2 new GPU regularizers, FGP objective fixed, FISTA_REC updated

11 files changed, 1016 insertions, 88 deletions

diff --git a/demos/DemoRD2.m b/demos/DemoRD2.m
index f177e26..717a55d 100644
--- a/demos/DemoRD2.m
+++ b/demos/DemoRD2.m
@@ -6,7 +6,7 @@ close all
 %%
 % % adding paths
 addpath('../data/');
-addpath('../main_func/'); addpath('../main_func/regularizers_CPU/');
+addpath('../main_func/'); addpath('../main_func/regularizers_CPU/'); addpath('../main_func/regularizers_GPU/NL_Regul/'); addpath('../main_func/regularizers_GPU/Diffus_HO/');
 addpath('../supp/');
 
 load('DendrRawData.mat') % load raw data of 3D dendritic set
@@ -30,7 +30,7 @@ Weights3D = single(data_raw3D); % weights for PW model
 clear data_raw3D
 %%
 % set projection/reconstruction geometry here
-Z_slices = 1;
+Z_slices = 5;
 det_row_count = Z_slices;
 proj_geom = astra_create_proj_geom('parallel3d', 1, 1, det_row_count, size_det, angles_rad);
 vol_geom = astra_create_vol_geom(recon_size,recon_size,Z_slices);
@@ -107,26 +107,47 @@ tic; [X_fista_GH_TVLLT, outputGH_TVLLT] = FISTA_REC(params); toc;
 figure; imshow(X_fista_GH_TVLLT(:,:,params.slice) , [0, 2.5]); title ('FISTA-OS-GH-TV-LLT reconstruction');
 
 %%
-% fprintf('%s\n', 'Reconstruction using FISTA-OS-PB...');
-% % very-slow on CPU
-% clear params
-% params.proj_geom = proj_geom; % pass geometry to the function
-% params.vol_geom = vol_geom;
-% params.sino = Sino3D(:,:,1);
-% params.iterFISTA  = 12;
-% params.Regul_LambdaPatchBased = 1; % PB regularization parameter 
-% params.Regul_PB_h = 0.1; % threhsold parameter
-% params.Ring_LambdaR_L1 = 0.002; % Soft-Thresh L1 ring variable parameter
-% params.Ring_Alpha = 21; % to boost ring removal procedure
-% params.weights = Weights3D(:,:,1);
-% params.subsets = 16; % the number of ordered subsets 
-% params.show = 1;
-% params.maxvalplot = 2.5; params.slice = 1;
-% 
-% tic; [X_fista_GH_PB, outputPB] = FISTA_REC(params); toc;
-% figure; imshow(X_fista_GH_PB(:,:,params.slice) , [0, 2.5]); title ('FISTA-OS-PB reconstruction');
+fprintf('%s\n', 'Reconstruction using FISTA-OS-GH-HigherOrderDiffusion...');
+% !GPU version!
+clear params
+params.proj_geom = proj_geom; % pass geometry to the function
+params.vol_geom = vol_geom;
+params.sino = Sino3D(:,:,1:5);
+params.iterFISTA  = 25;
+params.Regul_LambdaDiffHO = 2; % DiffHO regularization parameter 
+params.Regul_DiffHO_EdgePar = 0.05; % threshold parameter
+params.Regul_Iterations = 150;
+params.Ring_LambdaR_L1 = 0.002; % Soft-Thresh L1 ring variable parameter
+params.Ring_Alpha = 21; % to boost ring removal procedure
+params.weights = Weights3D(:,:,1:5);
+params.subsets = 16; % the number of ordered subsets 
+params.show = 1;
+params.maxvalplot = 2.5; params.slice = 1;
+ 
+tic; [X_fista_GH_HO, outputHO] = FISTA_REC(params); toc;
+figure; imshow(X_fista_GH_HO(:,:,params.slice) , [0, 2.5]); title ('FISTA-OS-HigherOrderDiffusion reconstruction');
 
 %%
+fprintf('%s\n', 'Reconstruction using FISTA-PB...');
+% !GPU version!
+clear params
+params.proj_geom = proj_geom; % pass geometry to the function
+params.vol_geom = vol_geom;
+params.sino = Sino3D(:,:,1);
+params.iterFISTA  = 25;
+params.Regul_LambdaPatchBased_GPU = 3; % PB regularization parameter 
+params.Regul_PB_h = 0.04; % threhsold parameter
+params.Regul_PB_SearchW = 3;
+params.Regul_PB_SimilW  = 1;
+params.Ring_LambdaR_L1 = 0.002; % Soft-Thresh L1 ring variable parameter
+params.Ring_Alpha = 21; % to boost ring removal procedure
+params.weights = Weights3D(:,:,1);
+params.show = 1;
+params.maxvalplot = 2.5; params.slice = 1;
+ 
+tic; [X_fista_GH_PB, outputPB] = FISTA_REC(params); toc;
+figure; imshow(X_fista_GH_PB(:,:,params.slice) , [0, 2.5]); title ('FISTA-OS-PB reconstruction');
+%%
 fprintf('%s\n', 'Reconstruction using FISTA-OS-GH-TGV...');
 % still testing...
 clear params
@@ -146,6 +167,7 @@ params.maxvalplot = 2.5; params.slice = 1;
 tic; [X_fista_GH_TGV, outputTGV] = FISTA_REC(params); toc;
 figure; imshow(X_fista_GH_TGV(:,:,params.slice) , [0, 2.5]); title ('FISTA-OS-GH-TGV reconstruction');
 
+
 %%
 % fprintf('%s\n', 'Reconstruction using FISTA-Student-TV...');
 % clear params
diff --git a/main_func/FISTA_REC.m b/main_func/FISTA_REC.m
index 00e59ab..edccbe1 100644
--- a/main_func/FISTA_REC.m
+++ b/main_func/FISTA_REC.m
@@ -1,6 +1,15 @@
 function [X,  output] = FISTA_REC(params)
 
 % <<<< FISTA-based reconstruction routine using ASTRA-toolbox >>>>
+% This code solves regularised PWLS problem using FISTA approach.
+% The code contains multiple regularisation penalties as well as it can be
+% accelerated by using ordered-subset version. Various projection
+% geometries supported.
+
+% DISCLAIMER
+% It is recommended to use ASTRA version 1.8 or later in order to avoid
+% crashing due to GPU memory overflow for big datasets
+
 % ___Input___:
 % params.[] file:
 %----------------General Parameters------------------------
@@ -18,11 +27,17 @@ function [X,  output] = FISTA_REC(params)
 %       2 .Regul_Lambda_SBTV (SplitBregman-TV regularization parameter)
 %       3 .Regul_LambdaLLT (Higher order LLT regularization parameter)
 %          3.1 .Regul_tauLLT (time step parameter for LLT (HO) term)
-%       4 .Regul_LambdaPatchBased (Patch-based nonlocal regularization parameter)
+%       4 .Regul_LambdaPatchBased_CPU (Patch-based nonlocal regularization parameter)
 %          4.1  .Regul_PB_SearchW (ratio of the searching window (e.g. 3 = (2*3+1) = 7 pixels window))
 %          4.2  .Regul_PB_SimilW (ratio of the similarity window (e.g. 1 = (2*1+1) = 3 pixels window))
 %          4.3  .Regul_PB_h (PB penalty function threshold)
-%       5 .Regul_LambdaTGV (Total Generalized variation regularization parameter)
+%       5 .Regul_LambdaPatchBased_GPU (Patch-based nonlocal regularization parameter)
+%          5.1  .Regul_PB_SearchW (ratio of the searching window (e.g. 3 = (2*3+1) = 7 pixels window))
+%          5.2  .Regul_PB_SimilW (ratio of the similarity window (e.g. 1 = (2*1+1) = 3 pixels window))
+%          5.3  .Regul_PB_h (PB penalty function threshold)
+%       6 .Regul_LambdaDiffHO (Higher-Order Diffusion regularization parameter)
+%          6.1  .Regul_DiffHO_EdgePar (edge-preserving noise related parameter)
+%       7 .Regul_LambdaTGV (Total Generalized variation regularization parameter)
 %       - .Regul_tol (tolerance to terminate regul iterations, default 1.0e-04)
 %       - .Regul_Iterations (iterations for the selected penalty, default 25)
 %       - .Regul_Dimension ('2D' or '3D' way to apply regularization, '3D' is the default)
@@ -173,11 +188,16 @@ if (isfield(params,'Regul_tauLLT'))
 else
     tauHO = 0.0001;
 end
-if (isfield(params,'Regul_LambdaPatchBased'))
-    lambdaPB = params.Regul_LambdaPatchBased;
+if (isfield(params,'Regul_LambdaPatchBased_CPU'))
+    lambdaPB = params.Regul_LambdaPatchBased_CPU;
 else
     lambdaPB = 0;
 end
+if (isfield(params,'Regul_LambdaPatchBased_GPU'))
+    lambdaPB_GPU = params.Regul_LambdaPatchBased_GPU;
+else
+    lambdaPB_GPU = 0;
+end
 if (isfield(params,'Regul_PB_SearchW'))
     SearchW = params.Regul_PB_SearchW;
 else
@@ -193,6 +213,16 @@ if (isfield(params,'Regul_PB_h'))
 else
     h_PB = 0.1; % default
 end
+if (isfield(params,'Regul_LambdaDiffHO'))
+    LambdaDiff_HO = params.Regul_LambdaDiffHO;
+else
+    LambdaDiff_HO = 0;
+end
+if (isfield(params,'Regul_DiffHO_EdgePar'))
+    LambdaDiff_HO_EdgePar = params.Regul_DiffHO_EdgePar;
+else
+    LambdaDiff_HO_EdgePar = 0.01;
+end
 if (isfield(params,'Regul_LambdaTGV'))
     LambdaTGV = params.Regul_LambdaTGV;
 else
@@ -305,16 +335,16 @@ if (subsets == 0)
         t_old = t;
         r_old = r;
         
