In this paper, we demonstrate based on the linear model of Kite 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 nears infinity 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.