• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.307-315
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• 2019

In this paper we construct orthogonal two-direction scaling function of order 3 and corresponding wavelet function. In this paper we propose a different approach using orthogonal symmetric/antisymmetric multiwavelets of order 3. An example for constructing orthogonal two-direction scaling function of order 3 and corresponding wavelet function is given.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.1053-1067
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• 2015

A two-direction multiscaling function ${\phi}$ satisfies a recursion relation that uses scaled and translated versions of both itself and its reverse. This offers a more general and flexible setting than standard one-direction wavelet theory. In this paper, we investigate how to find and normalize point values and derivative values of two-direction multiscaling and multiwavelet functions. Determination of point values is based on the eigenvalue approach. Normalization is based on normalizing conditions for the continuous moments of ${\phi}$. Examples for illustrating the general theory are given.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.181-189
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• 2017

A method for recovering Chui-Lian's orthogonal symmetric/antisymmetric multiwavelets of order 2 from orthogonal two-direction wavelets of order 2 was proposed by Yang and Xie. In this paper we pursue the converse, that is, we propose a method for constructing orthogonal two-direction wavelets of order 2 from orthogonal symmetric/antisymmetric multiwavelets of order 2.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.305-334
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• 2005

The objective of this study is to analyze the decay characteristics of the hat interpolation wavelet coefficients of some smooth functions defined in a two-dimensional space. The motivation of this research is to establish some fundamental mathematical foundations needed in justifying the adaptive multiresolution analysis of the hat-interpolation wavelet-Galerkin method. Though the hat-interpolation wavelet-Galerkin method has been successful in some classes of problems, no complete error analysis has been given yet. As an effort towards this direction, we give estimates on the decaying ratios of the wavelet coefficients at children interpolation points to the wavelet coefficient at the parent interpolation point. We also give an estimate for the difference between non-adaptively and adaptively interpolated representations.

• Journal of Korea Society of Digital Industry and Information Management
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• v.9 no.1
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• pp.165-176
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• 2013

This paper introduces the high density discrete wavelet transform using quincunx sampling, which is a discrete wavelet transformation that combines the high density discrete transformation and non-separable processing method, each of which has its own characteristics and advantages. The high density discrete wavelet transformation is one that expands an N point signal to M transform coefficients with M > N. The high density discrete wavelet transformation is a new set of dyadic wavelet transformation with two generators. The construction provides a higher sampling in both time and frequency. This new transform is approximately shift-invariant and has intermediate scales. In two dimensions, this transform outperforms the standard discrete wavelet transformation in terms of shift-invariant. Although the transformation utilizes more wavelets, sampling rates are high costs and some lack a dominant spatial orientation, which prevents them from being able to isolate those directions. A solution to this problem is a non separable method. The quincunx lattice is a non-separable sampling method in image processing. It treats the different directions more homogeneously than the separable two dimensional schemes. Proposed wavelet transformation can generate sub-images of multiple degrees rotated versions. Therefore, This method services good performance in image processing fields.

• Korean Journal of Remote Sensing
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• v.10 no.2
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• pp.49-62
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• 1994

Look direction bias in a single look SAR image can often be misinterpreted in the geological application of radar data. This paper investigates digital processing techniques for SAR image data integration and compensation of the SAR data look direction bias. The two important approaches for reducing look direction bias and integration of multiple SAR data sets are (1) principal component analysis (PCA), and (2) wavelet transform(WT) integration techniques. These two methods were investigated and tested with the ERS-1 (VV-polarization) and CCRS*s airborne (HH-polarization) C-SAR image data sets recorded over the Sudbury test site, Canada. The PCA technique has been very effective for integration of more than two layers of digital image data. When there only two sets of SAR data are available, the PCA thchnique requires at least one more set of auxiliary data for proper rendition of the fine surface features. The WT processing approach of SAR data integration utilizes the property which decomposes images into approximated image ( low frequencies) characterizing the spatially large and relatively distinct structures, and detailed image (high frequencies) in which the information on detailed fine structures are preserved. The test results with the ERS-1and CCRS*s C-SAR data indicate that the new WT approach is more efficient and robust in enhancibng the fine details of the multiple SAR images than the PCA approach.