-        % if the geometry is parallel use slice-by-slice projection-backprojection routine 
+        % if the geometry is parallel use slice-by-slice projection-backprojection routine
         if (strcmp(proj_geom.type,'parallel') || strcmp(proj_geom.type,'parallel3d'))
-			sino_updt = zeros(size(sino),'single');
-			for kkk = 1:SlicesZ			
-			  [sino_id, sino_updt(:,:,kkk)] = astra_create_sino3d_cuda(X_t(:,:,kkk), proj_geomT, vol_geomT);
-			  astra_mex_data3d('delete', sino_id);
-			end
-		else
-		% for divergent 3D geometry (for Matlab watch the GPU memory overflow)
-        [sino_id, sino_updt] = astra_create_sino3d_cuda(X_t, proj_geom, vol_geom);
+            sino_updt = zeros(size(sino),'single');
+            for kkk = 1:SlicesZ
+                [sino_id, sino_updt(:,:,kkk)] = astra_create_sino3d_cuda(X_t(:,:,kkk), proj_geomT, vol_geomT);
+                astra_mex_data3d('delete', sino_id);
+            end
+        else
+            % for divergent 3D geometry (watch the GPU memory overflow in earlier ASTRA versions < 1.8)
+            [sino_id, sino_updt] = astra_create_sino3d_cuda(X_t, proj_geom, vol_geom);
         end
         
         if (lambdaR_L1 > 0)
@@ -332,17 +362,17 @@ if (subsets == 0)
             residual = weights.*(sino_updt - sino);
         end
         
-        objective(i) = (0.5*norm(residual(:))^2)/(Detectors*anglesNumb*SlicesZ); % for the objective function output
+        objective(i) = (0.5*sum(residual(:).^2)); % for the objective function output
         
-        % if the geometry is parallel use slice-by-slice projection-backprojection routine 
+        % if the geometry is parallel use slice-by-slice projection-backprojection routine
         if (strcmp(proj_geom.type,'parallel') || strcmp(proj_geom.type,'parallel3d'))
-        x_temp = zeros(size(X),'single');
-			for kkk = 1:SlicesZ	        
-			[id, x_temp(:,:,kkk)] = astra_create_backprojection3d_cuda(squeeze(residual(:,:,kkk)), proj_geomT, vol_geomT);
-			astra_mex_data3d('delete', id);
-			end
+            x_temp = zeros(size(X),'single');
+            for kkk = 1:SlicesZ
+                [id, x_temp(:,:,kkk)] = astra_create_backprojection3d_cuda(squeeze(residual(:,:,kkk)), proj_geomT, vol_geomT);
+                astra_mex_data3d('delete', id);
+            end
         else
-        [id, x_temp] = astra_create_backprojection3d_cuda(residual, proj_geom, vol_geom);
+            [id, x_temp] = astra_create_backprojection3d_cuda(residual, proj_geom, vol_geom);
         end
         X = X_t - (1/L_const).*x_temp;
         astra_mex_data3d('delete', sino_id);
@@ -360,7 +390,7 @@ if (subsets == 0)
                 % 3D regularization
                 [X, f_val] = FGP_TV(single(X), lambdaFGP_TV, IterationsRegul, tol, 'iso');
             end
-            objective(i) = objective(i) + f_val;
+            objective(i) = (objective(i) + f_val)./(Detectors*anglesNumb*SlicesZ);
         end
         if (lambdaSB_TV > 0)
             % Split Bregman regularization
@@ -390,7 +420,7 @@ if (subsets == 0)
             
         end
         if (lambdaPB > 0)
-            % Patch-Based regularization (can be slow on CPU)
+            % Patch-Based regularization (can be very slow on CPU)
             if ((strcmp('2D', Dimension) == 1))
                 % 2D regularization
                 for kkk = 1:SlicesZ
@@ -400,13 +430,35 @@ if (subsets == 0)
                 X = PatchBased_Regul(single(X), SearchW, SimilW, h_PB, lambdaPB);
             end
         end
-        if (LambdaTGV > 0)
-                % Total Generalized variation (currently only 2D)
-                lamTGV1 = 1.1; % smoothing trade-off parameters, see Pock's paper
-                lamTGV2 = 0.8; % second-order term
+        if (lambdaPB_GPU > 0)
+            % Patch-Based regularization (GPU CUDA implementation)
+            if ((strcmp('2D', Dimension) == 1))
+                % 2D regularization
                 for kkk = 1:SlicesZ
-                X(:,:,kkk) = TGV_PD(single(X(:,:,kkk)), LambdaTGV, lamTGV1, lamTGV2, IterationsRegul);
+                    X(:,:,kkk) = NLM_GPU(single(X(:,:,kkk)), SearchW, SimilW, h_PB, lambdaPB_GPU);
                 end
+            else
+                X = NLM_GPU(single(X), SearchW, SimilW, h_PB, lambdaPB_GPU);
+            end
+        end
+        if (LambdaDiff_HO > 0)
+            % Higher-order diffusion penalty (GPU CUDA implementation)
+            if ((strcmp('2D', Dimension) == 1))
+                % 2D regularization
+                for kkk = 1:SlicesZ
+                    X(:,:,kkk) = Diff4thHajiaboli_GPU(single(X(:,:,kkk)), LambdaDiff_HO_EdgePar, LambdaDiff_HO, IterationsRegul);
+                end
+            else
+                X = Diff4thHajiaboli_GPU(X, LambdaDiff_HO_EdgePar, LambdaDiff_HO, IterationsRegul);
+            end
+        end
+        if (LambdaTGV > 0)
+            % Total Generalized variation (currently only 2D)
+            lamTGV1 = 1.1; % smoothing trade-off parameters, see Pock's paper
+            lamTGV2 = 0.8; % second-order term
+            for kkk = 1:SlicesZ
+                X(:,:,kkk) = TGV_PD(single(X(:,:,kkk)), LambdaTGV, lamTGV1, lamTGV2, IterationsRegul);
+            end
         end
         
         if (lambdaR_L1 > 0)
@@ -470,7 +522,7 @@ else
                 
                 % the ring removal part (Group-Huber fidelity)
                 % first 2 iterations do additional work reconstructing whole dataset to ensure
-                % stablility
+                % the stablility
                 if (i < 3)
                     [sino_id2, sino_updt2] = astra_create_sino3d_cuda(X_t, proj_geom, vol_geom);
                     astra_mex_data3d('delete', sino_id2);
@@ -546,7 +598,7 @@ else
                     % 3D regularization
                     X2 = LLT_model(single(X), lambdaHO/subsets, tauHO/subsets, iterHO, 2.0e-05, 0);
                 end
-                X = 0.5.*(X + X2); % averaged combination of two solutions
+                X = 0.5.*(X + X2); % the averaged combination of two solutions
             end
             if (lambdaPB > 0)
                 % Patch-Based regularization (can be slow on CPU)
@@ -559,14 +611,36 @@ else
                     X = PatchBased_Regul(single(X), SearchW, SimilW, h_PB, lambdaPB/subsets);
                 end
             end
+            if (lambdaPB_GPU > 0)
+                % Patch-Based regularization (GPU CUDA implementation)
+                if ((strcmp('2D', Dimension) == 1))
+                    % 2D regularization
+                    for kkk = 1:SlicesZ
+                        X(:,:,kkk) = NLM_GPU(single(X(:,:,kkk)), SearchW, SimilW, h_PB, lambdaPB_GPU);
+                    end
+                else
+                    X = NLM_GPU(single(X), SearchW, SimilW, h_PB, lambdaPB_GPU);
+                end
+            end
+            if (LambdaDiff_HO > 0)
+                % Higher-order diffusion penalty (GPU CUDA implementation)
+                if ((strcmp('2D', Dimension) == 1))
+                    % 2D regularization
+                    for kkk = 1:SlicesZ
+                        X(:,:,kkk) = Diff4thHajiaboli_GPU(single(X(:,:,kkk)), LambdaDiff_HO_EdgePar, LambdaDiff_HO, round(IterationsRegul/subsets));
+                    end
+                else
+                    X = Diff4thHajiaboli_GPU(X, LambdaDiff_HO_EdgePar, LambdaDiff_HO, round(IterationsRegul/subsets));
+                end
+            end
             if (LambdaTGV > 0)
                 % Total Generalized variation (currently only 2D)
                 lamTGV1 = 1.1; % smoothing trade-off parameters, see Pock's paper
                 lamTGV2 = 0.5; % second-order term
                 for kkk = 1:SlicesZ
-                X(:,:,kkk) = TGV_PD(single(X(:,:,kkk)), LambdaTGV/subsets, lamTGV1, lamTGV2, IterationsRegul);
+                    X(:,:,kkk) = TGV_PD(single(X(:,:,kkk)), LambdaTGV/subsets, lamTGV1, lamTGV2, IterationsRegul);
                 end
-            end           
+            end
             
             if (lambdaR_L1 > 0)
                 r =  max(abs(r)-lambdaR_L1, 0).*sign(r); % soft-thresholding operator for ring vector
diff --git a/main_func/regularizers_CPU/FGP_TV.c b/main_func/regularizers_CPU/FGP_TV.c
index 5d8cfb9..cfe5b9e 100644
--- a/main_func/regularizers_CPU/FGP_TV.c
+++ b/main_func/regularizers_CPU/FGP_TV.c
@@ -54,7 +54,7 @@ void mexFunction(
 {
     int number_of_dims, iter, dimX, dimY, dimZ, ll, j, count, methTV;
     const int  *dim_array;
-    float *A, *D=NULL, *D_old=NULL, *P1=NULL, *P2=NULL, *P3=NULL, *P1_old=NULL, *P2_old=NULL, *P3_old=NULL, *R1=NULL, *R2=NULL, *R3=NULL, lambda, tk, tkp1, re, re1, re_old, epsil, funcval;
+    float *A, *D=NULL, *D_old=NULL, *P1=NULL, *P2=NULL, *P3=NULL, *P1_old=NULL, *P2_old=NULL, *P3_old=NULL, *R1=NULL, *R2=NULL, *R3=NULL, lambda, tk, tkp1, re, re1, re_old, epsil;
     
     number_of_dims = mxGetNumberOfDimensions(prhs[0]);
     dim_array = mxGetDimensions(prhs[0]);
@@ -78,7 +78,6 @@ void mexFunction(
         mxFree(penalty_type);
     }
     /*output function value (last iteration) */
-    funcval = 0.0f;
     plhs[1] = mxCreateNumericMatrix(1, 1, mxSINGLE_CLASS, mxREAL);  
     float *funcvalA = (float *) mxGetData(plhs[1]);
         
