• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.3
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• pp.156-184
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• 2022

In this article, we propose a novel variational model for restoring color images corrupted by mixed multiplicative Gamma noise and additive Gaussian noise. The model involves a data-fidelity term that characterizes the mixed noise as an infimal convolution of two noise distributions and the saturation-value total variation (SVTV) regularization. The data-fidelity term facilitates suitable separation of the multiplicative Gamma and Gaussian noise components, promoting simultaneous elimination of the mixed noise. Furthermore, the SVTV regularization enables adequate denoising of homogeneous regions, while maintaining edges and details and diminishing the color artifacts induced by noise. To solve the proposed nonconvex model, we exploit an alternating minimization approach, and then the alternating direction method of multipliers is adopted for solving subproblems. This contributes to an efficient iterative algorithm. The experimental results demonstrate the superior performance of the proposed model compared to other existing or related models, with regard to visual inspection and image quality measurements.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.411-420
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• 2013

We consider fractional Gussian noise and FARIMA sequence with Gaussian innovations and show that the suitably scaled distributions of the FARIMA sequences converge to fractional Gaussian noise in the sense of finite dimensional distributions. Finally, we figure out ACF function and estimate the self-similarity parameter H of FARIMA(0, $d$, 0) by using R/S method.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.7
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• pp.1-7
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• 1995

In this paper, we generalize the method to calculate the outage probability in the presence of multiple rayleigh faded cochannel interferences and additive white Gaussian noise. Our result is a computational formula that can be applied with or without Gaussian noise in Rayleigh faded cochannel interferences. Without Gaussian noise, the situation degenerates to usual case of the cochannel interferences. The result can be appiled also in the presence of Gaussian noise with or without cochannel interferences.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.7
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• pp.3497-3515
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• 2018

Differential privacy has broadly applied to statistical analysis, and its mainly objective is to ensure the tradeoff between the utility of noise data and the privacy preserving of individual's sensitive information. However, an individual could not achieve expected data utility under differential privacy mechanisms, since the adding noise is random. To this end, we proposed an adaptive Gaussian mechanism based on expected data utility under conditional filtering noise. Firstly, this paper made conditional filtering for Gaussian mechanism noise. Secondly, we defined the expected data utility according to the absolute value of relative error. Finally, we presented an adaptive Gaussian mechanism by combining expected data utility with conditional filtering noise. Through comparative analysis, the adaptive Gaussian mechanism satisfies differential privacy and achieves expected data utility for giving any privacy budget. Furthermore, our scheme is easy extend to engineering implementation.

• ETRI Journal
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• v.33 no.6
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• pp.949-952
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• 2011

In this letter, a simplified suboptimum receiver based on soft-limiting for the detection of binary antipodal signals in non-Gaussian noise modeled as a generalized normal-Laplace (GNL) distribution combined with Gaussian noise is presented. The suboptimum receiver has low computational complexity. Furthermore, when the number of diversity branches is small, its performance is very close to that of the Neyman-Pearson optimum receiver based on the probability density function obtained by the Fourier inversion of the characteristic function of the GNL-plus-Gaussian distribution.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.38C no.4
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• pp.365-370
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• 2013

In this paper, we propose robust blind estimators for the frequency offset of orthogonal frequency division multiplexing in non-Gaussian noise environments. We first propose a maximum likelihood (ML) estimator in non-Gaussian noise modeled as a complex isotropic Cauchy process, and then, a simpler estimator based on the ML estimator is proposed. From numerical results, we confirm that the proposed estimators are robust to the non-Gaussian noise and have a better estimation performance over the conventional estimator in non-Gaussian noise environments.

• Structural Engineering and Mechanics
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• v.28 no.4
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• pp.373-386
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• 2008

In this study stochastic analysis of non-linear dynamical systems under ${\alpha}$-stable, multiplicative white noise has been conducted. The analysis has dealt with a special class of ${\alpha}$-stable stochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of the probability density function or of the characteristic function of the dynamical response may be obtained considering the dynamical system forced by a Gaussian white noise with an uncertain factor with ${\alpha}/2$- stable distribution. This consideration yields the probability density function or the characteristic function of the response by means of a simple integral involving the probability density function of the system under Gaussian white noise and the probability density function of the ${\alpha}/2$-stable random parameter. Some numerical applications have been reported assessing the reliability of the proposed formulation. Moreover a proper way to perform digital simulation of the sub-Gaussian ${\alpha}$-stable random process preventing dynamical systems from numerical overflows has been reported and discussed in detail.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.21 no.3
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• pp.629-635
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• 2017

In this paper, we proposed a nonlinear synthesis filter for noise reduction to reduce the effects of Gaussian noise and impulse noise. When the centralization of the local mask is judged to be Gaussian noise by the noise judgment, the weight value of the weight filter are applied differently according to the spatial weight filter and the pixel change by using the sample variance in the local mask. And if it is determined as the impulse noise, we proposed an algorithm that applies different weights of local histogram weight filter and standard median filter according to noise density of mask. In order to evaluate the performance of the proposed filter algorithm, we used PSNR(peak signal to noise ratio) and compared existing methods and proposed filter algorithm in the mixed noise environment with Gaussian noise, impulsive noise, and two noises mixed.

• Journal of information and communication convergence engineering
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• v.19 no.1
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• pp.54-60
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• 2021

Various digital devices were supplied throughout the Fourth Industrial Revolution. Accordingly, the importance of data processing has increased. Data processing significantly affects equipment reliability. Thus, the importance of data processing has increased, and various studies have been conducted on this topic. This study proposes a modified Gaussian filter algorithm based on a fuzzy membership function. The proposed algorithm calculates the Gaussian filter weight considering the standard deviation of the filtering mask and computes an estimate according to the fuzzy membership function. The final output is calculated by adding or subtracting the Gaussian filter output and estimate. To evaluate the proposed algorithm, simulations were conducted using existing additive white Gaussian noise removal algorithms. The proposed algorithm was then analyzed by comparing the peak signal-to-noise ratio and differential image. The simulation results show that the proposed algorithm has superior noise reduction performance and improved performance compared to the existing method.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.13 no.7
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• pp.679-686
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• 2002

Based on the alternating series expansion of error probability function due to phase noise in PSK systems, the performance evaluations for Tikhonov and Gaussian probability density functions were performed in this paper. The range of the signal-to-noise ratio of recovered carrier signal which provides the same dependency between the error performances by Tikhonov function and Gaussian function was analyzed via loss evaluation due to phase noise. The phase noise with 1/f$^2$ characteristic was generated based on the relationship of the phase noise spectral density and the modulation index for frequency modulation signal. Using the generated phase noise as the input signal for digital satellite communication receiver, the performance losses due to the phase noise were measured and evaluated with the analyzed performance characteristics.