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In this paper, we discuss the discrete Hilbert transform (DHT) method of stabilizing unstable two-dimensional (2-D) recursive digital filters originally proposed by Read and Treitel. We show that even in the one-dimensional case, the DHT method may yield an unstable polynomial when the given unstable polynomial has zeros on the unit circle. This is the case in the example presented by Read and Treitel, where the given 2-D polynomial has zeros on the unit bicircle. We show that the DHT method cannot guarantee stability if the unstable 2-D polynomial has zeros on the unit bicircle.

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We present a fast, non-iterative technique for producing grayscale images from error diffused and dithered halftones. The first stage of the algorithm consists of a Gaussian filter and a median filter, while the second stage consists of a bandpass filter, a thresholding operation, and a median filter. The second stage enhances the rendering of edges in the inverse halftone. We compare our algorithm to the best reported statistical smoothing, wavelet, and Bayesian algorithms to show that it delivers comparable PSNR and subjective quality at a fraction of the computation and memory requirements. For error diffused halftones, our technique is seven times faster than the MAP estimation method and 75 times faster than the wavelet method. For dithered halftones, our technique is 200 times faster than the MAP estimation method. A C implementation of the algorithm is available at http: //www. ece .utexas . edu/ "bevans/projects/inverseHalftoning.html.