• Korean Journal of Mathematics
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• v.24 no.2
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• pp.235-271
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• 2016

By using the Heckman-Opdam theory on ${\mathbb{R}}^d$ given in [20], we define and study in this paper, the generalized wavelets on ${\mathbb{R}}^d$ and the generalized wavelet transform on ${\mathbb{R}}^d$, and we establish their properties. Next, we prove for the generalized wavelet transform Plancherel and inversion formulas.

• Journal of the Institute of Convergence Signal Processing
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• v.9 no.4
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• pp.295-303
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• 2008

In general, transform domain adaptive filters show faster convergence speed than the time domain adaptive filters, but the amount of calculation increases dramatically as the filter order increases. This problem can be solved by making use of the subband structure in transform domain adaptive filters. In this paper, to increase the convergence speed on the generalized subband decomposition FIR adaptive filters, a structure of the adaptive filter with subfilter of dyadic sparsity factor in wavelet transform domain is designed. And, in this adaptive filter, the equivalent input in transform domain is derived and, by using the input, the convergence properties for the LMS algorithm is analyzed and evaluated. By using this sub band adaptive filter, the inverse system modeling and the periodic noise canceller were designed, and, by computer simulation, the convergence speeds of the systems on LMS algorithm were compared with that of the subband adaptive filter using DFT(discrete Fourier transform).

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.11
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• pp.4118-4136
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• 2014

To preserve the spatial consistency of low-level features, generalized Riesz-wavelet transform (GRWT) is adopted for fusing multi-modality images. The proposed method can capture the directional image structure arbitrarily by exploiting a suitable parameterization fusion model and additional structural information. Its fusion patterns are controlled by a heuristic fusion model based on image phase and coherence features. It can explore and keep the structural information efficiently and consistently. A performance analysis of the proposed method applied to real-world images demonstrates that it is competitive with the state-of-art fusion methods, especially in combining structural information.

• The Journal of the Acoustical Society of Korea
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• v.15 no.4E
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• pp.53-57
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• 1996

An extension of the well-known Fourier transform is developed in this paper. It is denoted as the generalized Fourier transform(GFT), since it encompasses the Fourier transform as its special case. The first idea of this extension can be found on [1]. In the definition of the N-point discrete GFT, it first construct a passband in time which functions as a window in the time domain. An appropriate interpretation of each variables are introduced during the definition of the GFT, followed by the formal derivation of the inverse GFT. This transform pair is similar to the windowing in the frequency domain such as the subband coding technique (or filter bank approach) and could be extended to the wavelet transform.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.43 no.5 s.311
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• pp.52-61
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• 2006

Orthogonal wavelet tansform which is generally used in image and signal processing applications has limited performance because of lack of shift invariance and low directional selectivity. To overcome these demerits complex wavelet transform has been proposed. In this paper, we present an efficient image denoising method using dual-tree complex wavelet transform and Bernoulli-Gauss prior model. In estimating hyper-parameters for Bernoulli-Gaussian model, we present two simple and non-iterative methods. We use hypothesis-testing technique in order to estimate the mixing parameter, Bernoulli random variable. Based on the estimated mixing parameter, variance for clean signal is obtained by using maximum generalized marginal likelihood (MGML) estimator. We simulate our denoising method using dual-tree complex wavelet and compare our algorithm to well blown denoising schemes. Experimental results show that the proposed method can generate good denoising results for high frequency image with low computational cost.

• Structural Engineering and Mechanics
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• v.37 no.6
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• pp.575-592
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• 2011

For seismic resistant design of critical structures, a dynamic analysis, either response spectrum or time history is frequently required. Owing to the lack of recorded data and the randomness of earthquake ground motion that may be experienced by structure in the future, usually it is difficult to obtain recorded data which fit the requirements (site type, epicenteral distance, etc.) well. Therefore, the artificial seismic records are widely used in seismic designs, verification of seismic capacity and seismic assessment of structures. The purpose of this paper is to develop a numerical method using Artificial Neural Network (ANN) and wavelet packet transform in best basis method which is presented for the decomposition of artificial earthquake records consistent with any arbitrarily specified target response spectra requirements. The ground motion has been modeled as a non-stationary process using wavelet packet. This study shows that the procedure using ANN-based models and wavelet packets in best-basis method are applicable to generate artificial earthquakes compatible with any response spectra. Several numerical examples are given to verify the developed model.

• Kyungpook Mathematical Journal
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• v.61 no.2
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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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• v.26 no.6
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• pp.709-723
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• 2007

Considering the vast usage of time-history dynamic analyses to calculate structural responses and lack of sufficient and suitable earthquake records, generation of artificial accelerograms is very necessary. The main target of this paper is to present a novel method based on nonstationary Kanai-Tajimi model and wavelet transform to generate more artificial earthquake records, which are compatible with target spectrum. In this regard, the generalized nonstationary Kanai-Tajimi model to include the nonstationary evaluation of amplitude and dominant frequency of ground motion and properties of wavelet transform is used to generate ground acceleration time history. Application of the method for El Centro 1940 earthquake and two Iranian earthquakes (Tabas 1978 and Manjil 1990) is presented. It is shown that the model and identification algorithms are able to accurately capture the nonstationary features of these earthquake accelerograms. The statistical characteristics of the spectral response of the generated accelerograms are compared with those for the actual records to demonstrate the effectiveness of the method. Also, for comparison of the presented method with other methods, the response spectra of the synthetic accelerograms compared with the models of Fan and Ahmadi (1990) and Rofooei et al. (2001) and it is shown that the response spectra of the synthetic accelerograms with the method of this paper are close to those of actual earthquakes.

• Journal of Korea Multimedia Society
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• v.6 no.3
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• pp.508-517
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• 2003

This paper presents perceptual model with a stochastic multiresolution characteristic that can be applied with watermark embedding in the biorthogonal wavelet domain. The perceptual model with adaptive watermarking algorithm embeds at the texture and edge region for more strongly embedded watermark by the SSQ. The watermark embedding is based on the computation of a NVF that has local image properties. This method uses non- stationary Gaussian and stationary Generalized Gaussian models because watermark has noise properties. The particularities of embedding in the stationary GG model use shape parameter and variance of each subband regions in multiresolution. To estimate the shape parameter, we use a moment matching method. Non-stationary Gaussian model uses the local mean and variance of each subband. The experiment results of simulation were found to be excellent invisibility and robustness. Experiments of such distortion are executed by Stirmark 3.1 benchmark test.

• Journal of Korea Multimedia Society
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• v.6 no.6
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• pp.1008-1014
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• 2003

In this paper, we propose the image retrieval method based on object regions using bidirectional round filter in the wavelet transform domain. A conventional method that includes unnecessary background information reduce retrieval efficiency, because of the extraction of feature vectors from the whole region of subband. On proposed method, it extracts accurate feature vectors and keep certainly retrieval efficiency in case of reduced feature vectors, because of the extraction of feature vectors from the only extracted object region. Furthermore, it improve retrieval efficiency by removing unnecessary background information. Consequently, the retrieval efficiency is improved with 2.5%∼5.5% values, which have a little chances to vary according to characteristics of image.