• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.99-117
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• 1998

Let $(B, H, p_1)$ be an abstract Wiener space and $F(B)$ the Fresnel class on $(B, H, p_1)$ which consists of functionals F of the form : $$ F(x) = \int_{H} exp{i(h,x)^\sim} df(h), x \in B, $$ where $(\cdot, \cdot)^\sim$ is a stochastic inner product between H and B, and f is in $M(H)$, the space of complex Borel measures on H. We introduce an $L_1$ analytic Fourier-Feynman transforms for functionls in $F(B)$. Furthermore, we introduce a convolution on $F(B)$, and then verify the existence of the $L_1$ analytic Fourier-Feynman transform for the convolution product of two functionals in $F(B)$, and we establish the relationships between the $L_1$ analytic Fourier-Feynman tranform of the convolution product for two functionals in $F(B)$ and the $L_1$ analytic Fourier-Feynman transforms for each functional. Finally, we show that most results in [7] follows from our results in Section 3.

• Journal of Broadcast Engineering
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• v.20 no.6
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• pp.807-817
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• 2015

This paper is to propose an encryption method for only an allowed user to see the content for a digital hologram, that is a high value-added content. This paper uses a characteristic of Fresnel transform that the object region is concentrated to a relatively small part of the diffraction plane. By encrypting the concentrated part only the region to be encrypted and in turn the amount of data to be encrypted is reduced a lot, which results in an high efficiency with low encryption rate. As the methodology, a digital hologram is first Fresnel transformed for reconstruction and the result is secondly Fresnel transformed to concentrate the energy into the center of the diffraction plane to encrypt the concentrated region only. For the 2nd transform, energy concentration degree is determined by adjusting the diffraction distance and encryption strength is determined by adjusting the scaling factor. For this we analyze the optimal encryption area according to the diffraction distance and the scaling factor. When applying the proposed method with diffraction distance of 20m the object information was visually unrecognizable with the encryption ratio only 0.005% ~ 0.02%.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2012.07a
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• pp.409-410
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• 2012

본 논문에서는 디지털 홀로그램의 저작권 보호를 위한 영상암호화 알고리즘을 제안한다. 이 기술은 자연영상과는 상이한 특성을 보이는 디지털 홀로그램의 화소분포를 고려하여, 디지털 홀로그램을 복원영역으로 변환한 후 데이터의 일부분을 암호화 하는 기법이다. 실험결과 제안한 암호화 알고리즘은 디지털 홀로그램 데이터의 일부분만을 조작하여 홀로그래픽 복원영상을 효율적으로 은닉하는 것을 확인할 수 있었다.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2015.07a
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• pp.58-61
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• 2015

본 논문에서는 디지털 홀로그램(digital hologram)을 2 차원 비디오 압축기를 사용하여 압축하는 방법을 다룬다. 그 방법은 디지털 홀로그램을 다수개의 부홀로그램(sub-hologram)으로 나누어 배열하고, 각 부홀로그램을 2 차원영상화하여 부홀로그램 배열을 동영상 시퀀스로 만들어 2 차원 동영상 압축기로 압축하는 방법이다. 본 논문에서는 각 부홀로그램을 2 차원 영상으로 만드는 방법으로 DCT(Discrete Cosine Transform)와 Fresnel 변환 변환(Fresnel Transform)을 사용한다. 2 차원 비디오 압축 방법으로는 H.264/AVC 와 HEVC 를 사용하여, 두 방법의 압축결과를 비교, 분석한다.

• Journal of Korea Multimedia Society
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• v.19 no.6
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• pp.1043-1051
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• 2016

In this paper, double encryption technique of binary image using random phase mask and 2-step phase-shifting digital holography is proposed. After phase modulating of binary image, firstly, random phase mask to be used as key image is generated through the XOR operation with the binary phase image. And the first encrypted image is encrypted again through the fresnel transform and 2-step phase-shifting digital holography. In the decryption, simple arithmetic operation and inverse Fresnel transform are used to get the first decryption image, and second decryption image is generated through XOR operation between first decryption image and key image. Finally, the original binary image is recovered through phase modulation.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2015.11a
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• pp.77-80
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• 2015

