• Journal of the Institute of Electronics Engineers of Korea SC
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• v.44 no.6
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• pp.42-48
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• 2007

In x-ray imaging system, two kinds of noises are involved. First, the charge generated from the radiation interaction with the detector during exposure. Second, the signal is then added by readout electronics noise. But, x-ray images are not modeled by Gaussian noise but as the realization of a Poisson process. In this paper, we apply a new approach to remove Poisson noise from medical X-ray image in the wavelet domain, the applied methods shows more excellent results in cone-beam CT.

• Communications for Statistical Applications and Methods
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• v.9 no.3
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• pp.765-774
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• 2002

Suppose one is given a vector X of a finite set of quantities $X_i$ which are independent Poisson random variables. A null hypothesis $H_0$ about E(X) is to be tested against an alternative hypothesis $H_1$. A quantity $\sum\limits_{i}w_ix_i$ is to be computed and used for the test. The optimal values of $W_i$ are calculated for three cases: (1) signal to noise ratio is used in the test, (2) normal approximations with unequal variances to the Poisson distributions are used in the test, and (3) the Poisson distribution itself is used. The above three cases are considered to the situations that are without background noise and with background noise. A comparison is made of the optimal values of $W_i$ in the three cases for both situations.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.1
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• pp.101-104
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• 2013

We computed Cramer-Rao bound for estimating amplitude and decay parameters of exponentially decaying function under Poisson noise. Since Cramer-Rao bound is the lowest variance bound for any unbiased estimator, the computed Cramer-Rao bound can be used for evaluating the performance of estimators under Poisson noise. In addition, we show that the performance of maximum-likelihood estimator is close to the Cramer-Rao bound by simulations.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.269-289
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• 2005

An infinite system of stochastic differential equations (SDE)driven by Brownian motions and compensated Poisson random measures for the locations and weights of a collection of particles is considered. This is an analogue of the work by Kurtz and Xiong where compensated Poisson random measures are replaced by white noise. The particles interact through their weighted measure V, which is shown to be a solution of a stochastic differential equation. Also a limit theorem for system of SDE is proved when the corresponding Poisson random measures in SDE converge to white noise.

• Journal of Information Processing Systems
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• v.12 no.1
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• pp.35-45
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• 2016

To resolve the problems of Poisson/impulse noise, blurriness, and sharpness in degraded X-ray images, a novel and efficient enhancement algorithm based on X-ray image fusion using a discrete wavelet transform is proposed in this paper. The proposed algorithm consists of two basics. First, it applies the techniques of boundary division to detect Poisson and impulse noise corrupted pixels and then uses the Wiener filter approach to restore those corrupted pixels. Second, it applies the sharpening technique to the same degraded X-ray image. Thus, it has two source X-ray images, which individually preserve the enhancement effects. The details and approximations of these sources X-ray images are fused via different fusion rules in the wavelet domain. The results of the experiment show that the proposed algorithm successfully combines the merits of the Wiener filter and sharpening and achieves a significant proficiency in the enhancement of degraded X-ray images exhibiting Poisson noise, blurriness, and edge details.

• Proceedings of the Korean Society of Medical Physics Conference
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• 2002.09a
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• pp.331-334
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• 2002

It has been reported that maximum-likelihood position-estimation (MLPE) algorithms offer advantages of improved spatial resolution and linearity over conventional Anger algorithm in gamma cameras. The purpose of this study is to evaluate the performances of the noise models, Poisson and Gaussian, in MLPE for the localization of photons in a small gamma camera (SGC) using NaI(Tl) plate and PSPMT. The SGC consists of a single NaI(Tl) crystal, 10 cm diameter and 6 mm thick, optically coupled to a PSPMT (Hamamatsu R3292-07). The PSPMT was read out using a resistive charge divider, which multiplexes 28(X) by 28(Y) cross wire anodes into four channels. Poisson and Gaussian based MLPE methods have been implemented using experimentally measured light response functions. The system resolutions estimated by Poisson and Gaussian based MLPE were 4.3 mm and 4.0 mm, respectively. Integral uniformities were 29.7% and 30.6%, linearities were 1.5 mm and 1.0 mm and count rates were 1463 cps and 1388 cps in Poisson and Gaussian based MLPE, respectively. The results indicate that Gaussian based MLPE, which is convenient to implement, has better performances and is more robust to statistical noise than Poisson based MLPE.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.45 no.5
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• pp.95-102
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• 2008

