Approximated fast estimator for the shape parameter of generalized Gaussian distribution

Krupiński, Robert; Purczyński, Jan

doi:10.1016/j.sigpro.2005.05.003

Cited by 59 publications

(30 citation statements)

References 12 publications

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“…It can also model symmetric platykurtic densities whose tails are heavier than normal or symmetric leptokurtic densities whose tails are lighter than normal . Applications include noise modeling in image, speech, and multimedia processing [61]- [64].…”

Section: Maximum-likelihood Binary Signal Detection In Symmetric mentioning

confidence: 99%

Noise Benefits in Quantizer-Array Correlation Detection and Watermark Decoding

Patel

Kosko

2011

IEEE Trans. Signal Process.

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Abstract-Quantizer noise can improve statistical signal detection in array-based nonlinear correlators in Neyman-Pearson and maximum-likelihood (ML) detection. This holds even for infinitevariance symmetric alpha-stable channel noise and for generalized-Gaussian channel noise. Noise-enhanced correlation detection leads to noise-enhanced watermark extraction based on such nonlinear detection at the pixel or bit level. This yields a noise-based algorithm for digital watermark decoding using two new noisebenefit theorems. The first theorem gives a necessary and sufficient condition for quantizer noise to increase the detection probability of a constant signal for a fixed false-alarm probability if the channel noise is symmetric and if the sample size is large. The second theorem shows that the array must contain more than one quantizer for such a stochastic-resonance noise benefit if the symmetric channel noise is unimodal. It also shows that the noise-benefit rate improves in the small-quantizer noise limit as the number of array quantizers increases. The second theorem further shows that symmetric uniform quantizer noise gives the optimal rate for an initial noise benefit among all finite-variance symmetric scalefamily noise. Two corollaries give similar results for stochastic-resonance noise benefits in ML detection of a signal sequence with known shape but unknown amplitude. Fig. 1 shows an SR noise benefit in the ML watermark extraction of the "yin-yang" image embedded in the discrete-cosine transform (DCT-2) coefficients of the "Lena" image [32]. The yin-yang image of Fig. 1(a) is the 64 64 binary watermark message embedded in the midfrequency DCT-2 coefficients of the 512 512 gray-scale Lena image using direct-sequence spread spectrum [33]. Fig. 1(b) shows the result when the yin-yang figure watermarks the Lena image. Figs. 1(c)-1(g) shows that small amounts of additive uniform quantizer noise improve the watermark-extraction performance of the noisy quantizer-array ML detector while too much noise degrades the performance. Uniform quantizer noise with standard deviation reduces more than 33% of the pixel-detection errors in the extracted watermark image. Section VI gives the details of such noise-enhanced watermark decoding. IndexThe quantizer-array detector consists of two parts. It consists of a nonlinear preprocessor that precedes a correlator and a likelihood-ratio test of the correlator's output. This nonlinear detector takes samples of a noise-corrupted signal and then sends each sample to the nonlinear preprocessor array of noisy quantizers connected in parallel. Each quantizer in the array adds its independent quantizer noise to the noisy input sample and then quantizes this doubly noisy data sample into a binary value. The quantizer array output for each sample is just the sum of all quantizer outputs. The correlator then correlates these preprocessed samples with the signal. The detector's final stage applies either the NP likelihood-ratio test in Section II or the ML-ratio test in Section V.Sect...

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Section: Maximum-likelihood Binary Signal Detection In Symmetric mentioning

confidence: 99%

Noise Benefits in Quantizer-Array Correlation Detection and Watermark Decoding

Patel

Kosko

2011

IEEE Trans. Signal Process.

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“…This problem can either be solved using the combination of a lookup-table and some sort of interpolation method (see [18]), or by employing the approximation of Krupinski [19] where the author proposes to define an invertible approximation R(c) = exp(k + lc m ) to F (c) and solves a non-linear curve fitting problem for certain ranges of c. In this work, we do not split the range of c and obtain k = −0.2667, l = −0.4172 and m = −1.1585 as the corresponding coefficients (using the MATLAB Curve Fitting Toolbox). Moment matching then reduces to the simple function evaluation R −1 (c) which has a closed-form expression.…”

Section: A Generalized Gaussian Distributionmentioning

confidence: 99%

Lightweight Detection of Additive Watermarking in the DWT-Domain

Kwitt

Meerwald

Uhl

2011

IEEE Trans. on Image Process.

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Abstract-This article aims at lightweight, blind detection of additive spread-spectrum watermarks in the DWT domain. We focus on two host signal noise models and two types of hypothesis tests for watermark detection. As a crucial point of our work we take a closer look at the computational requirements of watermark detectors. This involves the computation of the detection response, parameter estimation and threshold selection. We show that by switching to approximate host signal parameter estimates or even fixed parameter settings we achieve a remarkable improvement in runtime performance without sacrificing detection performance. Our experimental results on a large number of images confirm the assumption that there is not necessarily a trade-off between computation time and detection performance.

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“…Likewise, for model parameter estimation simple counting of 1 bits is necessary to establish the parameters pi of the Product Bernoulli distribution. For the Generalized Gaussian distribution, maximum likelihood estimation of the parameters requires to carry out an iterative Newton-Raphson algorithm [6], even though fast, approximative methods [9] are available.…”

Section: Computational Analysismentioning

confidence: 99%

Watermark detection on quantized transform coefficients using product bernoulli distributions

Meerwald

Uhl

2010

Proceedings of the 12th ACM Workshop on Multimedia and Security

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Detection performance of additive spread-spectrum watermarks depends on the statistical host signal model employed to derive the detection statistic. When transform coefficients are heavily quantized, the assumption of a Cauchy or Generalized Gaussian Distribution (GGD) is hard to justify and the estimation of model parameters becomes inaccurate. In this paper we derive a Likelihood-Ratio Test (LRT) based on the product of Bernoulli distributions. The watermark detector is designed to operate on quantized (integer) transform coefficients and therefore permits straightforward integration of the watermarking scheme in popular image and video codecs. Detection performance surpasses the linear correlation detector and is competitive with the computationally more demanding LRT based on a GGD.

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Approximated fast estimator for the shape parameter of generalized Gaussian distribution

Cited by 59 publications

References 12 publications

Noise Benefits in Quantizer-Array Correlation Detection and Watermark Decoding

Noise Benefits in Quantizer-Array Correlation Detection and Watermark Decoding

Lightweight Detection of Additive Watermarking in the DWT-Domain

Watermark detection on quantized transform coefficients using product bernoulli distributions

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