We propose a new linogram algorithm for the high quality Fourier reconstruc
tion of digital N x N images from their Radon transform. The algorithm is b
ased on univariate fast Fourier transforms for nonequispaced data in the ti
me domain and in the frequency domain. The algorithm requires only O(N-2 lo
g N) arithmetic operations and preserves the good reconstruction quality of
the filtered backprojection.