Fast progressive reconstruction of a transformed image

Fast methods for performing progressive reconstruction of Fourier and Hadamard transformed images have been developed. Reconstruction of an N \times N point transformed image can be evaluated in order N^{2} \log_{2} N instructions. Accumulation of round-off errors due to iteration is reduced by the factor (\log_{2} N + 1) / N^{2} , compared with direct evaluation of the inverse transform.