@@ -117,7 +116,7 @@ void mexFunction(
             
             /*updating R and t*/
             tkp1 = (1.0f + sqrt(1.0f + 4.0f*tk*tk))*0.5f;
-            Rupd_func2D(P1, P1_old, P2, P2_old, R1, R2, tkp1, tk, dimX, dimY);
+            Rupd_func2D(P1, P1_old, P2, P2_old, R1, R2, tkp1, tk, dimX, dimY);                
             
             /* calculate norm */
             re = 0.0f; re1 = 0.0f;
@@ -129,23 +128,17 @@ void mexFunction(
             re = sqrt(re)/sqrt(re1);
             if (re < epsil)  count++;
             if (count > 3) {
-                Obj_func2D(A, D, P1, P2, lambda, dimX, dimY);            
-                funcval = 0.0f; 
-                for(j=0; j<dimX*dimY*dimZ; j++) funcval += pow(D[j],2);                           
-                funcvalA[0] = sqrt(funcval);     
+                Obj_func_CALC2D(A, D, funcvalA, lambda, dimX, dimY); 
                 break; }
             
             /* check that the residual norm is decreasing */
             if (ll > 2) {
                 if (re > re_old) {
-                    Obj_func2D(A, D, P1, P2, lambda, dimX, dimY);            
-                    funcval = 0.0f; 
-                    for(j=0; j<dimX*dimY*dimZ; j++) funcval += pow(D[j],2);                           
-                    funcvalA[0] = sqrt(funcval);                     
+                    Obj_func_CALC2D(A, D, funcvalA, lambda, dimX, dimY);                                   
                     break; }}            
             re_old = re;
-            /*printf("%f %i %i \n", re, ll, count); */
-            
+            /*printf("%f %i %i \n", re, ll, count); */                      
+          
             /*storing old values*/
             copyIm(D, D_old, dimX, dimY, dimZ);
             copyIm(P1, P1_old, dimX, dimY, dimZ);
@@ -153,12 +146,7 @@ void mexFunction(
             tk = tkp1;
             
             /* calculating the objective function value */
-            if (ll == (iter-1)) {
-            Obj_func2D(A, D, P1, P2, lambda, dimX, dimY);            
-            funcval = 0.0f; 
-            for(j=0; j<dimX*dimY*dimZ; j++) funcval += pow(D[j],2);                           
-            funcvalA[0] = sqrt(funcval);            
-            }
+            if (ll == (iter-1)) Obj_func_CALC2D(A, D, funcvalA, lambda, dimX, dimY);            
         }
         printf("FGP-TV iterations stopped at iteration %i with the function value %f \n", ll, funcvalA[0]);
     }
@@ -202,21 +190,14 @@ void mexFunction(
             /* stop if the norm residual is less than the tolerance EPS */
             if (re < epsil)  count++;
             if (count > 3) {
-                Obj_func3D(A, D, P1, P2, P3,lambda, dimX, dimY, dimZ);
-                funcval = 0.0f; 
-                for(j=0; j<dimX*dimY*dimZ; j++) funcval += pow(D[j],2);                           
-                funcvalA[0] = sqrt(funcval);                  
+                Obj_func_CALC3D(A, D, funcvalA, lambda, dimX, dimY, dimZ);                            
                 break;}
             
             /* check that the residual norm is decreasing */
             if (ll > 2) {
                 if (re > re_old) {
-                Obj_func3D(A, D, P1, P2, P3,lambda, dimX, dimY, dimZ);
-                funcval = 0.0f; 
-                for(j=0; j<dimX*dimY*dimZ; j++) funcval += pow(D[j],2);                           
-                funcvalA[0] = sqrt(funcval);  
-                break; }}
-            
+                Obj_func_CALC3D(A, D, funcvalA, lambda, dimX, dimY, dimZ);
+                }}            
             re_old = re;
             /*printf("%f %i %i \n", re, ll, count); */
             
@@ -227,13 +208,7 @@ void mexFunction(
             copyIm(P3, P3_old, dimX, dimY, dimZ);
             tk = tkp1;
             
-            if (ll == (iter-1)) {
-            Obj_func3D(A, D, P1, P2, P3,lambda, dimX, dimY, dimZ);
-            funcval = 0.0f; 
-            for(j=0; j<dimX*dimY*dimZ; j++) funcval += pow(D[j],2);                           
-            funcvalA[0] = sqrt(funcval);            
-            }
-            
+            if (ll == (iter-1)) Obj_func_CALC3D(A, D, funcvalA, lambda, dimX, dimY, dimZ);            
         }
         printf("FGP-TV iterations stopped at iteration %i with the function value %f \n", ll, funcvalA[0]);
     }
diff --git a/main_func/regularizers_CPU/FGP_TV_core.c b/main_func/regularizers_CPU/FGP_TV_core.c
index a55991c..9cde327 100644
--- a/main_func/regularizers_CPU/FGP_TV_core.c
+++ b/main_func/regularizers_CPU/FGP_TV_core.c
@@ -47,6 +47,30 @@ limitations under the License.
 
 /* 2D-case related Functions */
 /*****************************************************************/
+float Obj_func_CALC2D(float *A, float *D, float *funcvalA, float lambda, int dimX, int dimY)
+{   
+    int i,j;
+    float f1, f2, val1, val2;
+    
+    /*data-related term */
+    f1 = 0.0f;
+    for(i=0; i<dimX*dimY; i++) f1 += pow(D[i] - A[i],2);    
+    
+    /*TV-related term */
+    f2 = 0.0f;
+    for(i=0; i<dimX; i++) {
+        for(j=0; j<dimY; j++) {
+            /* boundary conditions  */
+            if (i == dimX-1) {val1 = 0.0f;} else {val1 = A[(i+1)*dimY + (j)] - A[(i)*dimY + (j)];}
+            if (j == dimY-1) {val2 = 0.0f;} else {val2 = A[(i)*dimY + (j+1)] - A[(i)*dimY + (j)];}    
+            f2 += sqrt(pow(val1,2) + pow(val2,2));
+        }}  
+    
+    /* sum of two terms */
+    funcvalA[0] = 0.5f*f1 + lambda*f2;     
+    return *funcvalA;
+}
+
 float Obj_func2D(float *A, float *D, float *R1, float *R2, float lambda, int dimX, int dimY)
 {
 	float val1, val2;
@@ -131,6 +155,31 @@ float Rupd_func2D(float *P1, float *P1_old, float *P2, float *P2_old, float *R1,
 
 /* 3D-case related Functions */
 /*****************************************************************/
+float Obj_func_CALC3D(float *A, float *D, float *funcvalA, float lambda, int dimX, int dimY, int dimZ)
+{   
+    int i,j,k;
+    float f1, f2, val1, val2, val3;
+    
+    /*data-related term */
+    f1 = 0.0f;
+    for(i=0; i<dimX*dimY*dimZ; i++) f1 += pow(D[i] - A[i],2);    
+    
+    /*TV-related term */
+    f2 = 0.0f;
+    for(i=0; i<dimX; i++) {
+        for(j=0; j<dimY; j++) {
+            for(k=0; k<dimZ; k++) {
+            /* boundary conditions  */
+            if (i == dimX-1) {val1 = 0.0f;} else {val1 = A[(dimX*dimY)*k + (i+1)*dimY + (j)] - A[(dimX*dimY)*k + (i)*dimY + (j)];}
+            if (j == dimY-1) {val2 = 0.0f;} else {val2 = A[(dimX*dimY)*k + (i)*dimY + (j+1)] - A[(dimX*dimY)*k + (i)*dimY + (j)];}    
+            if (k == dimZ-1) {val3 = 0.0f;} else {val3 = A[(dimX*dimY)*(k+1) + (i)*dimY + (j)] - A[(dimX*dimY)*k + (i)*dimY + (j)];}    
+            f2 += sqrt(pow(val1,2) + pow(val2,2)  + pow(val3,2));
+        }}}     
+    /* sum of two terms */
+    funcvalA[0] = 0.5f*f1 + lambda*f2;     
+    return *funcvalA;
+}
+
 float Obj_func3D(float *A, float *D, float *R1, float *R2, float *R3, float lambda, int dimX, int dimY, int dimZ)
 {
 	float val1, val2, val3;
diff --git a/main_func/regularizers_CPU/FGP_TV_core.h b/main_func/regularizers_CPU/FGP_TV_core.h
index e5328fb..697fd84 100644
--- a/main_func/regularizers_CPU/FGP_TV_core.h
+++ b/main_func/regularizers_CPU/FGP_TV_core.h
@@ -29,8 +29,10 @@ float Obj_func2D(float *A, float *D, float *R1, float *R2, float lambda, int dim
 float Grad_func2D(float *P1, float *P2, float *D, float *R1, float *R2, float lambda, int dimX, int dimY);
 float Proj_func2D(float *P1, float *P2, int methTV, int dimX, int dimY);
 float Rupd_func2D(float *P1, float *P1_old, float *P2, float *P2_old, float *R1, float *R2, float tkp1, float tk, int dimX, int dimY);
+float Obj_func_CALC2D(float *A, float *D, float *funcvalA, float lambda, int dimX, int dimY);
 
 float Obj_func3D(float *A, float *D, float *R1, float *R2, float *R3, float lambda, int dimX, int dimY, int dimZ);
 float Grad_func3D(float *P1, float *P2, float *P3, float *D, float *R1, float *R2, float *R3, float lambda, int dimX, int dimY, int dimZ);
 float Proj_func3D(float *P1, float *P2, float *P3, int dimX, int dimY, int dimZ);
 float Rupd_func3D(float *P1, float *P1_old, float *P2, float *P2_old, float *P3, float *P3_old, float *R1, float *R2, float *R3, float tkp1, float tk, int dimX, int dimY, int dimZ);
+float Obj_func_CALC3D(float *A, float *D, float *funcvalA, float lambda, int dimX, int dimY, int dimZ);
diff --git a/main_func/regularizers_GPU/Diffus_HO/Diff4thHajiaboli_GPU.cpp b/main_func/regularizers_GPU/Diffus_HO/Diff4thHajiaboli_GPU.cpp
new file mode 100644
index 0000000..5a8c7c0
--- /dev/null
+++ b/main_func/regularizers_GPU/Diffus_HO/Diff4thHajiaboli_GPU.cpp
@@ -0,0 +1,114 @@
+#include "mex.h"