This paper presents an appropriate approach for modeling noise in Computed Radiography(CR) images of high strength materials. The approach is specifically designed for types of noise with the statistical and nonlinear properties. CR images Ere degraded even before they are encoded by computer process. Various types of noise often contribute to contaminate radiography image, although they are detected on digitalization. Quantum noise, which is Poisson distributed, is a shot noise, but the photon distribution on Image Plate(IP) of CR system is not always Poisson process. The statistical properties are relative and case-dependant due to its material characteristics. The usual assumption of a distribution of Poisson, binomial and Gaussian statistics are considered. Nonlinear effect is also represented in the process of statistical noise model. It leads to estimate the noise variance in regions from high to low intensity, specifying analytical model. The analysis approach is tested on a database of steel tube step-wedge CR images. The results are available for the comparative parameter studies which measure noise coherence, distribution, signal/noise ratios(SNR) and nonlinear interpolation.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.307-315
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• 2002

Suppose one is given a vector X of a finite set of quantities $X_i$ which are independent Poisson signals. A null hypothesis $H_0$ about E(X) is to be tested against an alternative hypothesis $H_1$. A quantity $$\sum\limits_{i}\omega_ix_i$$ is to be computed and used for the test. The optimal values of $\omega_i$ are calculated for three cases : (1) signal to noise ratio is used in the test, (2) normal approximations with unequal variances to the Poisson distributions are used in the test, and (3) the Poisson distribution it self is used. A comparison is made of the optimal values of $\omega_i$ in the three cases as parameter goes to infinity.

• Progress in Medical Physics
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• v.32 no.2
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• pp.50-58
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• 2021

Purpose: In this study, we investigated the relationship between the noise characteristics and the number of projected images in tomosynthesis using a digital phantom. Methods: The digital phantom consisted of a columnar phantom in the center of the image and a spherical phantom with a diameter of 80 pixels. A virtual scan was performed, and 128 projected images (Tomo_w/o) of the phantoms were obtained. The image noise according to the Poisson distribution was added to the projected images (Tomo_×1). Furthermore, another projected image with additional noise was prepared (Tomo_×1/2). For each dataset, we created datasets with 64 (half) and 32 (quarter) projections by removing the even-numbered images twice from the 128 (fully) projected images. Tomosynthesis images were reconstructed by filtered back projection (FBP). The modulation transfer function (MTF) was estimated using the sphere method, and the noise power spectrum (NPS) was estimated using the two-dimensional Fourier transform method. Results: The MTFs did not change between datasets, and the NPSs improved as the number of projected images increased. The noise characteristics of the Tomo_×1_half images were the same as those of the Tomo_×1/2_full. Conclusions: To achieve a reduction in the patient dose in tomosynthesis acquisition, we recommend reducing the number of projected images rather than reducing the dose per projection.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.41 no.8
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• pp.851-858
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• 2016

This paper presents a new statistical voice activity detection (VAD) based on the probabilistic interpretation of nonnegative matrix factorization (NMF). The objective function of the NMF using Kullback-Leibler divergence coincides with the negative log likelihood function of the data if the distribution of the data given the basis and encoding matrices is modeled as Poisson distributions. Based on this probabilistic NMF, the VAD is constructed using the likelihood ratio test assuming that speech and noise follow Poisson distributions. Experimental results show that the proposed approach outperformed the conventional Gaussian model-based and NMF-based methods at 0-15 dB signal-to-noise ratio simulation conditions.