• Structural Engineering and Mechanics
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• v.35 no.2
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• pp.175-190
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• 2010

One of the intractable problems in multiresolution structural analysis is the decoupling computation between scales, which can be realized by the operator-orthogonal wavelets based on the lifting scheme. The multiresolution finite element space is described and the formulation of multiresolution finite element models for structural problems is discussed. Various operator-orthogonal wavelets are constructed by the lifting scheme according to the operators of multiresolution finite element models. A dynamic multiresolution algorithm using operator-orthogonal wavelets is proposed to solve structural problems. Numerical examples demonstrate that the lifting scheme is a flexible and efficient tool to construct operator-orthogonal wavelets for multiresolution structural analysis with high convergence rate.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.289-305
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• 1998

We consider unimodular wavelets and scalling functions whose Fourier transforms are supported in a finite disjoint uniof of closed intervals. In particular, we characterize those unimodular wavelets which can be associated with multiresolution analysis. As an application we have a criterion to determine whether a wavelet from a class of unimodular wavelets of Ha et al. can be associated with multiresolution analysis or not.

• Korean Journal of Computational Design and Engineering
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• v.14 no.3
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• pp.137-149
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• 2009

For recent years, there has been significant research achievement on the feature-based multiresolution modeling technique along with widely application of three-dimensional feature-based CAD system in the areas of design, analysis, and manufacturing. The research has focused on several topics: topological frameworks for representing multiresolution solid model, criteria for the LOD, generation of valid models after rearrangement of features, and applications. This paper surveys the relevant research on these topics and suggests the future work for dissemination of this technology.

• IEIE Transactions on Smart Processing and Computing
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• v.5 no.6
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• pp.403-417
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• 2016

This paper reviews recent published works dealing with the application of wavelets to image processing based on multiresolution analysis. After revisiting the basics of wavelet transform theory, various applications of wavelets and multiresolution analysis are reviewed, including image denoising, image enhancement, super-resolution, and image compression. In addition, we introduce the concept and theory of quaternion wavelets for the future advancement of wavelet transform and quaternion multiresolution applications.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.3
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• pp.251-258
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• 2004

Since the multiscale wavelet-based numerical methods allow effective adaptive analysis, they have become new analysis tools. However, the main applications of these methods have been mainly on elliptic problems, they are rarely used for eigenvalue analysis. The objective of this paper is to develop a new multiscale wavelet-based adaptive Galerkin method for eigenvalue analysis. To this end, we employ the hat interpolation wavelets as the basis functions of the finite-dimensional trial function space and formulate a multiresolution analysis approach using the multiscale wavelet-Galerkin method. It is then shown that this multiresolution formulation makes iterative eigensolvers very efficient. The intrinsic difference-checking nature of wavelets is shown to play a critical role in the adaptive analysis. The effectiveness of the present approach will be examined in terms of the total numbers of required nodes and CPU times.

• Structural Engineering and Mechanics
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• v.17 no.6
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• pp.819-828
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• 2004

A new process for estimating the natural frequency and the corresponding damping ratio in large structures is discussed. In a practical situation, it is very difficult to analyze large structures precisely because they are too complex to model using the finite element method and too heavy to excite using the exciting force method; in particular, the measured signals are seriously influenced by ambient noise. In order to identify the structural impulse response associated with the information of natural frequency and the corresponding damping ratio in large structures, the analysis process, a so-called "multiresolution blind system identification algorithm" which combines Mallat algorithm and the bicepstrum method. High time-frequency concentration is attained and the phase information is kept. The experimental result has demonstrated that the new analysis process exploiting the natural frequency and the corresponding damping ratio of structural response are useful tools in structural analysis application.

• Journal of the Korean Association of Geographic Information Studies
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• v.4 no.3
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• pp.61-70
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• 2001

This paper presents a new method to extract semi-automatically roads from high spatial resolution satellite imagery. This method is based both on wavelet transform and on multiresolution analysis combined in the "$\grave{a}$ trous" algorithm. As an urban road network consists on different classes of streets, multiresolution processing allows to extract the streets class by class. The method was applied to a KVR-1000 image on a part of Busan Metropolitan City. The method was carried out for the road extraction of three different widths and it succeeded in extracting good fitted strips. The accuracy analysis for three types of streets was also performed. The overall accuracy in 4 pixels of width is 80.5%. The result suggests that this method can be used to update road networks in the studied urban network. In summary, the multiresolution approach based on the wavelet transform, used in this study, is regarded as one of effective methods to extract urban road network from high spatial resolution satellite images.

• Proceedings of the IEEK Conference
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• 2002.07c
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• pp.1674-1677
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• 2002

In this paper, the new method to extract the features of iris signals is proposed; Multiresolution ICA (M-ICA) provides good properties to represent signals with time-frequency. The conventional methods were to use the technique of filter bank analysis, while ICA is unsupervised learning algorithm using high-order statistics. M-ICA could make use of strengths of learn- ing method and multiresolution. Also, we performed comparative studies of different feature extraction techniques applied to personal identification using iris pat- tern. To measure goodness of methods, we use Fisher’s discriminant ratio to quantify the class-separability of features generated by various techniques.

• Communications of the Korean Mathematical Society
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• v.16 no.1
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• pp.113-118
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• 2001

We discuss some conditions about the existence of the solution ø of the following integral equation ø(x) = λ∫h(2x-y)ø(y)dy and prove that the solution ø under certain condition generates a multiresolution analysis.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.10 no.6
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• pp.935-950
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• 1999

A multiresolution time-domain analysis scheme is derived for the analysis of microwave structures by using Haar wavelets to discretize the Maxwell's curl equation. This technique requires less computational effort than the conventional FDTD method because larger space grid can be used in the simulations. To validate this scheme, several 2-D·3-D microwave structures are simulated and the results are compared with those of the conventional FDTD scheme.