verticalalignment='top', bbox=props)
+imgplot = plt.imshow(rof_gpu3D[10,:,:], cmap="gray")
+plt.title('{}'.format('Recovered volume on the GPU using ROF-TV'))
+
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+print ("_______________FGP-TV (3D)__________________")
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+
+## plot 
+fig = plt.figure(2)
+plt.suptitle('Performance of FGP-TV regulariser using the GPU')
+a=fig.add_subplot(1,2,1)
+a.set_title('Noisy Image')
+imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
+
+# set parameters
+pars = {'algorithm' : FGP_TV, \
+        'input' : noisyVol,\
+        'regularisation_parameter':0.04, \
+        'number_of_iterations' :300 ,\
+        'tolerance_constant':0.00001,\
+        'methodTV': 0 ,\
+        'nonneg': 0 ,\
+        'printingOut': 0 
+        }
+
+print ("#############FGP TV GPU####################")
+start_time = timeit.default_timer()
+fgp_gpu3D = FGP_TV(pars['input'], 
+              pars['regularisation_parameter'],
+              pars['number_of_iterations'],
+              pars['tolerance_constant'], 
+              pars['methodTV'],
+              pars['nonneg'],
+              pars['printingOut'],'gpu')
+
+rms = rmse(idealVol, fgp_gpu3D)
+pars['rmse'] = rms
+
+txtstr = printParametersToString(pars)
+txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
+print (txtstr)
+a=fig.add_subplot(1,2,2)
+
+# these are matplotlib.patch.Patch properties
+props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
+# place a text box in upper left in axes coords
+a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
+         verticalalignment='top', bbox=props)
+imgplot = plt.imshow(fgp_gpu3D[10,:,:], cmap="gray")
+plt.title('{}'.format('Recovered volume on the GPU using FGP-TV'))
+
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+print ("_______________SB-TV (3D)__________________")
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+
+## plot 
+fig = plt.figure(3)
+plt.suptitle('Performance of SB-TV regulariser using the GPU')
+a=fig.add_subplot(1,2,1)
+a.set_title('Noisy Image')
+imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
+
+# set parameters
+pars = {'algorithm' : SB_TV, \
+        'input' : noisyVol,\
+        'regularisation_parameter':0.04, \
+        'number_of_iterations' :100 ,\
+        'tolerance_constant':1e-05,\
+        'methodTV': 0 ,\
+        'printingOut': 0 
+        }
+
+print ("#############SB TV GPU####################")
+start_time = timeit.default_timer()
+sb_gpu3D = SB_TV(pars['input'], 
+              pars['regularisation_parameter'],
+              pars['number_of_iterations'],
+              pars['tolerance_constant'], 
+              pars['methodTV'],
+              pars['printingOut'],'gpu')
+
+rms = rmse(idealVol, sb_gpu3D)
+pars['rmse'] = rms
+
+txtstr = printParametersToString(pars)
+txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
+print (txtstr)
+a=fig.add_subplot(1,2,2)
+
+# these are matplotlib.patch.Patch properties
+props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
+# place a text box in upper left in axes coords
+a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
+         verticalalignment='top', bbox=props)
+imgplot = plt.imshow(sb_gpu3D[10,:,:], cmap="gray")
+plt.title('{}'.format('Recovered volume on the GPU using SB-TV'))
+
+
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+print ("_______________NDF-TV (3D)_________________")
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+
+## plot 
+fig = plt.figure(4)
+plt.suptitle('Performance of NDF regulariser using the GPU')
+a=fig.add_subplot(1,2,1)
+a.set_title('Noisy Image')
+imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
+
+# set parameters
+pars = {'algorithm' : NDF, \
+        'input' : noisyVol,\
+        'regularisation_parameter':0.025, \
+        'edge_parameter':0.015,\
+        'number_of_iterations' :500 ,\
+        'time_marching_parameter':0.025,\
+        'penalty_type':  1
+        }
+
+print ("#############NDF GPU####################")
+start_time = timeit.default_timer()
+ndf_gpu3D = NDF(pars['input'], 
