• Communications of the Korean Mathematical Society
• /
• v.26 no.2
• /
• pp.273-289
• /
• 2011

In this paper we dene the concept of a conditional generalized Fourier-Feynman transform on very general function space $C_{a,b}$[0, T]. We then establish the existence of the conditional generalized Fourier-Feynman transform for functionals in a Fresnel type class. We also obtain several results involving the conditional transform. Finally we present functionals to apply our results. The functionals arise naturally in Feynman integration theories and quantum mechanics.

• Korean Journal of Mathematics
• /
• v.9 no.2
• /
• pp.133-147
• /
• 2001

In this paper, we introduce the concepts of multiple $L_p$ analytic Fourier-Feynman transform ($1{\leq}p$ < ${\infty})$ and a convolution product of functionals on abstract Wiener space and verify the existence of the multiple $L_p$ analytic Fourier-Feynman transform for functionls in the Fresnel class. Moreover, we verify that the Fresnel class is closed under the $L_p$ analytic Fourier-Feynman transformation and the convolution product, respectively. And we establish some relationships among the multiple $L_p$ analytic Fourier-Feynman transform and the convolution product on the Fresnel class.

• Journal of KIISE:Computing Practices and Letters
• /
• v.9 no.1
• /
• pp.70-76
• /
• 2003

Digital watermarking is a technique embedding hidden information into multimedia data imperceptibly such as images and sounds. Generally an original image is transformed and coded watermark data is embedded in frequency domain watermarking models. In this paper, We propose a new data embedding method using Fresnel transform. A watermark image is fresnel-transformed and the intensity of transformed pattern is embedded into original image. Our watermarking model has the flexibility In data embedding. It is possible to get many embedding patterns from a single watermark image by using various distance parameters with Fresnel transform. All kinds of image models such af shape, letter and photo ran be used as a watermark data. The watermarking experiments were conducted to show the validity of the proposed method, and the results show that our method has the robustness against lossy compression, filtering and geometric transformation.

• Korean Journal of Mathematics
• /
• v.25 no.3
• /
• pp.335-347
• /
• 2017

Time shifting and frequency shifting proprerties for the Fourier-Feynman transform of functionals in a generalized Fresnel class ${\mathcal{F}}_{A_1,A_2}$ are given. We discuss scaling and modulation proprerties for the Fourier-Feynman transform. These properties help us to obtain Fourier-Feynman transforms of new functionals from the Fourier-Feynman transforms of old functionals which we know their Fourier-Feynman transforms.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.3
• /
• pp.481-495
• /
• 2009

Huffman, Park and Skoug introduced various results for the $L_{p}$ analytic Fourier-Feynman transform and the convolution for functionals on classical Wiener space which belong to some Banach algebra $\mathcal{S}$ introduced by Cameron and Storvick. Also Chang, Kim and Yoo extended the above results to an abstract Wiener space for functionals in the Fresnel class $\mathcal{F}(B)$ which corresponds to $\mathcal{S}$. Moreover they introduced the $L_{p}$ analytic Fourier-Feynman transform for functionals on a product abstract Wiener space and then established the above results for functionals in the generalized Fresnel class $\mathcal{F}_{A1,A2}$ containing $\mathcal{F}(B)$. In this paper, we investigate more generalized relationships, between the Fourier-Feynman transform and the convolution product for functionals in $\mathcal{F}_{A1,A2}$, than the above results.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.16 no.7
• /
• pp.1505-1511
• /
• 2012

Since digital hologram includes an amount of data as can be seen at the process of digitization, it is necessary that the data representing digital hologram is reduced for storing, transmission, and processing. As the efforts that are to handle hologram with a type of digital information have been increased, various methods to compress digital hologram called by fringe pattern are groped. Suitable proposal is encoding of digital hologram. This paper analyzed the properties of digital hologram using tools of frequency transform, assuming that a generated digital hologram is a 2D image by introducing Fresnel Transform. The analysis results of digital hologram to be proposed in this paper are being expected to be used as the core techniques for an encoding of digital hologram.

• Journal of Broadcast Engineering
• /
• v.19 no.5
• /
• pp.606-615
• /
• 2014

This paper is to propose an algorithm for digital hologram watermarking by using a characteristic of the Fresnel diffraction model in 2D image. When 2D image is applied Fresnel transform, the result concentrates center region. When applied to a hologram, on the other hand, the result focused diffraction pattern of 2D form. Using this characteristic, to generate diffraction model by applying 2-th Fresnel transform to the hologram. Corner of diffraction model is mark space. This mark space is embedded watermark and extracted watermark. Experimental results showed that all the extracted watermarks after several kinds of attacks (Gaussian blurring, Sharpening, JPEG compression) showed visibilities good enough to be recognized to insist the ownership of the hologram.

• Korean Journal of Optics and Photonics
• /
• v.23 no.6
• /
• pp.251-254
• /
• 2012

Dual-wavelength holography has a better axial range than single-wavelength holography, allowing unambiguous phase imaging. The size of a reconstructed image depends on the reconstruction distance and wavelength. The two phase image sizes of different wavelength holograms should be the same in order to apply dual-wavelength holography. The Fresnel-Bluestein transform method is proposed to eliminate the dependence on the reconstruction distance and wavelength. We found that the Fresnel-Bluestein transform is very useful for making different reconstructed image sizes experimentally. Also we applied the Fresnel-Bluestein transform to make the same reconstruction image size in dual wavelength holography.

• Communications of the Korean Mathematical Society
• /
• v.22 no.1
• /
• pp.75-90
• /
• 2007

Huffman, Park and Skoug introduced various results for the $L_p$ analytic Fourier-Feynman transform and the convolution for functionals on classical Wiener space which belong to some Banach algebra S introduced by Cameron and Strovic. Also Chang, Kim and Yoo extended the above results to an abstract Wiener space for functionals in the Fresnel class F(B) which corresponds to S. Recently Kim, Song and Yoo investigated more generalized relationships between the Fourier-Feynman transform and the convolution product for functionals in a generalized Fresnel class $F_{A_1,A'_2}$ containing F(B). In this paper, we establish various interesting relationships and expressions involving the first variation and one or two of the concepts of the Fourier-Feynman transform and the convolution product for functionals in $F_{A_1,A_2}$.

• The Journal of the Korea Contents Association
• /
• v.6 no.7
• /
• pp.90-98
• /
• 2006

Digital watermarking is a technique embedding hidden information into multimedia data imperceptibly such as images and sounds. Generally an original image is transformed and coded watermark data is embedded in frequency domain watermarking models. In this paper, We propose a new color image watermarking technique using Fresnel transform. A watermark image is Fresnel - transformed and the intensity of transformed pattern is embedded into color image. In our watermarking model, an original image is converted from RGB components into YCrCb components and then the values of real number and imaginary number of a Fresnel-transformed pattern of a watermark image are embedded into Y component. The watermarking experiments were conducted to show the validity of the proposed method using PSNR value, and the results show that our method has the robustness against lossy compression like JPEG.