diff --git a/AugmentedInSilico/Fig3b_silicoaug_RSULM.m b/AugmentedInSilico/Fig3b_silicoaug_RSULM.m
new file mode 100644
index 0000000000000000000000000000000000000000..7bebc6c0c5cc6a9821153d8371ecad17a0bdea87
--- /dev/null
+++ b/AugmentedInSilico/Fig3b_silicoaug_RSULM.m
@@ -0,0 +1,167 @@
+%% silicoaug_RSULM.m 
+% 
+%
+% Based on the code created by Arthur Chavignon
+% Adapted for the Augmented in Silico Data.
+%
+% DATE 2020.12.17 - VERSION 1.1
+% AUTHORS: Arthur Chavignon, Baptiste Heiles, Vincent Hingot. CNRS, Sorbonne Universite, INSERM.
+% Laboratoire d'Imagerie Biomedicale, Team PPM. 15 rue de l'Ecole de Medecine, 75006, Paris
+% Code Available under Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (see https://creativecommons.org/licenses/by-nc-sa/4.0/)
+% ACADEMIC REFERENCES TO BE CITED
+% Details of the code in the article by Heiles, Chavignon, Hingot, Lopez, Teston and Couture.  
+% Performance benchmarking of microbubble-localization algorithms for ultrasound localization microscopy, Nature Biomedical Engineering, 2021.
+% General description of super-resolution in: Couture et al., Ultrasound localization microscopy and super-resolution: A state of the art, IEEE UFFC 2018
+
+clear
+%cd ./..
+%cd('PALA_silico');
+
+PALA_folder = fileparts(pwd); % location of the PALA folder
+% DEFINE THE ADDONS DIRECTORY ON YOUR COMPUTER
+addpath(genpath(fullfile(PALA_folder, 'PALA_addons')));
+
+%% Data parameters
+% A few parameters must be provided by the user depending of your input images (size of pixel, wavelength)
+% These parameters will be copied and used later during the creation of the ULM structure.
+% in this example, UF.TwFreq = 15MHz, UF.FrameRateUF = 1000Hz;
+UF.TwFreq = 14.8;
+UF.FrameRateUF = 1000;
+SR = 10;
+% Here you put the size of your data
+SizeOfBloc = [SR*84 SR*143 1000]; 
+
+% Here you put the size of pixel in the prefered unit. It can be um, mm, m, wavelength, or an arbitrary scale.
+ScaleOfPixel = [1 1];               % [pixel_size_z, pixel_size_x]
+
+% The imaging frame rate is required for velocity calculation, and temporal filtering.
+framerate = 500;          % imaging framerate in [Hz]
+
+% Number of blocs to process
+Nbuffers = 5;          % number of bloc to process (used in the parfor)
+
+% If pixel sizes are in wavelength, lambda must be provided for a velocity maps in mm/s,
+lambda = 0.09856;
+
+%% ULM parameters
+% this script can be run using different scaling, it can be wavelength, pixel size, mm, um.
+% In this example, input pixel are isotropic and equal to lambda (pixelPitch_x = pixelPitch_y = lambda)
+% All size defined later are expressed in lambda
+
+res = SR; 
+
+ULM = struct('numberOfParticles', 120,...  % Number of particles per frame. (30-100)
+    'size',[SizeOfBloc(1) SizeOfBloc(2) SizeOfBloc(3)],... % size of input data [nb_pixel_z nb_pixel_x nb_frame_per_bloc]
+    'scale',[ScaleOfPixel 1/framerate],...% Scale [z x dt], size of pixel in the scaling unit. (here, pixsize = 1*lambda)
+    'res',res,...                       % Resolution factor. Typically 10 for final image rendering at lambda/10.
+    'SVD_cutoff',[10 SizeOfBloc(3)],...  % SVD filtering, to be adapted to your clutter/SNR levels
+    'max_linking_distance',2,...        % Maximum linking distance between two frames to reject pairing, in pixels units (UF.scale(1)). (2-4 pixel).
+    'min_length', 15,...                % Minimum allowed length of the tracks in time. (5-20 frames)
+    'fwhm',[1 1]*3,...                  % Size [pixel] of the mask for localization. (3x3 for pixel at lambda, 5x5 at lambda/2). [fmwhz fmwhx]
+    'max_gap_closing', 0,...            % Allowed gap in microbubbles' pairing. (if you want to skip frames 0)
+    'interp_factor',1/res,...           % Interpfactor (decimation of tracks)
+    'LocMethod','Radial'...             % Select localization algorithm (WA,Interp,Radial,CurveFitting,NoLocalization)
+    );
+% ULM.ButterCuttofFreq = [50 249];        % Cutoff frequency (Hz) for additional filter. Typically [20 300] at 1kHz.
+ULM.parameters.NLocalMax = 3;           % Safeguard on the number of maxLocal in the fwhm*fwhm grid (3 for fwhm=3, 7 for fwhm=5)
+% [but_b,but_a] = butter(2,ULM.ButterCuttofFreq/(framerate/2),'bandpass');
+ULM.lambda = lambda;
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Load data and localize microbubbles %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+Track_tot = {};
+fprintf('--- ULM PROCESSING --- \n\n');t1=tic;
+SNR = '_20dB' 
+for hhh = 1:Nbuffers 
+    fprintf('Processing bloc %d/%d\n',hhh,Nbuffers);
+
+    % Load IQ data 
+    tmp = load(strcat(pwd,'/SilicoData',SNR,'/SilicoAug',int2str(hhh),'.mat'),'SilicoAug');
+    
+    % Filtering of IQ to remove clutter (optional)
+    IQ_filt = SVDfilter(tmp.SilicoAug,ULM.SVD_cutoff);tmp = [];
+
+    % Temporal filtering
+    % Removes MBs in the in Silico Data !