+#include <matrix.h>

+#include <math.h>

+#include <stdlib.h>

+#include <memory.h>

+#include <stdio.h>

+#include <iostream>

+#include "Diff4th_GPU_kernel.h"

+

+/*

+ * 2D and 3D CUDA implementation of the 4th order PDE denoising model by Hajiaboli

+ *

+ * Reference :

+ * "An anisotropic fourth-order diffusion filter for image noise removal" by M. Hajiaboli

+ * 

+ * Example

+ * figure;

+ * Im = double(imread('lena_gray_256.tif'))/255;  % loading image

+ * u0 = Im + .05*randn(size(Im)); % adding noise

+ * u = Diff4thHajiaboli_GPU(single(u0), 0.02, 150);

+ * subplot (1,2,1); imshow(u0,[ ]); title('Noisy Image')

+ * subplot (1,2,2); imshow(u,[ ]); title('Denoised Image')

+ *

+ *

+ * Linux/Matlab compilation:

+ * compile in terminal: nvcc -Xcompiler -fPIC -shared -o Diff4th_GPU_kernel.o Diff4th_GPU_kernel.cu

+ * then compile in Matlab: mex -I/usr/local/cuda-7.5/include -L/usr/local/cuda-7.5/lib64 -lcudart Diff4thHajiaboli_GPU.cpp Diff4th_GPU_kernel.o

+ */

+

+void mexFunction(

+        int nlhs, mxArray *plhs[],

+        int nrhs, const mxArray *prhs[])

+{

+    int numdims, dimZ, size;

+    float *A, *B, *A_L, *B_L;

+    const int *dims;    

+    

+    numdims = mxGetNumberOfDimensions(prhs[0]);

+    dims = mxGetDimensions(prhs[0]);       

+    

+    float sigma = (float)mxGetScalar(prhs[1]); /* edge-preserving parameter */

+    float lambda = (float)mxGetScalar(prhs[2]); /* regularization parameter */

+    int iter = (int)mxGetScalar(prhs[3]); /* iterations number */

+    

+    if (numdims == 2)  {

+        

+        int N, M, Z, i, j;

+        Z = 0; // for the 2D case

+        float tau = 0.01; // time step is sufficiently small for an explicit methods

+        

+        /*Input data*/

+        A = (float*)mxGetData(prhs[0]);        

+        N = dims[0] + 2;

+        M = dims[1] + 2;

+        A_L = (float*)mxGetData(mxCreateNumericMatrix(N, M, mxSINGLE_CLASS, mxREAL));

+        B_L = (float*)mxGetData(mxCreateNumericMatrix(N, M, mxSINGLE_CLASS, mxREAL));

+        

+        /*Output data*/

+        B = (float*)mxGetData(plhs[0] = mxCreateNumericMatrix(dims[0], dims[1], mxSINGLE_CLASS, mxREAL));        

+        

+        // copy A to the bigger A_L with boundaries

+        #pragma omp parallel for shared(A_L, A) private(i,j)

+        for (i=0; i < N; i++) {

+            for (j=0; j < M; j++) {

+                if (((i > 0) && (i < N-1)) &&  ((j > 0) && (j < M-1)))  A_L[i*M+j] = A[(i-1)*(dims[1])+(j-1)];

+            }}

+        

+        // Running CUDA code here

+        Diff4th_GPU_kernel(A_L, B_L, N, M, Z, (float)sigma, iter, (float)tau, lambda);

+        

+        // copy the processed B_L to a smaller B

+        #pragma omp parallel for shared(B_L, B) private(i,j)

+        for (i=0; i < N; i++) {

+            for (j=0; j < M; j++) {

+                if (((i > 0) && (i < N-1)) &&  ((j > 0) && (j < M-1)))   B[(i-1)*(dims[1])+(j-1)] = B_L[i*M+j];

+            }}

+    }

+    if (numdims == 3)  {

+        //  3D image denoising / regularization

+        int N, M, Z, i, j, k;

+        float tau = 0.0007; // Time Step is small for an explicit methods

+        A = (float*)mxGetData(prhs[0]);

+        N = dims[0] + 2;

+        M = dims[1] + 2;

+        Z = dims[2] + 2;

+        int N_dims[] = {N, M, Z};

+        A_L = (float*)mxGetPr(mxCreateNumericArray(3, N_dims, mxSINGLE_CLASS, mxREAL));

+        B_L = (float*)mxGetPr(mxCreateNumericArray(3, N_dims, mxSINGLE_CLASS, mxREAL));

+        

+        /* output data */

+        B = (float*)mxGetPr(plhs[0] = mxCreateNumericArray(3, dims, mxSINGLE_CLASS, mxREAL));

+        

+        // copy A to the bigger A_L with boundaries

+        #pragma omp parallel for shared(A_L, A) private(i,j,k)

+        for (i=0; i < N; i++) {

+            for (j=0; j < M; j++) {

+                for (k=0; k < Z; k++) {

+                    if (((i > 0) && (i < N-1)) &&  ((j > 0) && (j < M-1)) &&  ((k > 0) && (k < Z-1))) {

+                        A_L[(N*M)*(k)+(i)*M+(j)] = A[(dims[0]*dims[1])*(k-1)+(i-1)*dims[1]+(j-1)];

+                    }}}}

+        

+        // Running CUDA kernel here for diffusivity

+        Diff4th_GPU_kernel(A_L, B_L, N, M, Z, (float)sigma, iter, (float)tau, lambda);

+        

+        // copy the processed B_L to a smaller B

+        #pragma omp parallel for shared(B_L, B) private(i,j,k)

+        for (i=0; i < N; i++) {

+            for (j=0; j < M; j++) {

+                for (k=0; k < Z; k++) {

+                    if (((i > 0) && (i < N-1)) &&  ((j > 0) && (j < M-1)) &&  ((k > 0) && (k < Z-1))) {

+                        B[(dims[0]*dims[1])*(k-1)+(i-1)*dims[1]+(j-1)] = B_L[(N*M)*(k)+(i)*M+(j)];

+                    }}}}

+    }

+}
\ No newline at end of file
diff --git a/main_func/regularizers_GPU/Diffus_HO/Diff4th_GPU_kernel.cu b/main_func/regularizers_GPU/Diffus_HO/Diff4th_GPU_kernel.cu
new file mode 100644
index 0000000..178af00
--- /dev/null
+++ b/main_func/regularizers_GPU/Diffus_HO/Diff4th_GPU_kernel.cu
@@ -0,0 +1,270 @@
+#include <stdio.h>

+#include <stdlib.h>

+#include <memory.h>

+#include "Diff4th_GPU_kernel.h"

+

+#define checkCudaErrors(err)           __checkCudaErrors (err, __FILE__, __LINE__)

+

+inline void __checkCudaErrors(cudaError err, const char *file, const int line)

+{

+    if (cudaSuccess != err)

+    {

+        fprintf(stderr, "%s(%i) : CUDA Runtime API error %d: %s.\n",

+                file, line, (int)err, cudaGetErrorString(err));

+        exit(EXIT_FAILURE);

+    }

+}

+

+#define idivup(a, b) ( ((a)%(b) != 0) ? (a)/(b)+1 : (a)/(b) )

+#define sizeT (sizeX*sizeY*sizeZ)

+#define epsilon 0.00000001

+

+/////////////////////////////////////////////////

+// 2D Image denosing - Second Step (The second derrivative)

+__global__ void Diff4th2D_derriv(float* B, float* A, float *A0, int N, int M, float sigma, int iter, float tau, float lambda)

+{

+    float gradXXc = 0, gradYYc = 0;

+    int i = blockIdx.x*blockDim.x + threadIdx.x;

+    int j = blockIdx.y*blockDim.y + threadIdx.y;

+    

+    int index = j + i*N;

+    

+    if (((i < 1) || (i > N-2)) || ((j < 1) || (j > M-2))) {

+        return;    }

+    

+    int indexN = (j)+(i-1)*(N); if (A[indexN] == 0) indexN = index;

+    int indexS = (j)+(i+1)*(N); if (A[indexS] == 0) indexS = index;

+    int indexW = (j-1)+(i)*(N); if (A[indexW] == 0) indexW = index;

+    int indexE = (j+1)+(i)*(N); if (A[indexE] == 0) indexE = index;

+    

+    gradXXc = B[indexN] + B[indexS] - 2*B[index] ;

+    gradYYc = B[indexW] + B[indexE] - 2*B[index] ;

+    A[index]  = A[index] - tau*((A[index] - A0[index]) + lambda*(gradXXc + gradYYc));

+}

+

+// 2D Image denosing - The First Step

+__global__ void Diff4th2D(float* A, float* B, int N, int M, float sigma, int iter, float tau)

+{

+    float gradX, gradX_sq, gradY, gradY_sq, gradXX, gradYY, gradXY, sq_sum, xy_2,  V_norm, V_orth, c, c_sq;

+    

+    int i = blockIdx.x*blockDim.x + threadIdx.x;

+    int j = blockIdx.y*blockDim.y + threadIdx.y;

+    

+    int index = j + i*N;

+    

+    V_norm = 0.0f; V_orth = 0.0f;

+    

+    if (((i < 1) || (i > N-2)) || ((j < 1) || (j > M-2))) {

+        return;    }

+    

+    int indexN = (j)+(i-1)*(N); if (A[indexN] == 0) indexN = index;

+    int indexS = (j)+(i+1)*(N); if (A[indexS] == 0) indexS = index;

+    int indexW = (j-1)+(i)*(N); if (A[indexW] == 0) indexW = index;

+    int indexE = (j+1)+(i)*(N); if (A[indexE] == 0) indexE = index;

+    int indexNW = (j-1)+(i-1)*(N); if (A[indexNW] == 0) indexNW = index;

