• Journal of the Korea Institute of Information and Communication Engineering
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• v.16 no.5
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• pp.1040-1046
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• 2012

This paper propose a digital watermarking algorithm for a digital hologram which is the most valuable image content. It is highly necessary to protect the ownership of a digital hologram. This paper introduces a watermarking scheme, a method to protect the ownership of digital holograms using the Fresnel transform domain data as the ones to be watermarked. Experiment results indicated that the proposed scheme was very imperceptible in the digital hologram and in the reconstructed holographic image. Also, they showed quite strong resistance to most of the attacks. we expect that the conclusions of this paper can be the basis for further research on the digital watermarking for digital holograms.

• Korean Journal of Mathematics
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• v.26 no.3
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• pp.387-403
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• 2018

Shifting, scaling and modulation proprerties for the convolution product of the Fourier-Feynman transform of functionals in a generalized Fresnel class ${\mathcal{F}}_{A1,A2}$ are given. These properties help us to obtain convolution product of new functionals from the convolution product of old functionals which we know their convolution product.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.1031-1056
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• 2005

In this paper, we define the conditional first variation over Wiener paths in abstract Wiener space and investigate its properties. Using these properties, we also investigate relationships among first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transforms of functions in a Banach algebra which is equivalent to the Fresnel class. Finally, we provide another method evaluating the Fourier-Feynman transform for the product of a function in the Banach algebra with n linear factors.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.485-501
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• 2001

In this paper we express analytic Feynman integral of the first variation of a functional F in terms of analytic Feynman integral of the product F with a linear factor and obtain an integration by parts formula of the analytic Feynman integral of functionals on abstract Wiener space. We find the Fourier-Feynman transform for the product of functionals in the Fresnel class F(B) with n linear factors.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.223-245
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• 2011

In this paper, we de ne an $L_p$ analytic generalized Fourier Feynman transform and a convolution product of functionals in a Ba-nach algebra $\cal{F}$($C_{a,b}$[0, T]) which is called the Fresnel type class, and in more general class $\cal{F}_{A_1;A_2}$ of functionals de ned on general functio space $C_{a,b}$[0, T] rather than on classical Wiener space. Also we obtain some relationships between the $L_p$ analytic generalized Fourier-Feynman transform and convolution product for functionals in $\cal{F}$($C_{a,b}$[0, T]) and in $\cal{F}_{A_1,A_2}$.

• Journal of the Optical Society of Korea
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• v.20 no.3
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• pp.341-357
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• 2016

A novel asymmetric multiple-image encryption method using an octonion Fresnel transform (OFST) and a two-dimensional Sine Logistic modulation map (2D-SLMM) is presented. First, a new multiple-image information processing tool termed the octonion Fresneltransform is proposed, and then an efficient method to calculate the OFST of an octonion matrix is developed. Subsequently this tool is applied to process multiple plaintext images, which are represented by octonion algebra, holistically in a vector manner. The complex amplitude, formed from the components of the OFST-transformed original images and modulated by a random phase mask (RPM), is used to derive the ciphertext image by employing an amplitude- and phase-truncation approach in the Fresnel domain. To avoid sending whole RPMs to the receiver side for decryption, a random phase mask generation method based on SLMM, in which only the initial parameters of the chaotic function are needed to generate the RPMs, is designed. To enhance security, the ciphertext and two decryption keys produced in the encryption procedure are permuted by the proposed SLMM-based scrambling method. Numerical simulations have been carried out to demonstrate the proposed scheme's validity, high security, and high resistance to various attacks.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.183-198
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• 1999

Let $\mathcal{F}(B)$ be the Fresnel class on an abstract Wiener space (B, H, ${\omega}$) 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 $\mathcal{M}(H)$, the space of all complex-valued countably additive Borel measures on H. We introduce the concepts of an $L_p$ analytic Fourier-Feynman transform ($1{\leq}p{\leq}2$) and a convolution product on $\mathcal{F}(B)$ and verify the existence of the $L_p$ analytic Fourier-Feynman transforms for functionls in $\mathcal{F}(B)$. Moreover, we verify that the Fresnel class $\mathcal{F}(B)$ is closed under the $L_p$ analytic Fourier-Feynman transform and the convolution product, respectively. And we investigate some interesting properties for the $n$-repeated $L_p$ analytic Fourier-Feynman transform on $\mathcal{F}(B)$. Finally, we show that several results in [9] come from our results in Section 3.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.1
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• pp.79-99
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• 2006

In this paper, we define a class of functional defined on a very general function space $C_{a,b}[0,T]$ like a Fresnel class of an abstract Wiener space. We then define the multiple $L_p$ analytic generalized Fourier-Feynman transform and the generalized convolution product of functionals on function space $C_{a,b}[0,T]$. Finally, we establish some relationships between the multiple $L_p$ analytic generalized Fourier-Feynman transform and the generalized convolution product for functionals in $\mathcal{F}(C_{a,b}[0,T])$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.6C
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• pp.604-610
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• 2009

This paper propose a digital watermarking method for digital contents which satisfies both the invisibility and the robustness to attacks to prohibit counterfeiting, modification, illegal usage and illegal re-production of video contents. This watermarking algorithm insert a watermark(digital hologram) by generated using Fresnel transform which improve the robustness. The inserting positions of the watermark choose by considering the frequency property of an image and a watermark. Also the amount of watermarking for watermark bit decide by considering the level of 2DDWT. This algorithm was implemented by C++ and experimented for invisibility and robustness with optical system. The experiment results showed that the method satisfied enough the invisibility of the inserted watermark and robustness against attacks. For the general attacks, the error rate of the extracted watermark was less than 15%, which is enough in robustness against the attacks.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.15 no.5
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• pp.1073-1080
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• 2011

In this paper, we propose a novel digital watermarking method by virtual optics which secures multimedia information such as images, videos and sounds. To secure the multimedia data, we use Fresnel transform which describes the diffraction phenomena of the waves. Also, this method attaches the random phase function to Fresnel transform so that original image and watermark image would be gaussian random vectors. The complex numbers of watermark by Fresnel transform are separated the real part and the imaginary part. The former is embedded in original image as a encoding key imperceptibly and the latter is used for detecting the watermark as a decoding key. This method for digital watermarking ensures that watermark can be successfully registered and extracted from the watermarked image. Further, it provides the robustness to signal processing operation and geometric distortion and proves the strong resilience against cropping attack. The performance evaluation of the experiment is carried out with PSNR, and the numerical simulation results show the efficiency of the proposed method.