+    % IQ_filt = filter(but_b,but_a,IQ_filt,[],3); %(optional)
+    % IQ_filt(~isfinite(IQ_filt))=0;
+
+    % Detection and localization process (return a list of coordinates in pixel)
+    [MatTracking] = ULM_localization2D(abs(IQ_filt),ULM); IQ_filt=[];
+    % Convert pixel into isogrid (pixel are not necessary isometric);
+    MatTracking(:,2:3) = (MatTracking(:,2:3) - [1 1]).*ULM.scale(1:2);
+
+    save(strcat(pwd,'/SilicoData',SNR,'/Result/RSMatTrack',int2str(hhh),'.mat'),'MatTracking') 
+
+    % Tracking algorithm (list of tracks)
+    Track_tot_i = ULM_tracking2D(MatTracking,ULM);
+
+    % Saving part:
+    %--- if for, you can save tracks at each loop to avoid RAM out of memory
+    % save([workingdir filesep filename '_tracks' num2str(hhh,'%.3d') '.mat'],'Track_tot_i','ULM') %
+    %--- if parfor you can cat all tracks in a huge cells variable
+    Track_tot{hhh} = Track_tot_i;
+    Track_tot_i={};MatTracking = [];
+end
+Track_tot = cat(1,Track_tot{:});
+Tend = toc(t1);disp('Done')
+fprintf('ULM done in %d hours %.1f minutes.\n', floor(Tend/60/60), rem(Tend/60,60));
+
+
+%% Create individual variable to save using v6 version.
+% By cutting Tracks into different variables small than 2GB, the save v6 is faster than save v7.3
+% CutTracks = round(linspace(1,numel(Track_tot),4));
+% Track_tot_1 = Track_tot(CutTracks(1):CutTracks(2)-1);
+% Track_tot_2 = Track_tot(CutTracks(2):CutTracks(3)-1);
+% Track_tot_3 = Track_tot(CutTracks(3):end);
+% save(['example_tracks.mat'],'Track_tot_1','Track_tot_2','Track_tot_3','Tend','ULM','-v6')
+% clear Track_tot_1 Track_tot_2 Track_tot_3
+
+% load([workingdir filesep filename 'example_tracks.mat'])
+% Track_tot = cat(1,Track_tot_1,Track_tot_2,Track_tot_3);clear Track_tot_1 Track_tot_2 Track_tot_3
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Create MatOut %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% create the MatOut density with interpolated tracks for visual analysis, and with non interpolated tracks for aliasing index calculation.
+% Define the size of SRpixel for displaying (default 10)
+ULM.SRscale = ULM.scale(1)/ULM.res;
+ULM.SRsize = round(ULM.size(1:2).*ULM.scale(1:2)/ULM.SRscale); %
+
+% Convert tracks into SRpixel
+Track_matout = cellfun(@(x) (x(:,[1 2 3 4])+[1 1 0 0]*1)./[ULM.SRscale ULM.SRscale 1 1],Track_tot,'UniformOutput',0);
+llz = [0:ULM.SRsize(1)]*ULM.SRscale;llx = [0:ULM.SRsize(2)]*ULM.SRscale;
+
+%% Accumulate tracks on the final MatOut grid.
+fprintf('--- CREATING MATOUTS --- \n\n')
+MatOut = ULM_Track2MatOut(Track_matout,ULM.SRsize+[1 1]*1); %pos in superpix [z x]
+% MatOut_zdir = ULM_Track2MatOut(Track_matout,ULM.SRsize+[1 1]*1,'mode','2D_vel_z'); %pos in superpix [z x]
+% MatOut_vel = ULM_Track2MatOut(Track_matout,ULM.SRsize+[1 1]*1,'mode','2D_velnorm'); %pos in superpix [z x]
+% MatOut_vel = MatOut_vel*ULM.lambda; % Convert into [mm/s]
+
+save(strcat(pwd,'/SilicoData',SNR,'/Result/RSULMSilico10.mat'),'MatOut','ULM','lambda','llx','llz') %,'MatOut_zdir','MatOut_vel',
+
+MatOutGT = load('MatOutGT.mat', 'MatOut').MatOut;
+
+crossCorrMatrix = normxcorr2(MatOut,MatOutGT);
+[maxCorr, maxIndex] = max(abs(crossCorrMatrix(:)));
+[yPeak, xPeak] = ind2sub(size(crossCorrMatrix), maxIndex);
+
+xOffset = xPeak - size(MatOutGT, 2);
+yOffset = yPeak - size(MatOutGT, 1);
+
+MatOut = circshift(MatOut,[yOffset xOffset]);
+
+figure('WindowState', 'maximized');
+imagesc(log(MatOutGT+0.5));
+axis image
+colormap hot
+brighten(0.2);
+set(gca,'XColor', 'none','YColor','none')
+set(gca, 'color', 'none');
+
+figure('WindowState', 'maximized');
+imagesc(log(MatOut+0.5));
+axis image
+colormap hot
+brighten(0.2);
+set(gca,'XColor', 'none','YColor','none')
+set(gca, 'color', 'none');
diff --git a/AugmentedInSilico/Fig3c_silicoaug_SRPCA.m b/AugmentedInSilico/Fig3c_silicoaug_SRPCA.m
new file mode 100644
index 0000000000000000000000000000000000000000..0e743022ffd1445707cf38da5875077f6e9df351
--- /dev/null
+++ b/AugmentedInSilico/Fig3c_silicoaug_SRPCA.m
@@ -0,0 +1,173 @@
+%% silicoaug_SRPCA.m 
+% 
+%
+% Based on the code created by Arthur Chavignon
+% Adapted for the Augmented in Silico Data.
