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cvxProjection.m
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cvxProjection.m
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%======================================================================
% Projection onto lp-norm sphere
%======================================================================
function z = cvxProjection(y, mask, p, rho, normType)
if normType == 0
mask = logical(mask);
N = nnz(mask);
z = zeros(size(y));
cvx_begin quiet
cvx_solver sedumi;
variable x(N, 1);
minimize( norm(x-y(mask)) );
subject to
norm(x(:), p) <= rho;
x >= 0;
cvx_end
z(mask) = x;
elseif normType == 1
z = zeros(size(y));
for i = 1:size(y, 1)
cvx_begin quiet
cvx_solver sedumi;
variable x(1, sum(mask(i,:)));
minimize( norm(x-y(i,mask(i,:))) );
subject to
norm(x, p) <= rho;
x >= 0;
cvx_end
z(i,mask(i,:)) = x;
end
elseif normType == 2
z = zeros(size(y));
for j = 1:size(y, 2)
cvx_begin quiet
cvx_solver sedumi;
variable x(sum(mask(:,j)), 1);
minimize( norm(x-y(mask(:,j),j)) );
subject to
norm(x, p) <= rho;
x >= 0;
cvx_end
z(mask(:,j),j) = x;
end
end
end