+    int indexNE = (j+1)+(i-1)*(N); if (A[indexNE] == 0) indexNE = index;

+    int indexWS = (j-1)+(i+1)*(N); if (A[indexWS] == 0) indexWS = index;

+    int indexES = (j+1)+(i+1)*(N); if (A[indexES] == 0) indexES = index;

+    

+    gradX = 0.5f*(A[indexN]-A[indexS]);

+    gradX_sq = gradX*gradX;

+    gradXX = A[indexN] + A[indexS] - 2*A[index];

+    

+    gradY = 0.5f*(A[indexW]-A[indexE]);

+    gradY_sq = gradY*gradY;

+    gradYY = A[indexW] + A[indexE] - 2*A[index];

+    

+    gradXY = 0.25f*(A[indexNW] - A[indexNE] - A[indexWS] + A[indexES]);

+    xy_2 = 2.0f*gradX*gradY*gradXY;

+    sq_sum =  gradX_sq + gradY_sq;

+    

+    if (sq_sum <= epsilon) {

+        V_norm = (gradXX*gradX_sq + xy_2 + gradYY*gradY_sq)/epsilon;

+        V_orth = (gradXX*gradY_sq - xy_2 + gradYY*gradX_sq)/epsilon; }

+    else  {

+        V_norm = (gradXX*gradX_sq + xy_2 + gradYY*gradY_sq)/sq_sum;

+        V_orth = (gradXX*gradY_sq - xy_2 + gradYY*gradX_sq)/sq_sum;  }

+    

+    c = 1.0f/(1.0f + sq_sum/sigma);

+    c_sq = c*c;

+    B[index] =  c_sq*V_norm + c*V_orth;

+}

+

+/////////////////////////////////////////////////

+// 3D data parocerssing

+__global__ void Diff4th3D_derriv(float *B, float *A, float *A0, int N, int M, int Z, float sigma, int iter, float tau, float lambda)

+{

+    float gradXXc = 0, gradYYc = 0, gradZZc = 0;

+    int xIndex = blockDim.x * blockIdx.x + threadIdx.x;

+    int yIndex = blockDim.y * blockIdx.y + threadIdx.y;

+    int zIndex = blockDim.z * blockIdx.z + threadIdx.z;

+    

+    int index = xIndex + M*yIndex + N*M*zIndex;

+    

+    if (((xIndex < 1) || (xIndex > N-2)) || ((yIndex < 1) || (yIndex > M-2)) || ((zIndex < 1) || (zIndex > Z-2))) {

+        return;    }

+    

+    int indexN = (xIndex-1) + M*yIndex + N*M*zIndex; if (A[indexN] == 0) indexN = index;

+    int indexS = (xIndex+1) + M*yIndex + N*M*zIndex; if (A[indexS] == 0) indexS = index;

+    int indexW = xIndex + M*(yIndex-1) + N*M*zIndex; if (A[indexW] == 0) indexW = index;

+    int indexE = xIndex + M*(yIndex+1) + N*M*zIndex; if (A[indexE] == 0) indexE = index;

+    int indexU = xIndex + M*yIndex + N*M*(zIndex-1); if (A[indexU] == 0) indexU = index;

+    int indexD = xIndex + M*yIndex + N*M*(zIndex+1); if (A[indexD] == 0) indexD = index;

+    

+    gradXXc = B[indexN] + B[indexS] - 2*B[index] ;

+    gradYYc = B[indexW] + B[indexE] - 2*B[index] ;

+    gradZZc = B[indexU] + B[indexD] - 2*B[index] ;   

+        

+    A[index]  = A[index] - tau*((A[index] - A0[index]) + lambda*(gradXXc + gradYYc + gradZZc));    

+}

+

+__global__ void Diff4th3D(float* A, float* B, int N, int M, int Z, float sigma, int iter, float tau)

+{

+    float gradX, gradX_sq, gradY, gradY_sq, gradZ, gradZ_sq, gradXX, gradYY, gradZZ, gradXY, gradXZ, gradYZ, sq_sum, xy_2, xyz_1, xyz_2, V_norm, V_orth, c, c_sq;

+    

+    int xIndex = blockDim.x * blockIdx.x + threadIdx.x;

+    int yIndex = blockDim.y * blockIdx.y + threadIdx.y;

+    int zIndex = blockDim.z * blockIdx.z + threadIdx.z;

+    

+    int index = xIndex + M*yIndex + N*M*zIndex;

+    V_norm = 0.0f; V_orth = 0.0f;

+    

+    if (((xIndex < 1) || (xIndex > N-2)) || ((yIndex < 1) || (yIndex > M-2)) || ((zIndex < 1) || (zIndex > Z-2))) {

+        return;    }

+    

+    B[index] = 0;

+    

+    int indexN = (xIndex-1) + M*yIndex + N*M*zIndex; if (A[indexN] == 0) indexN = index;

+    int indexS = (xIndex+1) + M*yIndex + N*M*zIndex; if (A[indexS] == 0) indexS = index;

+    int indexW = xIndex + M*(yIndex-1) + N*M*zIndex; if (A[indexW] == 0) indexW = index;

+    int indexE = xIndex + M*(yIndex+1) + N*M*zIndex; if (A[indexE] == 0) indexE = index;

+    int indexU = xIndex + M*yIndex + N*M*(zIndex-1); if (A[indexU] == 0) indexU = index;

+    int indexD = xIndex + M*yIndex + N*M*(zIndex+1); if (A[indexD] == 0) indexD = index;

+    

+    int indexNW = (xIndex-1) + M*(yIndex-1) + N*M*zIndex;  if (A[indexNW] == 0) indexNW = index;

+    int indexNE = (xIndex-1) + M*(yIndex+1) + N*M*zIndex;  if (A[indexNE] == 0) indexNE = index;

+    int indexWS =  (xIndex+1) + M*(yIndex-1) + N*M*zIndex; if (A[indexWS] == 0) indexWS = index;

+    int indexES = (xIndex+1) + M*(yIndex+1) + N*M*zIndex;  if (A[indexES] == 0) indexES = index;

+    

+    int indexUW = (xIndex-1) + M*(yIndex) + N*M*(zIndex-1); if (A[indexUW] == 0) indexUW = index;

+    int indexUE = (xIndex+1) + M*(yIndex) + N*M*(zIndex-1); if (A[indexUE] == 0) indexUE = index;

+    int indexDW =  (xIndex-1) + M*(yIndex) + N*M*(zIndex+1); if (A[indexDW] == 0) indexDW = index;

+    int indexDE = (xIndex+1) + M*(yIndex) + N*M*(zIndex+1); if (A[indexDE] == 0) indexDE = index;

+    

+    int indexUN = (xIndex) + M*(yIndex-1) + N*M*(zIndex-1);  if (A[indexUN] == 0) indexUN = index;

+    int indexUS = (xIndex) + M*(yIndex+1) + N*M*(zIndex-1);  if (A[indexUS] == 0) indexUS = index;

+    int indexDN =  (xIndex) + M*(yIndex-1) + N*M*(zIndex+1); if (A[indexDN] == 0) indexDN = index;

+    int indexDS = (xIndex) + M*(yIndex+1) + N*M*(zIndex+1);  if (A[indexDS] == 0) indexDS = index;

+    

+    gradX = 0.5f*(A[indexN]-A[indexS]);

+    gradX_sq = gradX*gradX;

+    gradXX = A[indexN] + A[indexS] - 2*A[index];

+    

+    gradY = 0.5f*(A[indexW]-A[indexE]);

+    gradY_sq = gradY*gradY;

+    gradYY = A[indexW] + A[indexE] - 2*A[index];

+    

+    gradZ = 0.5f*(A[indexU]-A[indexD]);

+    gradZ_sq = gradZ*gradZ;

+    gradZZ = A[indexU] + A[indexD] - 2*A[index];

+    

+    gradXY = 0.25f*(A[indexNW] - A[indexNE] - A[indexWS] + A[indexES]);

+    gradXZ = 0.25f*(A[indexUW] - A[indexUE] - A[indexDW] + A[indexDE]);

+    gradYZ = 0.25f*(A[indexUN] - A[indexUS] - A[indexDN] + A[indexDS]);

+    

+    xy_2  = 2.0f*gradX*gradY*gradXY;

+    xyz_1 = 2.0f*gradX*gradZ*gradXZ;

+    xyz_2 = 2.0f*gradY*gradZ*gradYZ;

+    

+    sq_sum =  gradX_sq + gradY_sq + gradZ_sq;

+    

+    if (sq_sum <= epsilon) {

+        V_norm = (gradXX*gradX_sq + gradYY*gradY_sq + gradZZ*gradZ_sq + xy_2 + xyz_1 + xyz_2)/epsilon;

+        V_orth = ((gradY_sq + gradZ_sq)*gradXX + (gradX_sq + gradZ_sq)*gradYY + (gradX_sq + gradY_sq)*gradZZ - xy_2 - xyz_1 - xyz_2)/epsilon;  }

+    else  {

+        V_norm = (gradXX*gradX_sq + gradYY*gradY_sq + gradZZ*gradZ_sq + xy_2 + xyz_1 + xyz_2)/sq_sum;

+        V_orth = ((gradY_sq + gradZ_sq)*gradXX + (gradX_sq + gradZ_sq)*gradYY + (gradX_sq + gradY_sq)*gradZZ - xy_2 - xyz_1 - xyz_2)/sq_sum;  }

+    

+    c = 1;

+    if ((1.0f + sq_sum/sigma) != 0.0f)  {c = 1.0f/(1.0f + sq_sum/sigma);}

+    

+    c_sq = c*c;

+    B[index] =  c_sq*V_norm + c*V_orth;

+}

+

+/******************************************************/

+/********* HOST FUNCTION*************/

+extern "C" void Diff4th_GPU_kernel(float* A, float* B, int N, int M, int Z, float sigma, int iter, float tau, float lambda)

+{

+     int deviceCount = -1; // number of devices

+    cudaGetDeviceCount(&deviceCount);

+    if (deviceCount == 0) {

+        fprintf(stderr, "No CUDA devices found\n");

+        return;

+    }    

+    

+      int BLKXSIZE, BLKYSIZE,BLKZSIZE;