+%
+% DATE 2020.12.17 - VERSION 1.1
+% AUTHORS: Arthur Chavignon, Baptiste Heiles, Vincent Hingot. CNRS, Sorbonne Universite, INSERM.
+% Laboratoire d'Imagerie Biomedicale, Team PPM. 15 rue de l'Ecole de Medecine, 75006, Paris
+% Code Available under Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (see https://creativecommons.org/licenses/by-nc-sa/4.0/)
+% ACADEMIC REFERENCES TO BE CITED
+% Details of the code in the article by Heiles, Chavignon, Hingot, Lopez, Teston and Couture.  
+% Performance benchmarking of microbubble-localization algorithms for ultrasound localization microscopy, Nature Biomedical Engineering, 2021.
+% General description of super-resolution in: Couture et al., Ultrasound localization microscopy and super-resolution: A state of the art, IEEE UFFC 2018
+
+clear
+%cd ./..
+%cd('PALA_silico');
+
+PALA_folder = fileparts(pwd); % location of the PALA folder
+% DEFINE THE ADDONS DIRECTORY ON YOUR COMPUTER
+addpath(genpath(fullfile(PALA_folder, 'PALA_addons')));
+
+%% Data parameters
+% A few parameters must be provided by the user depending of your input images (size of pixel, wavelength)
+% These parameters will be copied and used later during the creation of the ULM structure.
+% in this example, UF.TwFreq = 15MHz, UF.FrameRateUF = 1000Hz;
+UF.TwFreq = 14.8;
+UF.FrameRateUF = 1000;
+SR = 10;
+% Here you put the size of your data
+SizeOfBloc = [SR*84 SR*143 1000]; 
+
+% Here you put the size of pixel in the prefered unit. It can be um, mm, m, wavelength, or an arbitrary scale.
+ScaleOfPixel = [1 1];               % [pixel_size_z, pixel_size_x]
+
+% The imaging frame rate is required for velocity calculation, and temporal filtering.
+framerate = 500;          % imaging framerate in [Hz]
+
+% Number of blocs to process
+Nbuffers = 5;          % number of bloc to process (used in the parfor)
+
+% If pixel sizes are in wavelength, lambda must be provided for a velocity maps in mm/s,
+lambda = 0.09856;
+
+%% ULM parameters
+% this script can be run using different scaling, it can be wavelength, pixel size, mm, um.
+% In this example, input pixel are isotropic and equal to lambda (pixelPitch_x = pixelPitch_y = lambda)
+% All size defined later are expressed in lambda
+
+res = SR; 
+
+ULM = struct('numberOfParticles', 120,...  % Number of particles per frame. (30-100)
+    'size',[SizeOfBloc(1) SizeOfBloc(2) SizeOfBloc(3)],... % size of input data [nb_pixel_z nb_pixel_x nb_frame_per_bloc]
+    'scale',[ScaleOfPixel 1/framerate],...% Scale [z x dt], size of pixel in the scaling unit. (here, pixsize = 1*lambda)
+    'res',res,...                       % Resolution factor. Typically 10 for final image rendering at lambda/10.
+    'SVD_cutoff',[10 SizeOfBloc(3)],...  % SVD filtering, to be adapted to your clutter/SNR levels
+    'max_linking_distance',2,...        % Maximum linking distance between two frames to reject pairing, in pixels units (UF.scale(1)). (2-4 pixel).
+    'min_length', 15,...                % Minimum allowed length of the tracks in time. (5-20 frames)
+    'fwhm',[1 1]*3,...                  % Size [pixel] of the mask for localization. (3x3 for pixel at lambda, 5x5 at lambda/2). [fmwhz fmwhx]
+    'max_gap_closing', 0,...            % Allowed gap in microbubbles' pairing. (if you want to skip frames 0)
+    'interp_factor',1/res,...           % Interpfactor (decimation of tracks)
+    'LocMethod','Radial'...             % Select localization algorithm (WA,Interp,Radial,CurveFitting,NoLocalization)
+    );
+% ULM.ButterCuttofFreq = [50 249];        % Cutoff frequency (Hz) for additional filter. Typically [20 300] at 1kHz.
+ULM.parameters.NLocalMax = 3;           % Safeguard on the number of maxLocal in the fwhm*fwhm grid (3 for fwhm=3, 7 for fwhm=5)
+% [but_b,but_a] = butter(2,ULM.ButterCuttofFreq/(framerate/2),'bandpass');
+ULM.lambda = lambda;
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Load data and localize microbubbles %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+load('RFbUpscaled.mat', 'RFb')
+SNR = '_20dB'
+
+t1=tic;Track_tot = {};
+fprintf('--- ULM PROCESSING --- \n\n');t1=tic;
+
+
+for hhh = 1:Nbuffers 
+    fprintf('Processing bloc %d/%d\n',hhh,Nbuffers);
+
+    % Load IQ data 
+    tmp = load(strcat(pwd,'/SilicoData',SNR,'/SilicoAug',int2str(hhh),'.mat'),'SilicoAug');
+
+    tmp.SilicoAug = imresize(tmp.SilicoAug,SR,"bicubic");
+
+    % Temporal filtering
+    % Removes MBs in the in Silico Data !
