• 대한수학회논문집
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• 제13권1호
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• pp.181-193
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• 1998

The Shannon sampling series is the prototype of an interpolating series or sampling series. Also the Shannon wavelet is one of the protypes of wavelets. But the coefficients of the Shannon sampling series are different function values at the point of discontinuity, we analyze the Gibbs phenomenon for the Shannon sampling series. We also find a way to go around this overshoot effect.

• Journal of information and communication convergence engineering
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• 제10권1호
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• pp.45-52
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• 2012

Thedenoising of a natural image corrupted by Gaussian noise is a long established problem in signal or image processing. Today the research is focus on the wavelet domain, especially using the wavelet threshold method. In this paper, a waveletbased image denoising modified adaptive thresholding method is proposed. The proposed method computes thethreshold adaptively based on the scale level and adaptively estimates wavelet coefficients by using a modified thresholding function that considers the dependency between the parent coefficient and child coefficient and the soft thresholding function at different scales. Experimental results show that the proposed method provides high peak signal-to-noise ratio results and preserves the detailed information of the original image well, resulting in a superior quality image.

• 한국통신학회논문지
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• 제22권2호
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• pp.392-400
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• 1997

In this paper we porposed WCHF-fSDF filter to obtain a roration and scale-invariant correlation output. WCHF-fSDF filter is synthesized by each single CHF exttracted from scale-changed and wavelet tranformed imagesfor a refereence image as tranining images. The wavelet transform is defined as the correlation of an input image with a wavelet function. Therefore two 4f optical correlation systems are needed for pattern recognition using wavelet transform. We here include the wavelet function for the input image in the process of the proposed filter design and substitute the two 4f optical correlation system with a single 4f optical correlation system. The Performances of the proposed filter are compared with conventional CHF-SDF, POCHF-SDF filters through the computer simulation. The results of computer simulation show that the proposed filter has the rotation and scale-invariant correlation output and it has better performances than thoseof the conventioanl filters.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2005년도 제36회 하계학술대회 논문집 D
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• pp.2681-2683
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• 2005

In this paper, we present the structure of fuzzy neural network(FNN) based on wavelet function, and apply this network structure to the identification of nonlinear systems. For adjusting the shape of membership function and the connection weights, the parameter learning method based on the gradient descent scheme is adopted. And an approach that uses adaptive learning rates is driven via a Lyapunov stability analysis to guarantee the fast convergence. Finally, to verify the efficiency of our network structure. we compare the Identification performance of proposed wavelet based fuzzy neural network(WFNN) with those of the FNN, the wavelet fuzzy model(WFM) and the wavelet neural network(WNN) through the computer simulation.

• 한국방송∙미디어공학회:학술대회논문집
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• 한국방송공학회 2009년도 IWAIT
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• pp.246-249
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• 2009

Due to the additive white Gaussian noise (AWGN), images are often corrupted. In recent days, Bayesian estimation techniques to recover noisy images in the wavelet domain have been studied. The probability density function (PDF) of an image in wavelet domain can be described using highly-sharp head and long-tailed shapes. If a priori probability density function having the above properties would be applied well adaptively, better results could be obtained. There were some frequently proposed PDFs such as Gaussian, Laplace distributions, and so on. These functions model the wavelet coefficients satisfactorily and have its own of characteristics. In this paper, mixture distributions of Gaussian and Laplace distribution are proposed, which attempt to corporate these distributions' merits. Such mixture model will be used to remove the noise in images by adopting Maximum a Posteriori (MAP) estimation method. With respect to visual quality, numerical performance and computational complexity, the proposed technique gained better results.

• 한국지능시스템학회논문지
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• 제10권4호
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• pp.338-342
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• 2000

In order to approximate a nonlinear function, wacelet neural networks combining wacelet theory and neural networks have been proposed as an alternative to conventional multi-layered neural networks. wacelet neural networks provide better approximating performance than conventional neural networks. In this paper, an effective method to construct an optimal wavelet neural network is proposed using genetic alogorithm. Genetic Algorithm is used to determine dilationa and translations of wavelet basic functions of wavelet neural networks. Then, these determined dilations dilations and translations, wavelet neural networks are funther trained by back propagation learning algorithm. The effectiveness of the final network is verified thrifigh the approximation result of a nonlinear function and comparison with conventional neural networks.

• 한국항해항만학회:학술대회논문집
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• 한국항해항만학회 2006년도 International Symposium on GPS/GNSS Vol.2
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• pp.91-96
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• 2006

Presently, cycle-slip detection is done between adjacent two points in many cycle-slip methods. Inherently, it is simple wavelet analysis. A new idea is put forward that the number of difference point can adjust by a parameter factor; we study this method to smooth raw data and detect cycle-slip with wavelet analysis. Taking CHAMP satellite data for example, we get some significant conclusions. It is showed that it is valid to detect cycle-slip in GPS phase measurement based on this wavelet function, and it is helpful to improve the precision of GPS data pre-processing and positioning.

• 대한수학회논문집
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• 제15권2호
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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.

• Kyungpook Mathematical Journal
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• 제61권2호
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• pp.371-381
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• 2021

In this paper, we attempt to obtain sufficient conditions for the existence of tight wavelet frame sets in locally compact abelian groups. The condition is generated by modulating a collection of characteristic functions that correspond to a generalized shift-invariant system via the Fourier transform. We present two approaches (for stationary and non-stationary wavelets) to construct the scaling function for L²(G) and, using the scaling function, we construct an orthonormal wavelet basis for L²(G). We propose an open problem related to the extension principle for Riesz wavelets in locally compact abelian groups.

• Structural Engineering and Mechanics
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• 제63권6호
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• pp.761-769
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• 2017

Accurately extracting the axle distribution information of a passing vehicle from bridge dynamic responses experiences a key and challenging step in non-pavement bridge weigh-in-motion (BWIM). In this article, the wavelet transformation is adopted and the wavelet coefficient curve is used as a substitute for dynamic response. The driving frequency is introduced and expanded to multi-axle vehicle, and the wavelet coefficient curve on specific scale corresponding to the driving frequency is confirmed to contain obvious axle information. On this basis, an automatic method for axle distribution information identification is proposed. The specific wavelet scale can be obtained through iterative computing, and the false peaks due to bridge vibration can be eliminated through cross-correlation analysis of the wavelet coefficients of two measure points. The integrand function that corresponds to the maximum value of the cross-correlation function is used to identify the peaks caused by axles. A numerical application of the proposed axle information identification method is carried out. Numerical results demonstrate that this method acquires precise axle information from the responses of an axle-insensitive structure (e.g., girder) and decreases the requirement of sensitivity structure of BWIM. Finally, an experimental study on a full-scale simply supported bridge is also conducted to verify the effectiveness of this method.