• 전자공학회논문지SC
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• 제44권6호
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• pp.42-48
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• 2007

X-ray 영상 시스템에서는, 크게 2 종류의 noise 성분이 함유되어있다. 먼저 x-ray 방사선이 조사되어질 때, 검출기에서의 방사선의 상호작용으로부터 발생되어지는 것으로서 랜덤하게 발생되어지는 Poisson noise 성분이다. 다음으로 noise 성분은 readout electronics noise, pixel pattern noise 그리고 off-set noise 등으로부터 발생되어지는 Gaussian noise 성분이다. 그러나, x-ray 영상에서는 Gaussian noise가 아닌, Poisson noise로 모델링 되어진다. Gaussian noise에 의해서 발생되어지는 noise 성분은 위너필터 혹은 웨이브렛을 사용하여 쉽게 제거가 가능하지만, Poisson noise와 같은 랜덤 noise를 제거하기 위해서는 복잡한 분석기법이 필요하게 한다. 이 논문에서는 웨이브렛 영역에서 x-ray 영상의 Poisson noise를 제거하고자 하였으며, 적용된 분석 기법은 최적화된 웨이브렛 분석기법인 IBS(Improved BayesShrink)을 사용하였다. 적용된 IBS 기법은 cone-beam CT의 x-ray 영상에서의 기존의 방법에 비해 향상된 결과를 보여주었다.

• Communications for Statistical Applications and Methods
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• 제9권3호
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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.

• 전기학회논문지
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• 제62권1호
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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.

• 대한수학회지
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• 제42권2호
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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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• 제12권1호
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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.

• 한국의학물리학회:학술대회논문집
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• 한국의학물리학회 2002년도 Proceedings
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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.

• 대한전자공학회논문지SP
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• 제45권5호
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• pp.95-102
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• 2008

이 논문은 고강도매질 CR(Computed Radiography) 영상의 잡음을 모델링하는 적절한 접근법을 제시한다. 잡음 유형의 통계적이고 비선형적 특성이 구체적으로 고안되었다. CR영상은 컴퓨터 처리에 의해 코드화되기 이전 이미 훼손된다. 다양한 형태의 잡음은 비록 디지털화된 상태로 검출된다 하더라도 통상 방사선 영상을 오염시킨다. 양자 방출시의 포아송 분포는 CR 영상판에서의 광자 분포에서 포아송 잡음 분포를 항상 유지하지 않는다. 그 통계적 특성은 재질 특성에 의해 상대적이며 경우의존적이다. 통계적 잡음모델링 과정에서 통상적인 포아송, 이항 내지는 가우스 통계분포의 가정이 고려되었으며 아울러 비선형 효과 또한 포함시켰다. 이는 잡음 영역의 고저 전 방사선량에 걸쳐 추정하는 해석적 모델을 구현한다. 그리고 이 분석적 접근은 고강도 강판튜브 스텝웨지의 방사선측정실험을 통해 관측한 CR 영상데이터에서 구현되었다. 그 결과는 매질의 두께변화에 따른 잡음의 일관성, 잡음분포특성, SNR 및 비선형 보간을 측정하는 상호비교의 파라미터연구에 유용하다.

• Journal of the Korean Data and Information Science Society
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• 제13권2호
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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.

• 한국의학물리학회지:의학물리
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• 제32권2호
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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.

• 한국통신학회논문지
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• 제41권8호
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• pp.851-858
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• 2016

본 논문은 비음수 행렬 인수분해(NMF)의 확률적 해석에 근거한 새로운 통계적 음성검출기법을 제안한다. NMF의 기저와 부호화 행렬들이 주어졌을 때, 데이터 행렬의 분포를 Poisson 분포로 가정한 로그 우도는 Kullback-Leibler 발산을 이용한 NMF의 목적 함수와 일치한다. 이러한 NMF의 확률모델에 근거하여 음성검출을 위해 DFT영역에서 잡음과 음성의 크기 스펙트럼을 Poisson 분포로 모델링하여 새로운 우도비 검출 규칙을 유도한다. 실험 결과를 통해 제안된 기법이 0-15dB 신호 대 잡음비의 시뮬레이션 환경에서 기존 Gaussian과 NMF을 사용한 기법보다 향상된 음성검출 결과를 보여준다.