+    % tmp.SilicoAug = filter(but_b,but_a,tmp.SilicoAug,[],3); %(optional)
+    % tmp.SilicoAug(~isfinite(tmp.SilicoAug))=0;
+
+    IQ = tmp.SilicoAug/max(abs(tmp.SilicoAug(:)));tmp = [];
+    IQ_filt = SRPCA(IQ, RFb, 1, 20); IQ = [];
+
+    % Detection and localization process (return a list of coordinates in pixel)
+    [MatTracking] = ULM_localization2DSR(abs(IQ_filt),ULM); IQ_filt=[];
+    MatTracking(:,2:3) = MatTracking(:,2:3)/SR;
+    % Convert pixel into isogrid (pixel are not necessary isometric);
+    MatTracking(:,2:3) = (MatTracking(:,2:3) - [1 1]).*ULM.scale(1:2);
+    %save(strcat(pwd,'/SilicoData',SNR,'/Result/SRPCAMatTrack',int2str(hhh),'.mat'),'MatTracking') 
+
+    % Tracking algorithm (list of tracks)
+    Track_tot_i = ULM_tracking2D(MatTracking,ULM);
+
+    % Saving part:
+    %--- if for, you can save tracks at each loop to avoid RAM out of memory
+    % save([workingdir filesep filename '_tracks' num2str(hhh,'%.3d') '.mat'],'Track_tot_i','ULM') %
+    %--- if parfor you can cat all tracks in a huge cells variable
+    Track_tot{hhh} = Track_tot_i;
+    Track_tot_i={};MatTracking = [];
+end
+Track_tot = cat(1,Track_tot{:});
+Tend = toc(t1);disp('Done')
+fprintf('ULM done in %d hours %.1f minutes.\n', floor(Tend/60/60), rem(Tend/60,60));
+
+
+%% Create individual variable to save using v6 version.
+% By cutting Tracks into different variables small than 2GB, the save v6 is faster than save v7.3
+% CutTracks = round(linspace(1,numel(Track_tot),4));
+% Track_tot_1 = Track_tot(CutTracks(1):CutTracks(2)-1);
+% Track_tot_2 = Track_tot(CutTracks(2):CutTracks(3)-1);
+% Track_tot_3 = Track_tot(CutTracks(3):end);
+% save(['example_tracks.mat'],'Track_tot_1','Track_tot_2','Track_tot_3','Tend','ULM','-v6')
+% clear Track_tot_1 Track_tot_2 Track_tot_3
+
+% load([workingdir filesep filename 'example_tracks.mat'])
+% Track_tot = cat(1,Track_tot_1,Track_tot_2,Track_tot_3);clear Track_tot_1 Track_tot_2 Track_tot_3
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Create MatOut %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% create the MatOut density with interpolated tracks for visual analysis, and with non interpolated tracks for aliasing index calculation.
+% Define the size of SRpixel for displaying (default 10)
+ULM.SRscale = ULM.scale(1)/ULM.res;
+ULM.SRsize = round(ULM.size(1:2).*ULM.scale(1:2)); %/ULM.SRscale
+
+% Convert tracks into SRpixel
+Track_matout = cellfun(@(x) (x(:,[1 2 3 4])+[1 1 0 0]*1)./[ULM.SRscale ULM.SRscale 1 1],Track_tot,'UniformOutput',0);
+llz = [0:ULM.SRsize(1)]*ULM.SRscale;llx = [0:ULM.SRsize(2)]*ULM.SRscale;
+
+%% Accumulate tracks on the final MatOut grid.
+fprintf('--- CREATING MATOUTS --- \n\n')
+MatOut = ULM_Track2MatOut(Track_matout,ULM.SRsize+[1 1]*1); %pos in superpix [z x]
+% MatOut_zdir = ULM_Track2MatOut(Track_matout,ULM.SRsize+[1 1]*1,'mode','2D_vel_z'); %pos in superpix [z x]
+% MatOut_vel = ULM_Track2MatOut(Track_matout,ULM.SRsize+[1 1]*1,'mode','2D_velnorm'); %pos in superpix [z x]
+% MatOut_vel = MatOut_vel*ULM.lambda; % Convert into [mm/s]
+
+save(strcat(pwd,'/SilicoData',SNR,'/Result/SRPCASilico10.mat'),'MatOut','ULM','lambda','llx','llz') %,'MatOut_zdir','MatOut_vel',
+
+MatOutGT = load('MatOutGT.mat', 'MatOut').MatOut;
+
+crossCorrMatrix = normxcorr2(MatOut,MatOutGT);
+[maxCorr, maxIndex] = max(abs(crossCorrMatrix(:)));
+[yPeak, xPeak] = ind2sub(size(crossCorrMatrix), maxIndex);
+
+xOffset = xPeak - size(MatOutGT, 2);
+yOffset = yPeak - size(MatOutGT, 1);
+
+MatOut = circshift(MatOut,[yOffset xOffset]);
+
+figure('WindowState', 'maximized');
+imagesc(log(MatOutGT+0.5));
+axis image
+colormap hot
+brighten(0.2);
+set(gca,'XColor', 'none','YColor','none')
+set(gca, 'color', 'none');
+
+figure('WindowState', 'maximized');
+imagesc(log(MatOut+0.5));
+axis image
+colormap hot
+brighten(0.2);
+set(gca,'XColor', 'none','YColor','none')
+set(gca, 'color', 'none');
diff --git a/AugmentedInSilico/MatOutGT.mat b/AugmentedInSilico/MatOutGT.mat
new file mode 100644
index 0000000000000000000000000000000000000000..bb4b711b2f97ee1ab54c16219e14708631780f89
Binary files /dev/null and b/AugmentedInSilico/MatOutGT.mat differ
diff --git a/AugmentedInSilico/RFbUpscaled.mat b/AugmentedInSilico/RFbUpscaled.mat
new file mode 100644
index 0000000000000000000000000000000000000000..d1448b494464b4f89128fbd4033fded8fb3b6a59
Binary files /dev/null and b/AugmentedInSilico/RFbUpscaled.mat differ
diff --git a/AugmentedInSilico/SRPCA.m b/AugmentedInSilico/SRPCA.m
new file mode 100644
index 0000000000000000000000000000000000000000..8f26557a62404520869a99ebb3ca752be2d4ed3d
--- /dev/null
+++ b/AugmentedInSilico/SRPCA.m
@@ -0,0 +1,119 @@
+function x = SRPCA8(S,H,lambda,mu,rho,max_iter)
+
+% Computational Super-Resolved RPCA.
