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SB_ATV.m
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SB_ATV.m
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function u = SB_ATV(g,mu)
% Split Bregman Anisotropic Total Variation Denoising
%
% u = arg min_u 1/2||u-g||_2^2 + mu*ATV(u)
%
% g : noisy image
% mu: regularisation parameter
% u : denoised image
%
% Refs:
% *Goldstein and Osher, The split Bregman method for L1 regularized problems
% SIAM Journal on Imaging Sciences 2(2) 2009
% *Micchelli et al, Proximity algorithms for image models: denoising
% Inverse Problems 27(4) 2011
%
% Benjamin Trémoulhéac
% University College London
% April 2012
g = g(:);
n = length(g);
[B Bt BtB] = DiffOper(sqrt(n));
b = zeros(2*n,1);
d = b;
u = g;
err = 1;k = 1;
tol = 1e-3;
lambda = 1;
while err > tol
fprintf('it. %g ',k);
up = u;
% size(speye(n))
% size(BtB)
[u,~] = cgs(speye(n)+BtB, g-lambda*Bt*(b-d),1e-5,100);
Bub = B*u+b;
fprintf(' %g ', norm(Bub))
d = max(abs(Bub)-mu/lambda,1).*sign(Bub);
b = Bub-d;
err = norm(up-u)/norm(u);
fprintf('err=%g \n',err);
k = k+1;
end
fprintf('Stopped because norm(up-u)/norm(u) <= tol=%.1e\n',tol);
end
function [B Bt BtB] = DiffOper(N)
D = spdiags([-ones(N,1) ones(N,1)], [0 1], N,N+1);
D(:,1) = [];
D(1,1) = 0;
B = [ kron(speye(N),D) ; kron(D,speye(N)) ];
size(B)
Bt = B';
BtB = Bt*B;
end