+              pars['regularisation_parameter'],
+              pars['edge_parameter'], 
+              pars['number_of_iterations'],
+              pars['time_marching_parameter'], 
+              pars['penalty_type'],'gpu')
+
+rms = rmse(idealVol, ndf_gpu3D)
+pars['rmse'] = rms
+
+txtstr = printParametersToString(pars)
+txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
+print (txtstr)
+a=fig.add_subplot(1,2,2)
+
+# these are matplotlib.patch.Patch properties
+props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
+# place a text box in upper left in axes coords
+a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
+         verticalalignment='top', bbox=props)
+imgplot = plt.imshow(ndf_gpu3D[10,:,:], cmap="gray")
+plt.title('{}'.format('Recovered volume on the GPU using NDF'))
+
+
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+print ("___Anisotropic Diffusion 4th Order (3D)____")
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+
+## plot 
+fig = plt.figure(5)
+plt.suptitle('Performance of DIFF4th regulariser using the GPU')
+a=fig.add_subplot(1,2,1)
+a.set_title('Noisy Image')
+imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
+
+# set parameters
+pars = {'algorithm' : DIFF4th, \
+        'input' : noisyVol,\
+        'regularisation_parameter':3.5, \
+        'edge_parameter':0.02,\
+        'number_of_iterations' :300 ,\
+        'time_marching_parameter':0.005
+        }
+        
+print ("#############DIFF4th CPU################")
+start_time = timeit.default_timer()
+diff4_gpu3D = DIFF4th(pars['input'], 
+              pars['regularisation_parameter'],
+              pars['edge_parameter'], 
+              pars['number_of_iterations'],
+              pars['time_marching_parameter'],'gpu')
+             
+rms = rmse(idealVol, diff4_gpu3D)
+pars['rmse'] = rms
+
+txtstr = printParametersToString(pars)
+txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
+print (txtstr)
+a=fig.add_subplot(1,2,2)
+
+# these are matplotlib.patch.Patch properties
+props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
+# place a text box in upper left in axes coords
+a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
+         verticalalignment='top', bbox=props)
+imgplot = plt.imshow(diff4_gpu3D[10,:,:], cmap="gray")
+plt.title('{}'.format('GPU results'))
+
+
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+print ("_______________FGP-dTV (3D)________________")
+print ("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
+
+## plot 
+fig = plt.figure(6)
+plt.suptitle('Performance of FGP-dTV regulariser using the GPU')
+a=fig.add_subplot(1,2,1)
+a.set_title('Noisy Image')
+imgplot = plt.imshow(noisyVol[10,:,:],cmap="gray")
+
+# set parameters
+pars = {'algorithm' : FGP_dTV, \
+        'input' : noisyVol,\
+        'refdata' : noisyRef,\
+        'regularisation_parameter':0.04, \
+        'number_of_iterations' :300 ,\
+        'tolerance_constant':0.00001,\
+        'eta_const':0.2,\
+        'methodTV': 0 ,\
+        'nonneg': 0 ,\
+        'printingOut': 0 
+        }
+
+print ("#############FGP TV GPU####################")
+start_time = timeit.default_timer()
+fgp_dTV_gpu3D = FGP_dTV(pars['input'],
+              pars['refdata'], 
+              pars['regularisation_parameter'],
+              pars['number_of_iterations'],
+              pars['tolerance_constant'], 
+              pars['eta_const'],
+              pars['methodTV'],
+              pars['nonneg'],
+              pars['printingOut'],'gpu')
+
+rms = rmse(idealVol, fgp_dTV_gpu3D)
+pars['rmse'] = rms
+
+txtstr = printParametersToString(pars)
+txtstr += "%s = %.3fs" % ('elapsed time',timeit.default_timer() - start_time)
+print (txtstr)
+a=fig.add_subplot(1,2,2)
+
+# these are matplotlib.patch.Patch properties
+props = dict(boxstyle='round', facecolor='wheat', alpha=0.75)
+# place a text box in upper left in axes coords
+a.text(0.15, 0.25, txtstr, transform=a.transAxes, fontsize=14,
+         verticalalignment='top', bbox=props)
+imgplot = plt.imshow(fgp_dTV_gpu3D[10,:,:], cmap="gray")
+plt.title('{}'.format('Recovered volume on the GPU using FGP-dTV'))
+#%%