+% Input
+% - S is a 2d+t data matrix (of size m x n x p) to be decomposed
+% - H: Point Spread Function (PSF)
+% - lambda: Sparse regularization parameter, default = 1/sqrt(max(n*m, p))
+% - mu: Low-Rank regularization parameter, default = 10
+% - rho: the augmented lagrangian parameter (convergence), default = 1e-3
+% - max_iter: maximum number of iterations, default = 20
+%
+% Ouput
+% - x is the high resolution blood
+% - T (not returned) is the tissue
+
+    [m, n, p] = size(S);
+    unobserved = isnan(S);
+    S(unobserved) = 0;
+
+   if nargin < 2 
+        H = 1;
+   else
+        H = H / sum(abs(H(:)));
+        [Mh, Nh] = size(H);
+        center = round([Mh, Nh] / 2);
+        H = fft2(circshift(padarray(H, [m - Mh, n - Nh], 'post'), 1 - center));
+   end
+
+  
+   if nargin < 3
+        lambda = 1/sqrt(m*n); 
+   else
+        lambda = lambda/sqrt(m*n);
+   end
+
+   if nargin < 4
+        mu = 10; 
+   end
+
+   if nargin < 5
+        rho = 1e-3;
+   end
+
+   if nargin < 6
+        max_iter = 20;
+   end
+
+
+   rho_max = 1;
+   eps = 1.5;
+
+    %% initial solution
+    T = single(zeros(m, n, p));
+    y = single(zeros(m, n, p));
+    x = single(zeros(m, n, p));
+    Z = single(zeros(m, n, p));
+    N = single(zeros(m, n, p));   
+    W = single(zeros(m, n, p));  
+    Hx = single(zeros(m, n, p));
+
+    Dt = conj(H);
+    DD = abs(H).^2;
+
+    for iter = (1:max_iter-1)
+        y = (S-Hx  + rho*(T - W))./(1+rho);
+
+        x = ifft2(fft2(ifft2(Dt.*fft2(S-y)) + rho*(Z - N))./(DD + rho));
+
+        Hx = ifft2(H.*fft2(x));
+
+        T = fastDo(y + W, mu);
+        Z = So(lambda, x + N);
+
+        W = W + y - T;  %gamma2
+        N = N + x - Z; %gamma1
+        
+        rho = min(rho*eps, rho_max);
+        
+    end
+   
+      y = (S-Hx  + rho*(T - W))./(1+rho);
+
+      x = ifft2(fft2(ifft2(Dt.*fft2(S-y)) + rho*(Z - N))./(DD + rho));
+
+
+end
+
+function r = So(tau, S)
+    % shrinkage operator
+    r = sign(S) .* max(abs(S) - tau, 0);
+end
+
+% Matlab SVD implementation is slow
+% function r = Do(tau, S)
+%     % shrinkage operator for singular values
+%     [U, D, V] = svd(S, 'econ');
+%     r = U*So(tau, D)*V';
+% end
+
+function SX = fastDo(IQ,tau)
+
+    % Fast SVD implementation based on the code of 
+    % Vipin Vijayan, Fast SVD and PCA, https://www.mathworks.com/matlabcentral/fileexchange/47132-fast-svd-and-pca
+
+    initsize = size(IQ);
+    X = reshape(IQ,prod(initsize(1:end-1)),initsize(end));
+
+    C = X'*X; 
+    [V,D] = eig(double(C));
+    clear C;
+    U = X*V; % convert evecs from X'*X to X*X'. the evals are the same.