본 논문에서는 디지털 홀로그램(digital hologram)을 2 차원 비디오 압축기를 사용하여 압축하는 방법을 다룬다. 그 방법은 디지털 홀로그램을 다수 개의 부홀로그램(sub-hologram)으로 나누고, 각 부홀로그램을 2 차원영상화한 후 그 결과를 배열하여 동영상 시퀀스로 만들어 2 차원 동영상 압축기로 압축하는 방법이다. 각 부홀로그램을 2 차원 영상으로 만드는 방법으로 DCT(Discrete Cosine Transform)와 Fresnel 변환 변환(Fresnel Transform)을 사용하며, 다양한 크기의 부홀로그램을 고려한다. 2 차원 비디오 압축 방법으로는 H.264/AVC 와 HEVC 를 사용한다. 본 논문에서는 2 차원 영상 변환 방법, 부홀로그램의 크기, 그리고 2 차원 영상압축 방법에 따른 성능을 비교하고 분석한다.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.21 no.4
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• pp.820-828
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• 2017

Service of digital hologram that has been recognized as a visual system for next generation requires various signal processing technologies. A transform is the most frequently used tool among signal processing techniques for 2-dimensional(D) and 3-D natural picture. A digital hologram has totally different property with a natural picture, so it is rarely efficient to apply transform tools used in 2-D image processing to a digital hologram. To overcome this a Fresnelet transform for a digital hologram has been proposed. We derive a Fresnelet transform by using the Daubechie's filter after applying an unitary Fresnel transform to a wavelet basis function. We also implement the transform as types of device and kernel code to improve operational performance. In consideration of the average time that is required for a pixel we can have observed the performance is improved up to 242 and 30 times for using the (9,7) and (5,3) filters in case of using device code.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.23 no.3
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• pp.291-298
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• 2019

In this paper, we propose a Fresnel transform method using various wavelet functions to efficiently decompose digital holograms. After implementing the proposed wavelet function-based Fresnelet transforms, we apply it to the digital hologram and analyze the energy characteristics of the coefficients. The implemented wavelet transform-based Fresnelet transform is well suited for reconstructing and processing holograms which are optically obtained or generated by computer-generated hologram technique. After analyzing the characteristics of the spline function, we discuss wavelet multiresolution analysis method based on it. Through this process, we proposed a transform tool that can effectively decompose fringe patterns generated by optical interference phenomena. We implement Fresnelet transform based on wavelet function with various decomposition properties and show the results of decomposing fringe pattern using it. The results show that the energy distribution of the coefficients is significantly different depending on whether the random phase is included or not.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.41 no.11
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• pp.43-51
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• 2004

In this paper, we propose a high-level optical encryption system, which is tolerant with noises and cropping, by encrypting the phase-encoded CGH pattern of original image with the phase-encoded Fresnel diffraction pattern of random key images. For encryption, the phase-encoded CGH pattern of original image is multiplied by conjugate components which are the phase-encoded Fresnel diffraction patterns of random key images. The original information can be reconstructed by multiplying encrypted image by phase-encoded Fresnel diffraction pattern of random key images and performing Fourier transform of the multiplication result. The proposed system is robust to noises and cropping due to characteristics of CGH pattern and can guarantee high-level encryption by using Fresnel diffraction information. We verified the validity of proposed system by computer simulations, numerical analysis of noises and cropping effect and optical experiment.

• Journal of Broadcast Engineering
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• v.19 no.6
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• pp.854-865
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• 2014

This paper proposes a method to generate a stereoscopic image pair from a digital hologram by considering the situation that digital hologram data is serviced but the end-user does not have the proper display equipment, etc. We use Fresnel transform as the method to convert a digital hologram into an image. Each image of the stereoscopic image pair uses a part of the given digital hologram and the sizes of the two partial digital holograms for the two images are chosen to be the same. Here, the size of the image is adjusted by the size of the partial digital hologram and the disparity between the pair images is adjusted by the distance between the centers of the two partial hologram. This paper also deals with how to adjust the size and the disparity of the images. In this paper the generated stereoscopic images are implemented as an anaglyphic display type to confirm the feeling of distance by wearing the red-blue glasses.