• The Journal of the Acoustical Society of Korea
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• v.18 no.1E
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• pp.13-19
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• 1999

This paper introduces an adaptive wavelet transform based on the lifting scheme, which is applied to signal denoising. The wavelet representation using orthogonal wavelet bases has received widespread attention. Recently the lifting scheme has been developed for the construction of biorthogonal wavelets in the spatial domain. Wavelet transforms are performed through three stages: the first stage or Lazy wavelet splits the data into two subsets, even and odd, the second stage calculates the wavelet coefficients (highpass) as the failure to interpolate or predict the odd set using the even, and the third stage updates the even set using neighboring odd points (wavelet coefficients) to compute the scaling function coefficients (lowpass). In this paper, we adaptively find some of the prediction coefficients for better representation of signals and this customizes wavelet transforms to provide an efficient framework for denoising. Special care has been given to the boundaries, where we design a set of different prediction coefficients to reduce the prediction error.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1367-1376
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• 2018

In practice, the density function of a random variable X is always unknown. Even its smoothness parameter is unknown to us. In this paper, we will consider a density smoothness parameter estimation problem via wavelet theory. The smoothness parameter is defined in the sense of equivalent Besov norms. It is well-known that it is almost impossible to estimate this kind of parameter in general case. But it becomes possible when we add some conditions (to our proof, we can not remove them) to the density function. Besides, the density function contains impurities. It is covered by some additive noises, which is the key point we want to show in this paper.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.463-473
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• 2009

A family of quasi-interpolatory wavelet system was introduced in [10], extending and unifing the biorthogonal Coiffman wavelet system. The corresponding refinable functions and wavelets have vanishing moment of a certain order (say, L), which is a key property for data representation and approximation. One of main advantages of this wavelet systems is that we can get optimal smoothness in the sense of smoothing factors in the scaling filters. In this paper, we first discuss the biorthogonality condition of the quisi-interpolatory wavelet system. Then, we study the properties of the scaling and wavelet filters, related to the polynomial reproduction and the vanishing moment respectively, which in fact determines the approximation orders of biorthogonal projections. In addition, we discuss the approximation orders of the wavelet projections.

• Proceedings of the Korean Information Science Society Conference
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• 2001.04b
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• pp.151-153
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• 2001

Feature Simplification is an essential method for multiple representations of spatial features in GIS. However, spatial features re various, complex and a alrge size. Among spatial features which describe spatial information. linear feature is the msot common. Therefore, an efficient linear feature simplification method is most critical for spatial feature simplification in GIS. This paper propose an original method, by which the problem of linear feature simplification is mapped into the signal processing field. This method avoids conventional geometric computing in existing methods and exploits the advantageous properties of wavelet transform. Experimental results are presented to show that the proposed method outperforms the existing methods and achieves the time complexity of O(n), where n is the number of points of a linear feature. Furthermore, this method is not bound to two-dimension but can be extended to high-dimension space.

• Journal of the Korean Institute of Intelligent Systems
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• v.9 no.6
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• pp.571-576
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• 1999

We consider a class of auto-associative memories namely N-Cubes (Neural-network Cubes) in which 2-D gray-level images and hidden sinusoidal 1-D wavelets are stored in cubical memories. First we develop a learning procedure based upon the least-squares algorithm, Therefore each 2-D training image is mapped into the associated 1-D waveform in the training phase. Second we show how the recall procedure minimizes errors among the orthogonal basis functions in the hidden layer. As a 2-D images ould be retrieved in the recall phase. Simulation results confirm the efficiency and the noise-free properties of N-Cubes.

• Proceedings of the KSRS Conference
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• 2007.10a
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• pp.620-624
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• 2007

Recently, Gonzalez-Audicana et al. proposed the substitute wavelet intensity (SWI) method which provided a solution based on the intensity-hue-saturation (IHS) method for the fusing of panchromatic (PAN) and multispectral (MS) images. Although the spectral quality of the fused MS images is enhanced, this method is not efficient enough to quickly merge massive volumes of data from satellite. To overcome this problem, we introduce a new SWI method based on a fast IHS transform to implement efficiently as an alternative procedure. In addition, we show that the method is well applicable for fusing IKONOS PAN with MS images.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.10
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• pp.194-202
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• 1999

A method for pattern recognition based on wavelet transform is proposed in this paper. The boundary of the object to be recognized includes shape information for object of machine parts. The contour is first represented using a one-dimensional signal and normalized about translation, rotation and scale, then is used to build the wavelet transform representation of the object. Wavelets allow us to decompose a function into multi-resolution hierarchy of localized frequency bands. The recognition of 2-dimensional object based on the wavelet is described to analyze the shape of analysis technique; the discrete wavelet transform(DWT). The feature vectors obtained using wavelet analysis is classified using a multi-layer neural network. The results show that, compared with the use of fourier descriptors, recognition using wavelet is more stable and efficient representation. And particularly the performance for objects corrupted with noise is better than that of other method.

• Journal of the Korean Statistical Society
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• v.27 no.3
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• pp.305-318
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• 1998

Smoothing tests based on an L$_2$ error between a truncated courier series estimator and a true function have shown good powers for a wide class of alternatives, These tests have the same form of the Neyman smooth test whose performance depends on the selected order, a basis, the farm of estimators. We construct flexible data driven Neyman smooth tests by changing a basis, combining model selection criteria and different series estimators. A simulation study shows that the generalized Neyman smooth test with the best basis provides good power for a wider class of alternatives compared with other data driven Neyman smooth tests based on a fixed form of estimator, a fixed basis and a fixed criterion.

• Communications for Statistical Applications and Methods
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• v.22 no.2
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• pp.159-172
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• 2015

This paper considers the problem of reconstructing an underlying signal from noisy data. This paper presents a reconstruction method based on synchrosqueezed wavelet transform recently developed for multiscale representation. Synchrosqueezed wavelet transform based on continuous wavelet transform is efficient to estimate the instantaneous frequency of each component that consist of a signal and to reconstruct components. However, an objective selection method for the optimal number of intrinsic mode type functions is required. The proposed method is obtained by coupling the synchrosqueezed wavelet transform with cross-validation scheme. Simulation studies and musical instrument sounds are used to compare the empirical performance of the proposed method with existing methods.

• Korean Journal of Geomatics
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• v.5 no.1
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• pp.1-6
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• 2005

When merging various datasets the perennial problem of relative weighting arises. In case of two datasets an iterative algorithm has been developed recently that allows the rigorous determination of optimal variance components of type repro-BIQUUE even for large amounts of data, along with the estimation of the joint parameters. Here we shall present this new algorithm, and show its versatility in an example that will entail the merging of two regional geoid estimates (derived from EGM 96 and CHAMP) in terms of certain series expansions which have been proven previously to belong to the most efficient ones (e.g., wavelets, Hardy's multi-quadrics, etc.). Future attempts will be devoted to the sequential merging of altimeter and tide gauge data.