+    s = sqrt(abs(diag(D)));
+    U = U./s';
+    s = max(s - tau, 0);
+    S = diag(s);
+    r=U*S*V';
+    SX = reshape(r,initsize);
+end
+
diff --git a/AugmentedInSilico/SilicoAugMetrics.m b/AugmentedInSilico/SilicoAugMetrics.m
new file mode 100644
index 0000000000000000000000000000000000000000..1b5973dfa2e547eb29f34f63a96b76a084665422
--- /dev/null
+++ b/AugmentedInSilico/SilicoAugMetrics.m
@@ -0,0 +1,140 @@
+clear
+numblocks = 5;
+NoiseLevels = {'_40dB','_20dB','_10dB','_0dB'};
+SR = 2;
+MatOutGT = load('MatOutGT.mat', 'MatOut').MatOut;
+
+
+%% 'SRPCA'
+
+for ijk = 1:length(NoiseLevels)
+SNR = NoiseLevels{ijk};
+formatSpec = ['SRPCA'  SNR ' prec %4.2f, sens  %4.2f, jacc %4.2f, ssim %4.2f, MSE %4.2f \n'];
+
+TP = zeros(numblocks,1);
+FP = zeros(numblocks,1);
+FN = zeros(numblocks,1);
+
+for hhh = 1:numblocks
+
+     load(strcat('BubbleGT/BubbleGT',int2str(SR),'_Silico',int2str(hhh),'.mat'))
+     sumBubbleGT=sum(BubbleGT,3);
+     load(strcat('SilicoData',SNR,'/Result/SRPCAMatTrack',int2str(hhh),'.mat'))
+
+Est = zeros(size(BubbleGT));
+
+for kk = 1:length(MatTracking)
+     Est(max(1, round( MatTracking(kk,2)*SR)),max(1, round( MatTracking(kk,3)*SR)),MatTracking(kk,4))=Est(max(1, round( MatTracking(kk,2)*SR)),max(1, round( MatTracking(kk,3)*SR)),MatTracking(kk,4))+1;
+end
+
+crossCorrMatrix = normxcorr2(sum(Est,3),sumBubbleGT);
+[~, maxIndex] = max(abs(crossCorrMatrix(:)));
+[yPeak, xPeak] = ind2sub(size(crossCorrMatrix), maxIndex);
+yOffset = yPeak - size(sumBubbleGT, 1);
+xOffset = xPeak - size(sumBubbleGT, 2);
+
+Est = circshift(Est,[yOffset xOffset 0]);
+
+temp = max(BubbleGT - Est, 0) ;
+NumBullesGT = sum(BubbleGT(:));
+NumUndetected = sum(temp(:));
+
+FN(hhh) = NumUndetected;
+
+TP(hhh)= NumBullesGT - NumUndetected;
+
+temp = min(BubbleGT - Est, 0) ;
+
+FP(hhh)= - sum(temp(:));
+
+
+end
+
+
+  J_p = mean(TP./(FP+TP)*100); % precision
+    J_r = mean(TP./(FN+TP)*100); % sensitivity
+    J_ac = mean(TP./(FP+FN+TP)*100); % Jaccard
+
+load(['SilicoData',SNR,'/Result/SRPCASilico10.mat'],'MatOut')
+
+crossCorrMatrix = normxcorr2(MatOut,MatOutGT);
+[maxCorr, maxIndex] = max(abs(crossCorrMatrix(:)));
+[yPeak, xPeak] = ind2sub(size(crossCorrMatrix), maxIndex);
+
+xOffset = xPeak - size(MatOutGT, 2);
+yOffset = yPeak - size(MatOutGT, 1);
+
+MatOut = circshift(MatOut,[yOffset xOffset]);
+
+ssimval = ssim(MatOut,MatOutGT)*100;
+cNRMSE = US_ADM_calc_PSNR(MatOutGT,MatOut).NRMSE*100;
+fprintf(formatSpec,J_p,J_r,J_ac,ssimval,cNRMSE)
+end
+
+%% 'RS ULM'
+for ijk = 1:length(NoiseLevels)
+SNR = NoiseLevels{ijk};
+
+formatSpec = ['RSULM'  SNR ' prec %4.2f, sens  %4.2f, jacc %4.2f, ssim %4.2f, MSE %4.2f \n'];
+
+
+TP = zeros(numblocks,1);
+FP = zeros(numblocks,1);
+FN = zeros(numblocks,1);
+
+for hhh = 1:numblocks
+
+     load(strcat('BubbleGT/BubbleGT',int2str(SR),'_Silico',int2str(hhh),'.mat'))
+     sumBubbleGT=sum(BubbleGT,3);
+     load(strcat('SilicoData',SNR,'/Result/RSMatTrack',int2str(hhh),'.mat'))
+
+Est = zeros(size(BubbleGT));
+
+for kk = 1:length(MatTracking)
+     Est(max(1, round( MatTracking(kk,2)*SR)),max(1, round( MatTracking(kk,3)*SR)),MatTracking(kk,4))=Est(max(1, round( MatTracking(kk,2)*SR)),max(1, round( MatTracking(kk,3)*SR)),MatTracking(kk,4))+1;
+end
+
+crossCorrMatrix = normxcorr2(sum(Est,3),sumBubbleGT);
+[~, maxIndex] = max(abs(crossCorrMatrix(:)));
+[yPeak, xPeak] = ind2sub(size(crossCorrMatrix), maxIndex);
+yOffset = yPeak - size(sumBubbleGT, 1);
+xOffset = xPeak - size(sumBubbleGT, 2);
+
+Est = circshift(Est,[yOffset xOffset 0]);
+
+temp = max(BubbleGT - Est, 0) ;
+NumBullesGT = sum(BubbleGT(:));
+NumUndetected = sum(temp(:));
+
+FN(hhh) = NumUndetected;
+
+TP(hhh)= NumBullesGT - NumUndetected;
+
+temp = min(BubbleGT - Est, 0) ;
+
+FP(hhh)= - sum(temp(:));
+
+
+end
+
+
+  J_p = mean(TP./(FP+TP)*100); % precision
+    J_r = mean(TP./(FN+TP)*100); % sensitivity
+    J_ac = mean(TP./(FP+FN+TP)*100); % Jaccard
+
+load(['SilicoData',SNR,'/Result/RSULMSilico10.mat'],'MatOut')
+
+crossCorrMatrix = normxcorr2(MatOut,MatOutGT);
+[maxCorr, maxIndex] = max(abs(crossCorrMatrix(:)));
+[yPeak, xPeak] = ind2sub(size(crossCorrMatrix), maxIndex);
+
+xOffset = xPeak - size(MatOutGT, 2);
+yOffset = yPeak - size(MatOutGT, 1);
+
+MatOut = circshift(MatOut,[yOffset xOffset]);
+
+ssimval = ssim(MatOut,MatOutGT)*100;
+cNRMSE = US_ADM_calc_PSNR(MatOutGT,MatOut).NRMSE*100;
+
+fprintf(formatSpec,J_p,J_r,J_ac,ssimval,cNRMSE)
+end
\ No newline at end of file
diff --git a/AugmentedInSilico/ULM_localization2DSR.m b/AugmentedInSilico/ULM_localization2DSR.m
new file mode 100644
index 0000000000000000000000000000000000000000..6059bcd7cd9edcc38b2c45c855ae640f23e177d0
--- /dev/null
+++ b/AugmentedInSilico/ULM_localization2DSR.m
@@ -0,0 +1,177 @@
+function MatTracking = ULM_localization2DSR(MatIn,ULM)
+% Adapted from ULM_localization2D for regional max detection only without using any localization method
+%% function MatTracking = ULM_localization2D(MatIn,ULM)
+% This function performs the detection, selection and sub-pixel localization of bubbles on
+% a list of input images (MatIn).
