Efficiency of the Approximated Shape Parameter Estimator in the Generalized Gaussian Distribution

González–Farías, Graciela; Molina, Julieta; Rodríguez‐Dagnino, Ramón M.

doi:10.1109/tvt.2009.2021270

Cited by 29 publications

(42 citation statements)

References 6 publications

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“…where M is the number of coefficients in scale N (k) and m y is the mean in the same scale m y = yi M . Using the noise variance estimate in (21) and noisy data variance estimate in (22), the estimate of noiseless data variance iŝ…”

Section: Parameter Estimation Of Ggdmentioning

confidence: 99%

Adaptive Bayesian Denoising for General Gaussian Distributed Signals

Hashemi

Beheshti

2014

IEEE Trans. Signal Process.

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Optimum Bayes estimator for General Gaussian Distributed (GGD) data in wavelet is provided. The GGD distribution describes a wide class of signals including natural images. A wavelet thresholding method for image denoising is proposed. Interestingly, we show that the Bayes estimator for this class of signals is well estimated by a thresholding approach. This result analytically confirms the importance of thresholding for noisy GGD signals. We provide the optimum soft thresholding value that mimics the behavior of the Bayes estimator and minimizes the resulting error.The value of the threshold in BayesShrink, which is one of the most used and efficient soft thresholding methods, has been provided heuristically in the literature. Our proposed method, denoted by Rigorous BayesShrink (R-BayesShrink), explains the theory of BayesShrink threshold and proves its optimality for a subclass of GDD signals. R-BayesShrink improves and generalizes the existing BayesShrink for the class of GGD signals. While the BayesShrink threshold is independent from the wavelet coefficient distribution and is just a function of noise and noiseless signal variance, our method adapts to the distribution of wavelet coefficients of each scale. It is shown that BayesShrink is a special case of our method when shape parameter in GGD is one or signal follows Laplace distribution. Our simulation results confirm the optimality of R-BayesShrink in GGD denoising with regards to Peak Signal to Noise Ratio (PSNR) and Structural Similarity (SSIM) index. Index Terms-Bayesian estimation, wavelet shrinkage and denoising, soft thresholding

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Section: Parameter Estimation Of Ggdmentioning

confidence: 99%

Adaptive Bayesian Denoising for General Gaussian Distributed Signals

Hashemi

Beheshti

2014

IEEE Trans. Signal Process.

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“…It is widely used to model the non-Gaussian noise such as heavy-tailed and impulsive noise [18]. The probability density function (pdf) of GGM with a variance σ 2 n and shape parameter ρ is given by…”

Section: ) Generalized Gaussian Model (Ggm): Ggm Is a Broadmentioning

confidence: 99%

A nonparametric approach for spectrum sensing using bootstrap techniques

Huang

Chung

Thompson

2014

2014 IEEE Global Communications Conference

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This paper deals with the blind spectrum sensing problem for arbitrary noise. The majority of current methods consider the Gaussian noise. However, this assumption cannot model the impulsive noise due to the artificial source. In this paper, we remove the requirement on Gaussianity and propose a detection method based on the bootstrap technique. By using multiple receiving antennas, the proposed detector exploits the eigenstructure of sample covariance matrix. Since there is no closed-form expression for the joint distribution of eigenvalues, the nonparametric bootstrap resampling is applied to estimate the null distribution of the test statistic. Simulation results show that the proposed detector performs well in different noise types and a performance gain can be expected when the noise is non-Gaussian.Index Terms-signal detection, bootstrap, non-Gaussian noise, spectrum sensing, cognitive radio.

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“…1) Generalized Gaussian (GG) noise model: GG noise model is widely used to characterize nonGaussian noise such as, atmospheric and impulsive noise [21], [22]. A random variable X is said to be distributed as GG, if it has the following pdf.…”

Section: B Noise Modelmentioning

confidence: 99%

Polarity-Coincidence-Array Based Spectrum Sensing for Multiple Antenna Cognitive Radios in the Presence of Non-Gaussian Noise

Wimalajeewa

Varshney

2011

IEEE Trans. Wireless Commun.

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ABSTRACT:One of the main requirements of the cognitive radio (CR) systems is the ability to perform spectrum sensing in a reliable manner in challenging environments that arise due to propagation channels which undergo multipath fading and non-Gaussian noise. While most existing literature on spectrum sensing has focused on impairments introduced by additive white Gaussian noise (AWGN), this assumption fails to model the behavior of certain types of noise in practice. In this paper, the use of a non-parametric and easily implementable detection device, namely polarity-coincidence-array (PCA) detector, is proposed for the detection of weak primary signals with a cognitive radio equipped with multiple antennas. Its performance is evaluated in the presence of heavy-tailed noise. The detector performance in terms of the probabilities of detection and false alarm is derived when the communication channels between the primary user transmitter and the multiple antennas at the cognitive radio are AWGN as well as when they undergo Rayleigh fading. From the numerical results, it is observed that a significant performance enhancement is achieved by the PCA detector compared to that of the energy detector with AWGN as well as fading channels as the heaviness of the tail of the non-Gaussian noise increases. KEYWORDS:Cognitive radio, spectrum sensing, non-Gaussian noise, Rayleigh fading, polarity-coincidencearray detectors AbstractOne of the main requirements of the cognitive radio (CR) systems is the ability to perform spectrum sensing in a reliable manner in challenging environments that arise due to propagation channels which undergo multipath fading and non-Gaussian noise. While most existing literature on spectrum sensing has focused on impairments introduced by additive white Gaussian noise (AWGN), this assumption fails to model the behavior of certain types of noise in practice. In this paper, the use of a non-parametric and easily implementable detection device, namely polarity-coincidence-array (PCA) detector, is proposed for the detection of weak primary signals with a cognitive radio equipped with multiple antennas. Its performance is evaluated in the presence of heavy-tailed noise. The detector performance in terms of the probabilities of detection and false alarm is derived when the communication channels between the primary user transmitter and the multiple antennas at the cognitive radio are AWGN as well as when they undergo Rayleigh fading. From the numerical results, it is observed that a significant performance enhancement is achieved by the PCA detector compared to that of the energy detector with AWGN as well as fading channels as the heaviness of the tail of the non-Gaussian noise increases.

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Efficiency of the Approximated Shape Parameter Estimator in the Generalized Gaussian Distribution

Cited by 29 publications

References 6 publications

Adaptive Bayesian Denoising for General Gaussian Distributed Signals

Adaptive Bayesian Denoising for General Gaussian Distributed Signals

A nonparametric approach for spectrum sensing using bootstrap techniques

Polarity-Coincidence-Array Based Spectrum Sensing for Multiple Antenna Cognitive Radios in the Presence of Non-Gaussian Noise

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