# Denoising an image containing K blurred lines

• Generate lines with parameters , blurred with a spread, in an image of size degraded by noise
• Launch the minimization algorithm with parameters • From the solution , estimate the lines by Prony

## DATA GENERATION

W=65;               % image width (must be odd W=2M+1)
H=65;               % image height
K=3;                % number of lines
spread=1;           % std of the gaussian blur
noiselevel=200;     % level of noise
randomgen=0;        % boolean if lines are generated randomly of manually
rng(0);             % seed of random numbers generator
plotData=1;         % display images v, x and y
plotComp=0;         % display others comparaisons theo vs. emp

t_k=[pi/6 -pi/5 pi/16]; % array containing angles of lines
a_k=[255 255 255];      % array containing amplitude of lines
p_k=[10 0 -15];         % array containing offset of lines

data_generation;    % Generate the blurred image xstar
% of these K lines with additional
% noise y=xstar+randn(H,W)*noiselevel ## MINIMIZATION ALGORITHM

Nbiter=2000;            % number of iterations
rho=1.9;                % weigth coefficient
tau=0.6;                % primal step (sigma is then computed from tau)
c=700;                  % smaller than c_oracle to remove more noise
plotError=1;            % compute and display error
displayIter=0;          % display the counter iteration
algo=2;                 % choose the minimization algorithm to use

minimization_Chambolle; % Find by minimization an approximation wr
% of wstar which is the horizontal Fourier
% transform of the deblurred image sstar

Elapsed time is 257.118283 seconds.   ## IMAGE RECONSTRUCTION AND LINES ESTIMATION

Reconstruct the denoised image xstar from wstar:

resynthesis; Estimate lines parameters and display it

cstar=sum(a_k./cos(t_k));  % theoritical atomic norm of each line
coef=cstar/c;              % factor between experimental and true amplitude
prony;

thetamean = -0.63663      0.1844     0.57194
alphamean = 202.1061      185.5782      155.9103
eta = -0.0572949     -15.0438      9.96126
(thetamean-t_k)/t_k = 0.013231   -0.060853    0.092319
(alphamean*coef-a_k)/a_k = -0.015351   -0.095873    -0.24041
eta-p_k = -0.057295   -0.043771   -0.038742 