Model-based Inverse Halftoning with Wavelet-Vaguelette Deconvolution
Ramesh Neelamani, Robert Nowak, Richard Baraniuk
(To appear in 2000 International Conference on Image Processing, ICIP--2000, September 10-13, Vancouver, BC, Canada.)
In this paper, we demonstrate based on the linear model of \cite{Kite,KiteJournal} that inverse halftoning is equivalent to the well-studied problem of deconvolution in the presence of colored noise. We propose the use of the simple and elegant wavelet-vaguelette deconvolution (WVD) algorithm to perform the inverse halftoning. Unlike previous wavelet-based algorithms, our method is model-based; hence it is adapted to different error diffusion halftoning techniques. Our inverse halftoning algorithm consists of inverting the convolution operator followed by denoising in the wavelet domain. For signals in a Besov space, our algorithm possesses asymptotically (as the number of samples $\rightarrow \infty$) near-optimal rates of error decay. Hence for images in a Besov space, it is impossible to improve significantly on the inverse halftoning performance of the WVD algorithm at high resolutions. Using simulations, we verify that our algorithm outperforms or matches the performances of the best published inverse halftoning techniques in the mean square error (MSE) sense and also provides excellent visual performance.

Support: This work was supported by the NSF grants CCR-9973188 and MIP--9701692, DARPA/AFOSR grant F49620-97-1-0513, ONR grant N00014-99-1-0219, ARO grant DAAD19-99-1-0349, and Texas Instruments.