We consider the problem of reconstructing a continuous-tone (contone) image from its halftoned version, where the halftoning process is done by error diffusion. We present an iterative nonlinear decoding algorithm for halftone-to-contone conversion, and show simulation results that compare the performance of the algorithm to that of conventional linear lowpass filtering. We find that the new technique results in subjectively superior reconstruction. As there is a natural relationship between error diffusion and $Sigma$Delta modulation, our reconstruction algorithm can also be applied to the decoding problem for $Sigma$Delta modulators.
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