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Estimating from Outputs of Oversampled DeltaSigma Modulation
"... . Oversampling a deltasigmamodulated sequence, one can compute unbiased sample estimates of averages of consecutive input elements for a wide variety of inputs. We prove that these estimates are most efficient in their class (that is, variances of sample means are minimum in the class of random bi ..."
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. Oversampling a deltasigmamodulated sequence, one can compute unbiased sample estimates of averages of consecutive input elements for a wide variety of inputs. We prove that these estimates are most efficient in their class (that is, variances of sample means are minimum in the class of random binary sequences g n , n = 1; : : : ; N , such that the expected values of g n are equal to the values of the corresponding inputs of deltasigma modulation) and consistent. Deltasigma modulation may also be described as onedimensional error diffusion (a technique for digital halftoning). However, deltasigma modulation is not a practical digital halftoning algorithm, because human vision averages small luminance deviations in two dimensions. We pose an open problem that invites the reader to extend our approach to the twodimensional case for the purpose of development of a practical digital halftoning algorithm. IEEE EDICS number: SP 3.8.2 Correspondence should be sent to: Dmitri A. Guse...
AntiCorrelation Digital Halftoning
"... A new class of digital halftoning algorithms is introduced. Anticorrelation digital halftoning (ACDH) combines the idea of a wellknown game, Russian roulette, with the statistical approach to bilevel quantization of digital images. A representative ofthe class, serpentine anticorrelation digital h ..."
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A new class of digital halftoning algorithms is introduced. Anticorrelation digital halftoning (ACDH) combines the idea of a wellknown game, Russian roulette, with the statistical approach to bilevel quantization of digital images. A representative ofthe class, serpentine anticorrelation digital halftoning, is described and compared to error di usion, ordered dither, and other important digital halftoning techniques. Serpentine ACDH causes fewer unpleasant correlated artifacts and less contouring than the benchmark algorithms. The quantization noise spectra associated with serpentine ACDH possess bene cial characteristics related to properties of the vision system. The term \violet noise " is proposed to describe quantization noise with stronger bias in favor of highfrequency components than that of blue noise. Novel techniques for color visualization of the noise spectra and the corresponding phase spectra are introduced, and the relative signi cance of the magnitudes and phases of the discrete Fourier transform of the quantization noise is studied. Unlike popular algorithms based on error di usion, serpentine ACDH does not enhance edges. This is good for applications to digital holography and medical imaging. A simple input preprocessing technique allowsonetointroduce edge enhancement if desired, while keeping it more isotropic than that of error di usion. The relation between unwanted transient boundary e ects and edge enhancement accompanying error di usion is examined, and approaches to reduction of boundary e ects are considered. Serpentine ACDH does not cause signi cant boundary e ects. The average intensity representation by di erent algorithms is studied for constant input levels (serpentine ACDH does remarkably well). Prospects for ACDH research are discussed.
iii To the Memory of Eugene A. Sandler iv Acknowledgments
, 1999
"... James T. Newkirk for their help and advice. Thomas Zeggel provided the code of his iterative convolution algorithm, and Vladimir Me~nkov helped me to incorporate it in myworking environment. Reg Heron taught me to use the re ection densitometer and helped with the density measurements. Jun Li made a ..."
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James T. Newkirk for their help and advice. Thomas Zeggel provided the code of his iterative convolution algorithm, and Vladimir Me~nkov helped me to incorporate it in myworking environment. Reg Heron taught me to use the re ection densitometer and helped with the density measurements. Jun Li made a black mask for the luminance measurements and conducted the subjective rating experiment. I am deeply grateful to Gregory Pogosyants for his permission to use the digitized portrait of his daughter, Anya Pogosyants (1969{1995), who was a computer science Ph.D. student at the