+      float *Ad, *Bd, *Cd;

+      sigma = sigma*sigma;

+    

+    if (Z == 0){

+        // 4th order diffusion for 2D case     

+        BLKXSIZE = 8;

+        BLKYSIZE = 16;

+        

+        dim3 dimBlock(BLKXSIZE,BLKYSIZE);

+        dim3 dimGrid(idivup(N,BLKXSIZE), idivup(M,BLKYSIZE));

+        

+        checkCudaErrors(cudaMalloc((void**)&Ad,N*M*sizeof(float)));

+        checkCudaErrors(cudaMalloc((void**)&Bd,N*M*sizeof(float)));

+        checkCudaErrors(cudaMalloc((void**)&Cd,N*M*sizeof(float)));

+        

+        checkCudaErrors(cudaMemcpy(Ad,A,N*M*sizeof(float),cudaMemcpyHostToDevice));

+        checkCudaErrors(cudaMemcpy(Bd,A,N*M*sizeof(float),cudaMemcpyHostToDevice));

+        checkCudaErrors(cudaMemcpy(Cd,A,N*M*sizeof(float),cudaMemcpyHostToDevice));

+        

+        int n = 1;

+        while (n <= iter) {

+            Diff4th2D<<<dimGrid,dimBlock>>>(Bd, Cd, N, M, sigma, iter, tau);

+            cudaDeviceSynchronize();

+            checkCudaErrors( cudaPeekAtLastError() );

+            Diff4th2D_derriv<<<dimGrid,dimBlock>>>(Cd, Bd, Ad, N, M, sigma, iter, tau, lambda);

+            cudaDeviceSynchronize();

+            checkCudaErrors( cudaPeekAtLastError() );

+            n++;

+        }

+        checkCudaErrors(cudaMemcpy(B,Bd,N*M*sizeof(float),cudaMemcpyDeviceToHost));

+        cudaFree(Ad); cudaFree(Bd); cudaFree(Cd);

+    }

+    

+    if (Z != 0){

+        // 4th order diffusion for 3D case

+        BLKXSIZE = 8;

+        BLKYSIZE = 8;

+        BLKZSIZE = 8;        

+        

+        dim3 dimBlock(BLKXSIZE,BLKYSIZE,BLKZSIZE);

+        dim3 dimGrid(idivup(N,BLKXSIZE), idivup(M,BLKYSIZE),idivup(Z,BLKXSIZE));

+        

+        checkCudaErrors(cudaMalloc((void**)&Ad,N*M*Z*sizeof(float)));

+        checkCudaErrors(cudaMalloc((void**)&Bd,N*M*Z*sizeof(float)));

+        checkCudaErrors(cudaMalloc((void**)&Cd,N*M*Z*sizeof(float)));

+        

+        checkCudaErrors(cudaMemcpy(Ad,A,N*M*Z*sizeof(float),cudaMemcpyHostToDevice));

+        checkCudaErrors(cudaMemcpy(Bd,A,N*M*Z*sizeof(float),cudaMemcpyHostToDevice));        

+        checkCudaErrors(cudaMemcpy(Cd,A,N*M*Z*sizeof(float),cudaMemcpyHostToDevice));

+        

+        int n = 1;

+        while (n <= iter) {

+            Diff4th3D<<<dimGrid,dimBlock>>>(Bd, Cd, N, M, Z, sigma, iter, tau);

+            cudaDeviceSynchronize();

+            checkCudaErrors( cudaPeekAtLastError() );

+            Diff4th3D_derriv<<<dimGrid,dimBlock>>>(Cd, Bd, Ad, N, M, Z, sigma, iter, tau, lambda);

+            cudaDeviceSynchronize();

+            checkCudaErrors( cudaPeekAtLastError() );

+            n++;

+        }

+        checkCudaErrors(cudaMemcpy(B,Bd,N*M*Z*sizeof(float),cudaMemcpyDeviceToHost));

+        cudaFree(Ad); cudaFree(Bd); cudaFree(Cd);

+    }

+}
\ No newline at end of file
diff --git a/main_func/regularizers_GPU/Diffus_HO/Diff4th_GPU_kernel.h b/main_func/regularizers_GPU/Diffus_HO/Diff4th_GPU_kernel.h
new file mode 100644
index 0000000..cfbb45a
--- /dev/null
+++ b/main_func/regularizers_GPU/Diffus_HO/Diff4th_GPU_kernel.h
@@ -0,0 +1,6 @@
+#ifndef __DIFF_HO_H_
+#define __DIFF_HO_H_
+
+extern "C" void Diff4th_GPU_kernel(float* A, float* B, int N, int M, int Z, float sigma, int iter, float tau, float lambda);
+
+#endif 
diff --git a/main_func/regularizers_GPU/NL_Regul/NLM_GPU.cpp b/main_func/regularizers_GPU/NL_Regul/NLM_GPU.cpp
new file mode 100644
index 0000000..ff0cc90
--- /dev/null
+++ b/main_func/regularizers_GPU/NL_Regul/NLM_GPU.cpp
@@ -0,0 +1,171 @@
+#include "mex.h"

+#include <matrix.h>

+#include <math.h>

+#include <stdlib.h>

+#include <memory.h>

+#include <stdio.h>

+#include <iostream>

+#include "NLM_GPU_kernel.h"

+

+/* CUDA implementation of the patch-based (PB) regularization  for 2D and 3D images/volumes  

+ * This method finds self-similar patches in data and performs one fixed point iteration to mimimize the PB penalty function

+ * 

+ * References: 1. Yang Z. & Jacob M. "Nonlocal Regularization of Inverse Problems"

+ *             2. Kazantsev D. at. all "4D-CT reconstruction with unified spatial-temporal patch-based regularization"

+ *

+ * Input Parameters (mandatory):

+ * 1. Image/volume (2D/3D)

+ * 2. ratio of the searching window (e.g. 3 = (2*3+1) = 7 pixels window)

+ * 3. ratio of the similarity window (e.g. 1 = (2*1+1) = 3 pixels window)

+ * 4. h - parameter for the PB penalty function

+ * 5. lambda - regularization parameter 

+

+ * Output:

+ * 1. regularized (denoised) Image/volume (N x N x N)

+ *

+ * In matlab check what kind of GPU you have with "gpuDevice" command,

+ * then set your ComputeCapability, here I use -arch compute_35

+ *

+ * Quick 2D denoising example in Matlab:   

+   Im = double(imread('lena_gray_256.tif'))/255;  % loading image

+   u0 = Im + .03*randn(size(Im)); u0(u0<0) = 0; % adding noise

+   ImDen = NLM_GPU(single(u0), 3, 2, 0.15, 1);

+ 

+ * Linux/Matlab compilation:

+ * compile in terminal: nvcc -Xcompiler -fPIC -shared -o NLM_GPU_kernel.o NLM_GPU_kernel.cu

+ * then compile in Matlab: mex -I/usr/local/cuda-7.5/include -L/usr/local/cuda-7.5/lib64 -lcudart NLM_GPU.cpp NLM_GPU_kernel.o

+ *

+ * D. Kazantsev 

+ * 2014-17

+ * Harwell/Manchester UK

+ */

+

+float pad_crop(float *A, float *Ap, int OldSizeX, int OldSizeY,  int OldSizeZ, int NewSizeX, int NewSizeY, int NewSizeZ, int padXY, int switchpad_crop);

+

+void mexFunction(

+        int nlhs, mxArray *plhs[],

+        int nrhs, const mxArray *prhs[])

+{

+    int N, M, Z, i_n, j_n, k_n, numdims, SearchW, SimilW, SearchW_real, padXY, newsizeX, newsizeY, newsizeZ, switchpad_crop, count, SearchW_full, SimilW_full;

+    const int  *dims;

+    float *A, *B=NULL, *Ap=NULL, *Bp=NULL, *Eucl_Vec, h, h2, lambda, val, denh2;

+    

+    numdims = mxGetNumberOfDimensions(prhs[0]);

+    dims = mxGetDimensions(prhs[0]);

+    

+    N = dims[0];

+    M = dims[1];

+    Z = dims[2];

+    

+    if ((numdims < 2) || (numdims > 3)) {mexErrMsgTxt("The input should be 2D image or 3D volume");}

+    if (mxGetClassID(prhs[0]) != mxSINGLE_CLASS) {mexErrMsgTxt("The input in single precision is required"); }

+    

+    if(nrhs != 5) mexErrMsgTxt("Five inputs reqired: Image(2D,3D), SearchW, SimilW, Threshold, Regularization parameter");

+    

+    /*Handling inputs*/

+    A  = (float *) mxGetData(prhs[0]);    /* the image to regularize/filter */

+    SearchW_real  = (int) mxGetScalar(prhs[1]); /* the searching window ratio */

+    SimilW =  (int) mxGetScalar(prhs[2]);  /* the similarity window ratio */

+    h =  (float) mxGetScalar(prhs[3]);  /* parameter for the PB filtering function */

+    lambda = (float) mxGetScalar(prhs[4]);

+    

+    if (h <= 0) mexErrMsgTxt("Parmeter for the PB penalty function should be > 0");

+      

+    SearchW = SearchW_real + 2*SimilW;

+    

+    SearchW_full = 2*SearchW + 1; /* the full searching window  size */

+    SimilW_full = 2*SimilW + 1;   /* the full similarity window  size */

+    h2 = h*h;

+    

+    padXY = SearchW + 2*SimilW; /* padding sizes */

+    newsizeX = N + 2*(padXY); /* the X size of the padded array */

+    newsizeY = M + 2*(padXY); /* the Y size of the padded array */

+    newsizeZ = Z + 2*(padXY); /* the Z size of the padded array */

+    int N_dims[] = {newsizeX, newsizeY, newsizeZ};

+    

+    /******************************2D case ****************************/

+    if (numdims == 2) {

+        /*Handling output*/

+        B = (float*)mxGetData(plhs[0] = mxCreateNumericMatrix(N, M, mxSINGLE_CLASS, mxREAL));

+        /*allocating memory for the padded arrays */

+        Ap = (float*)mxGetData(mxCreateNumericMatrix(newsizeX, newsizeY, mxSINGLE_CLASS, mxREAL));