+%
+% - The detection step is performed with the imregionalmax function. It returns the list of local maxima.
+% - The selection step consists of sorting intensities, in each frames, and keeping the highest maxima.
+% - The localization steps consists of applying a sub-wavelength localization kernel
+% (weighted average, interpolation, radial symmetry...) to a cropped image centered on a
+% local maxima (a 5x5 or 3x3 large image). Localization kernel are discussed in the cited article.
+%
+% This function can be easily adapt by anyone who wants to try a new localization kernel,
+% keeping all the framework unchanged.
+%
+% INPUTS:
+%       - MatIn is the sequence containing all the images
+%       - ULM structure must contains all parameters for localization method
+%           - NLocalMax : number of local maxima
+%           - LocMethod : localisation mehtod {'wa','interp','radial','curvefitting','nolocalization'};
+%           - InterpMethod : {'bicubic','lanczos3','spline'} (methods avaliable for imresize)
+%           - numberOfParticles is an estimation of the number of particles per image
+%           - fwhm is the fwhm of a bubble (usually 3 if pixel at \lambda, 5 if pixel at \lambda/2)
+% OUTPUT:
+%       - MatTracking is the table that stores the particles values and position in [pixel]
+% MatInReduced is the input matrix within a zeros frame of FWHM/2
+%
+% This function was created by Baptiste Heiles 07/04/17, last modifications Arthur Chavignon, 18/11/19
+%
+% DATE 2020.07.22 - VERSION 1.1
+% AUTHORS: Baptiste Heiles, Arthur Chavignon, Vincent Hingot. CNRS, Sorbonne Universite, INSERM.
+% Laboratoire d'Imagerie Biomedicale, Team PPM. 15 rue de l'Ecole de Medecine, 75006, Paris
+% Code Available under Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (see https://creativecommons.org/licenses/by-nc-sa/4.0/)
+% ACADEMIC REFERENCES TO BE CITED
+% Details of the code in the article by Heiles, Chavignon, Hingot, Lopez, Teston and Couture.  
+% Performance benchmarking of microbubble-localization algorithms for ultrasound localization microscopy, Nature Biomedical Engineering, 2021.
+% General description of super-resolution in: Couture et al., Ultrasound localization microscopy and super-resolution: A state of the art, IEEE UFFC 2018
+
+%% Get input data %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+fwhmz = ULM.fwhm(2);
+fwhmx = ULM.fwhm(1);
+
+% Building a vector from -FWHM to FWHM, this vector will be used for the mask's shifting
+vectfwhmz = -1*round(fwhmz/2):round(fwhmz/2);
+vectfwhmx = -1*round(fwhmx/2):round(fwhmx/2);
+
+[height,width,numberOfFrames]=size(MatIn);% Get sizes of the Matrix, height denotes number of rows/depth of imaging, width denotes number of lines/width of imaging,
+% numberOfFrames denotes the number of elements in the third dimension/number of Frames
+MatIn = abs(MatIn);% Make sure you work with the intensity matrix
+info = whos('MatIn');typename = info.class;
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Initialize structures
+% if fields are missing, they will be set with default values.
+if ~isfield(ULM,'LocMethod'),ULM.LocMethod = 'radial';end
+
+if ~isfield(ULM,'parameters')% Create an empty structure for parameters hosting
+    ULM.parameters = struct();
+end
+
+if strcmp(ULM.LocMethod,'interp')
+    if ~isfield(ULM.parameters,'InterpMethod')
+        ULM.parameters.InterpMethod = 'spline';
+    end
+    if sum(strcmp(ULM.parameters.InterpMethod,{'bilinear','bicubic'}))
+        warning('Faster but pixelated, Weighted Average will be faster and smoother.')
+    end
+end
+
+if ~isfield(ULM.parameters,'NLocalMax')
+    if fwhmz==3,ULM.parameters.NLocalMax = 2;
+    else,ULM.parameters.NLocalMax = 3;
+    end
+end
+
+%% 1 PREPARE INTENSITY MATRIX
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%% MATRIX CROPPING %%
+% Creates smaller matrix MatInReduced to avoid boundaries, where microbubbles cannot be localized. We avoided padding because padding would
+% result in erroneous localization in the boundaries.
