• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.419-426
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• 2009

In expansion of function by special basis functions, properties of expansion kernel are very important. In the Fourier series, the series are expressed by the convolution with Dirichlet kernel. We investigate some of properties of kernel in wavelet expansions both in one and higher dimensions.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.1C
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• pp.16-22
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• 2007

This study proposes a new wavelet watermark technique based on the Linear Bit Expansion. To ensure the security of the watermark, enlarged watermark by applying linear bit expansion is inserted in a given intensity to a low frequency subband of the image which is wavelet transformed after the Arnold Transformation. When detecting the presence of watermart F norm function is applied unlike the existing methods. The experiment results verify that the proposed watermarking technique has outstanding quality in regards to fidelity and robustness.

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.639-647
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• 1996

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.265-270
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• 2007

The modern approach for wavelets imposes a Bayesian prior model on the wavelet coefficients to capture the sparseness of the wavelet expansion. The idea is to build flexible probability models for the marginal posterior densities of the wavelet coefficients. In this note, we derive exact expressions for a popular model for the marginal posterior density.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.81-91
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• 2001

The expansion of a distribution of $K^r_M^r(R)$ in terms of regular orthogonal wavelets is considered. The expansion of a distribution of $K^r_M^r(R)$ is shown to converge pointwise to the value of the distribution where is exists.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.285-308
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• 2000

We generalize bi-orthogonal (non-orthogona) MRA to frame MRA in which the family of integer translates of a scaling func-tion forms a frame for the initial ladder space V0. We investigate the internal structure of frame MRA and establish the existence of a dual scaling function, and show that, unlike bi-orthogonal MRA, there ex-ists a frame MRA that has no (frame) 'wavelet'. Then we prove the existence of a dual wavelet under the assumption of the existence of a wavelet and present easy sufficient conditions for the existence of a wavelet. Finally we give a new proof of an equivalent condition for the translates of a function in L2(R) to be a frame of its closed linear span.

• Journal of the Korea Society of Computer and Information
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• v.8 no.4
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• pp.7-12
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• 2003

This paper propose the 1-pass spatially adaptive wavelet thresholding for image denosing. The method of wavelet thresholding for denosing, has been concentrated on finding the best uniform threshold or best basis. However, not much has been done to make this method adaptive to spatially changing statistics which is typical of a large class of images. This spatially adaptive thresholding is extended to the overcomplete wavelet expansion, which yields better results than the orthogonal transform. Experiments show that this proposed method does indeed remove noise significantly, especially for large noise power. Experimental results show that the proposed method outperforms level dependent thresholding techniques and is comparable to spatial Wiener filtering method, 2-pass spatially adaptive wavelet thresholding method in matlab.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2006.05a
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• pp.167-170
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• 2006

This study proposes a new wavelet watermark technique based on the Linear Bit Expansion. To ensure the security of the watermark, it is Amold Transformed before embedding. Then the wavelet transformation of watermark and original images is processed. Since the size of the watermark image is a quarter of the original site, it uses linear bit-expansion to enlarge the watermark image. Lastly, watermark is inserted in a given intensity to the corresponding low frequency subbands of the wavelet-transformed images proposed in this paper. When detecting the presence of watermark, the similarity between extracted watermark and the original watermark is compared applying the F norm function.

• Proceedings of the IEEK Conference
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• 2005.11a
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• pp.343-346
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• 2005

In this study, a basic concept of wavelet encoding and its advantages over Fourier based phase encoding application. Wavelet encoding has been proposed as an alternative way to Fourier based phase encoding in magnetic resonance imaging. In wavelet encoding, the RF pulse is designed to generate wavelet-shaped excitation profile of spins. From the resulting echo signals, the wavelet transform coefficients of spin distribution are acquired and an original spin density is reconstructed from wavelet expansion. Wavelet encoding has several advantages over phase encoding. By minimizing redundancy of the data acquisition in a dynamic series of images, we can avoid some encoding steps without serious loss of quality in reconstructed image. This strategy may be regarded as data compression during imaging. Although there are some limitations in wavelet encoding, it is a promising scheme in a dynamic imaging.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.529-534
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• 1997

Even though the Shannon wavelet is a prototype of wavelets are assumed to have. By providing a sufficient condition to compute the size of Gibbs phe-nomenon for the Shannon wavelet series we can see the overshoot is propotional to the jump at discontinuity. By comparing it with that of the Fourier series we also that these two have exactly the same Gibbs constant.