+        Bp = (float*)mxGetData(mxCreateNumericMatrix(newsizeX, newsizeY, mxSINGLE_CLASS, mxREAL));

+        Eucl_Vec = (float*)mxGetData(mxCreateNumericMatrix(SimilW_full*SimilW_full, 1, mxSINGLE_CLASS, mxREAL));

+        

+        /*Gaussian kernel */

+        count = 0;

+        for(i_n=-SimilW; i_n<=SimilW; i_n++) {

+            for(j_n=-SimilW; j_n<=SimilW; j_n++) {

+                val = (float)(i_n*i_n + j_n*j_n)/(2*SimilW*SimilW);

+                Eucl_Vec[count] = exp(-val);

+                count = count + 1;

+            }} /*main neighb loop */

+        

+        /**************************************************************************/

+        /*Perform padding of image A to the size of [newsizeX * newsizeY] */

+        switchpad_crop = 0; /*padding*/

+        pad_crop(A, Ap, M, N, 0, newsizeY, newsizeX, 0, padXY, switchpad_crop);

+        

+        /* Do PB regularization with the padded array  */

+        NLM_GPU_kernel(Ap, Bp, Eucl_Vec, newsizeY, newsizeX, 0, numdims, SearchW, SimilW, SearchW_real, (float)h2, (float)lambda);

+        

+        switchpad_crop = 1; /*cropping*/

+        pad_crop(Bp, B, M, N, 0, newsizeY, newsizeX, 0, padXY, switchpad_crop);

+    }

+    else

+    {

+        /******************************3D case ****************************/

+        /*Handling output*/

+        B = (float*)mxGetPr(plhs[0] = mxCreateNumericArray(3, dims, mxSINGLE_CLASS, mxREAL));

+        /*allocating memory for the padded arrays */

+        Ap = (float*)mxGetPr(mxCreateNumericArray(3, N_dims, mxSINGLE_CLASS, mxREAL));

+        Bp = (float*)mxGetPr(mxCreateNumericArray(3, N_dims, mxSINGLE_CLASS, mxREAL));

+        Eucl_Vec = (float*)mxGetData(mxCreateNumericMatrix(SimilW_full*SimilW_full*SimilW_full, 1, mxSINGLE_CLASS, mxREAL));

+        

+        /*Gaussian kernel */

+        count = 0;

+        for(i_n=-SimilW; i_n<=SimilW; i_n++) {

+            for(j_n=-SimilW; j_n<=SimilW; j_n++) {

+                for(k_n=-SimilW; k_n<=SimilW; k_n++) {

+                    val = (float)(i_n*i_n + j_n*j_n + k_n*k_n)/(2*SimilW*SimilW*SimilW);

+                    Eucl_Vec[count] = exp(-val);

+                    count = count + 1;

+                }}} /*main neighb loop */

+        /**************************************************************************/

+        /*Perform padding of image A to the size of [newsizeX * newsizeY * newsizeZ] */

+        switchpad_crop = 0; /*padding*/

+        pad_crop(A, Ap, M, N, Z, newsizeY, newsizeX, newsizeZ, padXY, switchpad_crop);

+        

+        /* Do PB regularization with the padded array  */

+        NLM_GPU_kernel(Ap, Bp, Eucl_Vec, newsizeY, newsizeX, newsizeZ, numdims, SearchW, SimilW, SearchW_real, (float)h2, (float)lambda);

+        

+        switchpad_crop = 1; /*cropping*/

+        pad_crop(Bp, B, M, N, Z, newsizeY, newsizeX, newsizeZ, padXY, switchpad_crop);

+    } /*end else ndims*/

+}

+

+float pad_crop(float *A, float *Ap, int OldSizeX, int OldSizeY, int OldSizeZ, int NewSizeX, int NewSizeY, int NewSizeZ, int padXY, int switchpad_crop)

+{

+    /* padding-cropping function */

+    int i,j,k;    

+    if (NewSizeZ > 1) {    

+           for (i=0; i < NewSizeX; i++) {

+            for (j=0; j < NewSizeY; j++) {

+              for (k=0; k < NewSizeZ; k++) {

+                if (((i >= padXY) && (i < NewSizeX-padXY)) &&  ((j >= padXY) && (j < NewSizeY-padXY)) &&  ((k >= padXY) && (k < NewSizeZ-padXY))) {

+                    if (switchpad_crop == 0)  Ap[NewSizeX*NewSizeY*k + i*NewSizeY+j] = A[OldSizeX*OldSizeY*(k - padXY) + (i-padXY)*(OldSizeY)+(j-padXY)];

+                    else  Ap[OldSizeX*OldSizeY*(k - padXY) + (i-padXY)*(OldSizeY)+(j-padXY)] = A[NewSizeX*NewSizeY*k + i*NewSizeY+j];

+                }

+            }}}   

+    }

+    else {

+        for (i=0; i < NewSizeX; i++) {

+            for (j=0; j < NewSizeY; j++) {

+                if (((i >= padXY) && (i < NewSizeX-padXY)) &&  ((j >= padXY) && (j < NewSizeY-padXY))) {

+                    if (switchpad_crop == 0)  Ap[i*NewSizeY+j] = A[(i-padXY)*(OldSizeY)+(j-padXY)];

+                    else  Ap[(i-padXY)*(OldSizeY)+(j-padXY)] = A[i*NewSizeY+j];

+                }

+            }}

+    }

+    return *Ap;

+}
\ No newline at end of file
diff --git a/main_func/regularizers_GPU/NL_Regul/NLM_GPU_kernel.cu b/main_func/regularizers_GPU/NL_Regul/NLM_GPU_kernel.cu
new file mode 100644
index 0000000..17da3a8
--- /dev/null
+++ b/main_func/regularizers_GPU/NL_Regul/NLM_GPU_kernel.cu
@@ -0,0 +1,239 @@
+#include <stdio.h>

+#include <stdlib.h>

+#include <memory.h>

+#include "NLM_GPU_kernel.h"

+

+#define checkCudaErrors(err)           __checkCudaErrors (err, __FILE__, __LINE__)

+

+inline void __checkCudaErrors(cudaError err, const char *file, const int line)

+{

+    if (cudaSuccess != err)

+    {

+        fprintf(stderr, "%s(%i) : CUDA Runtime API error %d: %s.\n",

+                file, line, (int)err, cudaGetErrorString(err));

+        exit(EXIT_FAILURE);

+    }

+}

+

+extern __shared__ float sharedmem[];

+

+// run PB den kernel here

+__global__ void NLM_kernel(float *Ad, float* Bd, float *Eucl_Vec_d, int N, int M, int Z, int SearchW, int SimilW, int SearchW_real, int SearchW_full, int SimilW_full, int padXY, float h2, float lambda,  dim3 imagedim, dim3 griddim, dim3 kerneldim, dim3 sharedmemdim, int nUpdatePerThread, float neighborsize)

+{

+    

+    int  i1, j1, k1, i2, j2, k2, i3, j3, k3, i_l, j_l, k_l, count;

+    float value, Weight_norm, normsum, Weight;

+    

+    int bidx = blockIdx.x;

+    int bidy = blockIdx.y%griddim.y;

+    int bidz = (int)((blockIdx.y)/griddim.y);

+    

+    // global index for block endpoint

+    int beidx = __mul24(bidx,blockDim.x);

+    int beidy = __mul24(bidy,blockDim.y);

+    int beidz = __mul24(bidz,blockDim.z);

+    

+    int tid = __mul24(threadIdx.z,__mul24(blockDim.x,blockDim.y)) +

+            __mul24(threadIdx.y,blockDim.x) + threadIdx.x;

+    

+    #ifdef __DEVICE_EMULATION__

+            printf("tid : %d", tid);

+    #endif

+            

+    // update shared memory

+    int nthreads = blockDim.x*blockDim.y*blockDim.z;

+    int sharedMemSize = sharedmemdim.x * sharedmemdim.y * sharedmemdim.z;

+    for(int i=0; i<nUpdatePerThread; i++)

+    {

+        int sid = tid + i*nthreads; // index in shared memory

+        if (sid < sharedMemSize)

+        {

+            // global x/y/z index in volume

+            int gidx, gidy, gidz;

+            int sidx, sidy, sidz, tid;

+            

+            sidz = sid / (sharedmemdim.x*sharedmemdim.y);

+            tid  = sid - sidz*(sharedmemdim.x*sharedmemdim.y);

+            sidy = tid / (sharedmemdim.x);

+            sidx = tid - sidy*(sharedmemdim.x);

+            

+            gidx = (int)sidx - (int)kerneldim.x + (int)beidx;

+            gidy = (int)sidy - (int)kerneldim.y + (int)beidy;

+            gidz = (int)sidz - (int)kerneldim.z + (int)beidz;

+            

+            // Neumann boundary condition

+            int cx = (int) min(max(0,gidx),imagedim.x-1);

+            int cy = (int) min(max(0,gidy),imagedim.y-1);

+            int cz = (int) min(max(0,gidz),imagedim.z-1);

+            

+            int gid = cz*imagedim.x*imagedim.y + cy*imagedim.x + cx;

+            

+            sharedmem[sid] = Ad[gid];

+        }

+    }

+    __syncthreads();

+    

+    // global index of the current voxel in the input volume

+    int idx = beidx + threadIdx.x;

+    int idy = beidy + threadIdx.y;

+    int idz = beidz + threadIdx.z;

+    

+    if (Z == 1) {

+        /* 2D case */

+        /*checking boundaries to be within the image and avoid padded spaces */

+        if( idx >= padXY && idx < (imagedim.x - padXY) &&

+                idy >= padXY && idy < (imagedim.y - padXY))

+        {

+            int i_centr = threadIdx.x + (SearchW); /*indices of the centrilized (main) pixel */

+            int j_centr = threadIdx.y + (SearchW); /*indices of the centrilized (main) pixel */

+            

+            if ((i_centr > 0) && (i_centr < N) && (j_centr > 0) && (j_centr < M)) {

+                

+                Weight_norm = 0; value = 0.0;

+                /* Massive Search window loop */

+                for(i1 = i_centr - SearchW_real ; i1 <= i_centr + SearchW_real; i1++) {