+MatInReduced = zeros(height,width,numberOfFrames,typename);
+MatInReduced(1+round(fwhmz/2)+1:height-round(fwhmz/2)-1,1+round(fwhmx/2)+1:width-round(fwhmx/2)-1,:) = MatIn(1+round(fwhmz/2)+1:height-round(fwhmz/2)-1, 1+round(fwhmx/2)+1:width-round(fwhmx/2)-1,:);
+[height,width,numberOfFrames] = size(MatInReduced);
+
+
+%% 2 DETECTION AND SELECTION OF MICROBUBBLES
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% DETECTION OF LOCAL MAXIMA %%
+% Concatenates MatInReduced into a 2D matrix with time and space in its rows and only space in columns to apply imregionalmax function
+% The imregionalmax connectivity is set to default (8), to consider the 8 adjacent pixels in the horizontal(2), vertical(2), and diagonal directions(4).
+% Generates an IntensityMatrix (3D) with only local maximal pixels with associated values.
+Mat2D = permute(MatInReduced, [1,3,2]); %so that all the frames are in columns
+Mat2D = reshape(Mat2D,height*numberOfFrames,width);% Concatenate Matrix
+mask2D = imregionalmax(Mat2D); clear Mat2D  % Perform imregionalmax
+mask = reshape(mask2D,height,numberOfFrames,width);clear mask2D % reshape concatenated mask
+mask = permute(mask,[1,3,2]); % so that we restore (z,x,t) table
+
+IntensityMatrix = MatInReduced.*mask; %Values of intensities at regional maxima
+
+% SELECTION OF MICROBUBBLES %%
+% Only the first numberOfParticles highest local max will be kept for localization.
+% Other local max will be considered as noise.
+% Sort intensites in each frames, and store pixel coordinates
+% At the end of this section, spatial and temporal coordinates microbubbles are
+% stored into: index_mask_z, index_mask_x, index_numberOfFrames
+[tempMatrix,~] = sort(reshape(IntensityMatrix,[],size(IntensityMatrix,3)),1,'descend');
+
+% Remove the last kept intensity values to each frame. This means that you cannot fix an intensity threshold,
+% we rely on number of particles. This is key for transparency/parallelization.
+IntensityFinal = IntensityMatrix - ones(size(IntensityMatrix)) .* reshape(tempMatrix( ULM.numberOfParticles+1,:),[1 1 numberOfFrames]);
+clear tempMatrix
+% Construction of the final mask with only the kept microbubbles low resolved and their associated intensity
+MaskFinal = (mask.*IntensityFinal)>0;
+MaskFinal(isnan(MaskFinal))=0;
+MaskFinal = (MaskFinal>0).*IntensityMatrix;
+
+% Preparing intensities and coordinates for further calculation of average, intensities etc...
+index_mask  = find(MaskFinal);
+[index_mask_z,index_mask_x,index_numberOfFrames]=ind2sub([height, width, numberOfFrames], index_mask);
+clear mask IntensityFinal MaskFinal IntensityMatrix
+clear index_mask
+
+
+%% 3 SUBWALENGTH LOCALIZATION OF MICROBUBBLES
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% LOCALIZATION OF MICROBUBBLES %%
+% The position of each microbubble will be localized with a subwavelength precision.
+% For example a microbubble at pixel coordinates [34 67] will be localized at [34.4 66.8]
+
+% Initialize variables averageXc, averageZc which are the super-resolved position of microbubbles
+averageXc = nan(1,size(index_mask_z,1),typename);
+averageZc = nan(1,size(index_mask_z,1),typename);
+
+for iscat=1:size(index_mask_z,1)
+    % For each microbubble, create a 2D intensity matrix of the Region of interest defined by fwhm
+    IntensityRoi = MatIn(index_mask_z(iscat)+vectfwhmz,index_mask_x(iscat)+vectfwhmx,index_numberOfFrames(iscat));
+
+    % NLocal max
+    % If there are too many localmax in the region of interest, the microbubble shape will be affected and the localization distorted.
+    % In that case, we set averageZc, averageXc to NaN value.
+    if nnz(imregionalmax(IntensityRoi))>ULM.parameters.NLocalMax
+        continue
+    end
+
+    % Apply the localization method selected
+    % functions are detailed at the end of the code (excepted LocRadialSym which requires an additional function)
+
+    % Store the final super-resolved position of the microbubble as its pixel position and an axial/lateral sub-pixel shift.
+    averageZc(iscat) = index_mask_z(iscat);
+    averageXc(iscat) = index_mask_x(iscat);
+
+    % Additional safeguards
+    % sigma evaluates the size of the microbubble. If it appears to be too large, the microbubble can be removed (optional)
+   
+
+    % If the final axial/lateral shift is higher that the fwhmz,
+    % localization has diverged and the microbubble is ignored.
+end
+keepIndex = ~isnan(averageXc);
+
+ind = sub2ind([height,width,numberOfFrames],index_mask_z(keepIndex),index_mask_x(keepIndex),index_numberOfFrames(keepIndex));
+clear index_mask_z index_mask_x IntensityRoi
+
+%% BUILD MATTRACKING %%
+% Creating the table which stores the high resolved microbubbles coordinates and the density value
+MatTracking = zeros(nnz(keepIndex),4,typename);
+
+MatTracking(:,1) = MatInReduced(ind);       % Initial intensity of the microbubble
+MatTracking(:,2) = averageZc(keepIndex);    % Super-resolved axial coordinate
+MatTracking(:,3) = averageXc(keepIndex);    % Super-resolved lateral coordinate
+MatTracking(:,4) = index_numberOfFrames(keepIndex); % Frame number of the microbubble
+clear averageXc averageZc index_numberOfFrames MatInReduced
+end
+