• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.1-27
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• 2000

위너공간과 추상 위너공간 위에서의 푸리에-파인만 변환, 푸리에-위너 변환 그리고 합성곱을 정의하고 여러가지 형태의 함수들에 대한 변환과 합성곱의 존재정리 및 여러가지 성질을 소개한다. 또한, 이 함수들의 파시발 관계와 프란셰렐 관계에 대해서도 알아본다.

• Journal for History of Mathematics
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• v.21 no.1
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• pp.97-108
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• 2008

In this paper, we investigate the analytic Feynman integral, the analytic Fourier-Feynman transform and convolution product on Wiener space. We then consider various results between these concepts.

• Journal of radiological science and technology
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• v.32 no.1
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• pp.17-24
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• 2009

Noise evaluation for an image has been performed by root mean square (RMS) granularity, autocorrelation function (ACF), and Wiener spectrum. RMS granularity stands for standard deviation of photon data and ACF is acquired by integration of 1 D function of distance variation. Fourier transform of ACF results in noise power spectrum which is called Wiener spectrum in image quality evaluation. Wiener spectrum represents noise itself. In addition, along with MTF, it is an important factor to produce detective quantum efficiency (DQE). The proposed evaluation method using Wiener spectrum is expected to contribute to educate the concept of Wiener spectrum in educational organizations, choose the appropriate imaging detectors for clinical applications, and maintain image quality in digital imaging systems.

• Communications of the Korean Mathematical Society
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• v.15 no.3
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• pp.435-451
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• 2000

섀논의 샘플링 정리는 여러 방향으로 확장 발전되어왔으나 본 논문에서는 초함수 이론으로 다룰 수 있는 방향, 즉 좀 더 큰 공간에 속하는 함수에 대한 샘플링 정리를 얻는 것이다. 먼저 샘플링이론의 기본정리인 섀논-코텔니코프 공식을 소개하고 그 자연스런 확장인 페일리-위너 공간, 번스타인 공간에서의 샘플링정리 등을 다루었고 번스타인 공간의 자연스런 확장인 유계인 받침을 갖는 초함수의 푸리에변환 즉, 실공간 위에서 다항식정도로 증가하는 전해석함수에 대한 샘플링 정리를 소개한다. 끝으로 우리의 최근 결과인 실공간 위에서 지수적으로 증가하는 전해석 함수에 대한 샘플링 정리와 그 응용, 그리고 오차추정 등을 다룬다.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.16 no.2
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• pp.113-122
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• 2016

In this paper, we suggest a approach which comprises fast Fourier transform inversion by wavelet noise attenuation. It represents an inverse filtering by adopting a factor into the Wiener filtering, and the optimal factor is chosen to minimize the overall mean squared error. in order to apply the Wiener filter, we have to compute the power spectrum of original image from the corrupted figure. Since the Wiener filtering contains the inverse filtering process, it expands the noise when the blurring filter is not invertible. To remove the large noises, the best is to remove the noise using wavelet threshold. Wavelet noise attenuation steps are consisted of inverse filtering and noise reduction by Wavelet functions. experimental results have not outperformed the other methods over the overall restoration performance.