+                    for(j1 = j_centr - SearchW_real ; j1<= j_centr + SearchW_real ; j1++) {

+                        /* if inside the searching window */

+                        count = 0; normsum = 0.0;

+                        for(i_l=-SimilW; i_l<=SimilW; i_l++) {

+                            for(j_l=-SimilW; j_l<=SimilW; j_l++) {

+                                i2 = i1+i_l; j2 = j1+j_l;

+                                i3 = i_centr+i_l; j3 = j_centr+j_l;  /*coordinates of the inner patch loop */                                

+                                if ((i2 > 0) && (i2 < N) && (j2 > 0) && (j2 < M)) {

+                                       if ((i3 > 0) && (i3 < N) && (j3 > 0) && (j3 < M)) {

+                                            normsum += Eucl_Vec_d[count]*pow((sharedmem[(j3)*sharedmemdim.x+(i3)] - sharedmem[j2*sharedmemdim.x+i2]), 2);

+                                            }}

+                                        count++;

+                                }}

+                                if (normsum != 0) Weight = (expf(-normsum/h2));

+                                else Weight = 0.0;

+                                Weight_norm += Weight;

+                                value += sharedmem[j1*sharedmemdim.x+i1]*Weight;

+                            }}      

+                                

+                if (Weight_norm != 0) Bd[idz*imagedim.x*imagedim.y + idy*imagedim.x + idx] = value/Weight_norm;

+                else Bd[idz*imagedim.x*imagedim.y + idy*imagedim.x + idx] = Ad[idz*imagedim.x*imagedim.y + idy*imagedim.x + idx];

+            }

+        }      /*boundary conditions end*/

+    }

+    else {

+        /*3D case*/

+        /*checking boundaries to be within the image and avoid padded spaces */

+        if( idx >= padXY && idx < (imagedim.x - padXY) &&

+                idy >= padXY && idy < (imagedim.y - padXY) &&

+                idz >= padXY && idz < (imagedim.z - padXY) )

+        {

+            int i_centr = threadIdx.x + SearchW; /*indices of the centrilized (main) pixel */

+            int j_centr = threadIdx.y + SearchW; /*indices of the centrilized (main) pixel */

+            int k_centr = threadIdx.z + SearchW; /*indices of the centrilized (main) pixel */

+            

+            if ((i_centr > 0) && (i_centr < N) && (j_centr > 0) && (j_centr < M) && (k_centr > 0) && (k_centr < Z)) {

+                

+                Weight_norm = 0; value = 0.0;

+                /* Massive Search window loop */

+                for(i1 = i_centr - SearchW_real ; i1 <= i_centr + SearchW_real; i1++) {

+                    for(j1 = j_centr - SearchW_real ; j1<= j_centr + SearchW_real ; j1++) {

+                        for(k1 = k_centr - SearchW_real ; k1<= k_centr + SearchW_real ; k1++) {

+                            /* if inside the searching window */

+                            count = 0; normsum = 0.0;

+                            for(i_l=-SimilW; i_l<=SimilW; i_l++) {

+                                for(j_l=-SimilW; j_l<=SimilW; j_l++) {

+                                    for(k_l=-SimilW; k_l<=SimilW; k_l++) {

+                                        i2 = i1+i_l; j2 = j1+j_l; k2 = k1+k_l;

+                                        i3 = i_centr+i_l; j3 = j_centr+j_l; k3 = k_centr+k_l;   /*coordinates of the inner patch loop */                              

+                                                    if ((i2 > 0) && (i2 < N) && (j2 > 0) && (j2 < M) && (k2 > 0) && (k2 < Z)) {

+                                                        if ((i3 > 0) && (i3 < N) && (j3 > 0) && (j3 < M) && (k3 > 0) && (k3 < Z)) {

+                                                            normsum += Eucl_Vec_d[count]*pow((sharedmem[(k3)*sharedmemdim.x*sharedmemdim.y + (j3)*sharedmemdim.x+(i3)] - sharedmem[(k2)*sharedmemdim.x*sharedmemdim.y + j2*sharedmemdim.x+i2]), 2);

+                                                        }}

+                                                    count++;

+                                                }}}

+                                       if (normsum != 0) Weight = (expf(-normsum/h2));

+                                       else Weight = 0.0;

+                                       Weight_norm += Weight;

+                                       value += sharedmem[k1*sharedmemdim.x*sharedmemdim.y + j1*sharedmemdim.x+i1]*Weight;                                                                

+                        }}}      /* BIG search window loop end*/

+                

+               

+                if (Weight_norm != 0) Bd[idz*imagedim.x*imagedim.y + idy*imagedim.x + idx] = value/Weight_norm;

+                else Bd[idz*imagedim.x*imagedim.y + idy*imagedim.x + idx] = Ad[idz*imagedim.x*imagedim.y + idy*imagedim.x + idx];

+            }

+        }      /* boundary conditions end */

+    }

+}

+        

+/////////////////////////////////////////////////

+// HOST FUNCTION

+extern "C" void NLM_GPU_kernel(float *A, float* B, float *Eucl_Vec, int N, int M, int Z, int dimension, int SearchW, int SimilW, int SearchW_real, float h2, float lambda)

+{

+    int deviceCount = -1; // number of devices

+    cudaGetDeviceCount(&deviceCount);

+    if (deviceCount == 0) {

+        fprintf(stderr, "No CUDA devices found\n");

+        return;

+    }

+    

+//     cudaDeviceReset();

+    

+    int padXY, SearchW_full, SimilW_full,  blockWidth, blockHeight, blockDepth, nBlockX, nBlockY, nBlockZ, kernel_depth;

+    float *Ad, *Bd, *Eucl_Vec_d;

+    

+    if (dimension == 2) {

+        blockWidth  = 16;

+        blockHeight = 16;

+        blockDepth  = 1;

+        Z = 1;

+        kernel_depth = 0;

+    }

+    else {

+        blockWidth  = 8;

+        blockHeight = 8;

+        blockDepth  = 8;

+        kernel_depth = SearchW;

+    }

+    

+    // compute how many blocks are needed

+    nBlockX = ceil((float)N / (float)blockWidth);

+    nBlockY = ceil((float)M / (float)blockHeight);

+    nBlockZ = ceil((float)Z / (float)blockDepth);

+    

+    dim3 dimGrid(nBlockX,nBlockY*nBlockZ);

+    dim3 dimBlock(blockWidth, blockHeight, blockDepth);

+    dim3 imagedim(N,M,Z);

+    dim3 griddim(nBlockX,nBlockY,nBlockZ);

+    

+    dim3 kerneldim(SearchW,SearchW,kernel_depth);

+    dim3 sharedmemdim((SearchW*2)+blockWidth,(SearchW*2)+blockHeight,(kernel_depth*2)+blockDepth);

+    int sharedmemsize = sizeof(float)*sharedmemdim.x*sharedmemdim.y*sharedmemdim.z;

+    int updateperthread = ceil((float)(sharedmemdim.x*sharedmemdim.y*sharedmemdim.z)/(float)(blockWidth*blockHeight*blockDepth));

+    float neighborsize = (2*SearchW+1)*(2*SearchW+1)*(2*kernel_depth+1);

+    

+    padXY = SearchW + 2*SimilW; /* padding sizes */

+    

+    SearchW_full = 2*SearchW + 1; /* the full searching window  size */

+    SimilW_full = 2*SimilW + 1;   /* the full similarity window  size */

+    

+    /*allocate space for images on device*/

+    checkCudaErrors( cudaMalloc((void**)&Ad,N*M*Z*sizeof(float)) );

+    checkCudaErrors( cudaMalloc((void**)&Bd,N*M*Z*sizeof(float)) );

+    /*allocate space for vectors on device*/

+    if (dimension == 2) {

+        checkCudaErrors( cudaMalloc((void**)&Eucl_Vec_d,SimilW_full*SimilW_full*sizeof(float)) );

+        checkCudaErrors( cudaMemcpy(Eucl_Vec_d,Eucl_Vec,SimilW_full*SimilW_full*sizeof(float),cudaMemcpyHostToDevice) );

+    }

+    else {

+        checkCudaErrors( cudaMalloc((void**)&Eucl_Vec_d,SimilW_full*SimilW_full*SimilW_full*sizeof(float)) );

+        checkCudaErrors( cudaMemcpy(Eucl_Vec_d,Eucl_Vec,SimilW_full*SimilW_full*SimilW_full*sizeof(float),cudaMemcpyHostToDevice) );

+    }

+    

+    /* copy data from the host to device */

+    checkCudaErrors( cudaMemcpy(Ad,A,N*M*Z*sizeof(float),cudaMemcpyHostToDevice) );

+    

+    // Run CUDA kernel here

+    NLM_kernel<<<dimGrid,dimBlock,sharedmemsize>>>(Ad, Bd, Eucl_Vec_d, M, N, Z, SearchW, SimilW, SearchW_real, SearchW_full, SimilW_full, padXY, h2, lambda, imagedim, griddim, kerneldim, sharedmemdim, updateperthread, neighborsize);

+    

+    checkCudaErrors( cudaPeekAtLastError() );

+//     gpuErrchk( cudaDeviceSynchronize() );

+    

+    checkCudaErrors( cudaMemcpy(B,Bd,N*M*Z*sizeof(float),cudaMemcpyDeviceToHost) );

+    cudaFree(Ad); cudaFree(Bd); cudaFree(Eucl_Vec_d);

+}

diff --git a/main_func/regularizers_GPU/NL_Regul/NLM_GPU_kernel.h b/main_func/regularizers_GPU/NL_Regul/NLM_GPU_kernel.h
new file mode 100644
index 0000000..bc9d4a3
--- /dev/null
+++ b/main_func/regularizers_GPU/NL_Regul/NLM_GPU_kernel.h
@@ -0,0 +1,6 @@
+#ifndef __NLMREG_KERNELS_H_
+#define __NLMREG_KERNELS_H_
+
+extern "C" void NLM_GPU_kernel(float *A, float* B, float *Eucl_Vec, int N, int M, int Z, int dimension, int SearchW, int SimilW, int SearchW_real, float denh2, float lambda);
+
+#endif