• Journal of Biomedical Engineering Research
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• v.29 no.2
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• pp.122-131
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• 2008

For B-mode ultrasound images, we propose an image enhancement algorithm based on a multi-resolution approach, which consists of edge enhancing and noise reducing procedures. Edge enhancement processing is applied sequentially to coarse-to-fine resolution images obtained from wavelet-transformed data. In each resolution, the structural features of each pixel are examined through eigen analysis. Then, if a pixel belongs to an edge region, we perform two-step filtering: that is, directional smoothing is conducted along the tangential direction of the edge to improve continuity and directional sharpening is conducted along the normal direction to enhance the contrast. In addition, speckle noise is alleviated by proper attenuation of the wavelet coefficients of the homogeneous regions at each band. This region-based speckle-reduction scheme is differentiated from other methods that are based on the magnitude statistics of the wavelet coefficients. The proposed algorithm enhances edges regardless of changes in the resolution of an image, and the algorithm efficiently reduces speckle noise without affecting the sharpness of the edge. Hence, compared with existing algorithms, the proposed algorithm considerably improves the subjective image quality without providing any noticeable artifacts.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.1209-1211
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• 2003

The wavelet and semivariogram analysis method are used to identify the city landscape and farmland landscape pattern on the 1m resolution IKONOS images. The results prove that wavelet method is a potential way for landscape pattern analysis. Compared to semivariogram analysis, Wavelet analysis can not only detect the overall spatial pattern, but also find multi-scale and direction structures. In this experiment, the wavelet analysis results indicate: (1) the city landscape image is mainly composed of three level structures whose spatial pattern characters appear at 2m, 16m, 128m and 256m accordingly; (2) the farmland landscape is mainly two scale spatial patterns appearing at the 2m, 128m and 256m. IKONOS Remote sensing, with the high spatial and spectral information, is a powerful tool that can use in many ecological systems research and sustainable management.

• Structural Engineering and Mechanics
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• v.38 no.1
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• pp.81-97
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• 2011

In this research, the wavelet transform is used to analyze time response of a cracked beam carrying moving mass for damage detection. In this respect, a new damage detection method based on the combined use of continuous and discrete wavelet transforms is proposed. It is shown that this method is more capable in making damage signature evident than the traditional two approaches based on direct investigation of the wavelet coefficients of structural response. By the proposed method, it is concluded that strain data outperforms displacement data at the same point in revealing damage signature. In addition, influence of moving mass-induced terms such as gravitational, Coriolis, centrifuge forces, and pure inertia force along the deflection direction to damage detection is investigated on a sample case. From this analysis it is concluded that centrifuge force has the most influence on making both displacement and strain data damage-sensitive. The Coriolis effect is the second to improve the damage-sensitivity of data. However, its impact is considerably less than the former. The rest, on the other hand, are observed to be insufficient alone.

• Journal of Korea Society of Digital Industry and Information Management
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• v.7 no.4
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• pp.119-131
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• 2011

In this paper, we explore the application of 2-D dual-tree discrete wavelet transform (DDWT), which is a directional and redundant transform, for image coding. DDWT main property is a more computationally efficient approach to shift invariance. Also, the DDWT gives much better directional selectivity when filtering multidimensional signals. The dual-tree DWT of a signal is implemented using two critically-sampled DWTs in parallel on the same data. The transform is 2-times expansive because for an N-point signal it gives 2N DWT coefficients. If the filters are designed is a specific way, then the sub-band signals of the upper DWT can be interpreted as the real part of a complex wavelet transform, and sub-band signals of the lower DWT can be interpreted as the imaginary part. The quincunx lattice is a sampling method in image processing. It treats the different directions more homogeneously than the separable two dimensional schemes. Quincunx lattice yields a non separable 2D-wavelet transform, which is also symmetric in both horizontal and vertical direction. And non-separable wavelet transformation can generate sub-images of multiple degrees rotated versions. Therefore, non-separable image processing using DDWT services good performance.