• Communications for Statistical Applications and Methods
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• 제2권1호
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• pp.194-200
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• 1995

The baker's transformation is an ergodic transformation defined on the half open unit square. This paper considers the limiting begavior of the partial sum process of a martingale sequence constructed from the baker's transformation in the context of an invariance principle of a uniform central limit theorm.

• 대한수학회지
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• 제33권4호
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• pp.909-928
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• 1996

In this paper, an empirical law of the iterated logarithm is investigated in the context of a stationary and ergodic martingale differences whose values taking in a measurable space.

• 대한수학회논문집
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• 제12권2호
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• pp.347-354
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• 1997

The conharmonic transforamtion is a conformal transformation which satisfies a specified differential equation. Such a transformation was defined by Y. Ishi and we generalize his results. In particular, we obtain a necessary and sufficient condition for the invariance of critical Riemannian metrics under the conharmonic transformation.

• 한국정보처리학회논문지
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• 제5권4호
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• pp.959-966
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• 1998

본 논문에서 $m{\times}n\;(m{\geq}n)$ 인 토플리즈 행렬의 빠른 QR 인수분해 알고리즘들을 제안한다. 본 알고리즘들은 위치가 변환되어도 불변하는 (shift-invariance) 토플리즈 행렬의 특성을 효과적으로 이용하였다. 알고리즘들의 주요 변환 도구로 안정된 하우스홀더 변환과 하이퍼볼릭 하우스홀더 변환을 사용하였다. 본 알고리즘들은 O(mn)의 연산을 필요로하며, 분산메모리 병렬 컴퓨터에서 쉽게 구현될 수 있다.

• 디지털산업정보학회논문지
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• 제8권2호
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• pp.131-143
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• 2012

This paper introduces the double-density discrete wavelet transform using 3 direction separable processing method, which is a discrete wavelet transform that combines the double-density discrete wavelet transform and quincunx sampling method, each of which has its own characteristics and advantages. The double-density discrete wavelet transform is nearly shift-invariant. But there is room for improvement because not all of the wavelets are directional. That is, although the double-density DWT utilizes more wavelets, some lack a dominant spatial orientation, which prevents them from being able to isolate those directions. The dual-tree discrete wavelet transform has a more computationally efficient approach to shift invariance. Also, the dual-tree discrete wavelet transform gives much better directional selectivity when filtering multidimensional signals. But this transformation has more cost complexity Because it needs eight digital filters. Therefor, we need to hybrid transform which has the more directional selection and the lower cost complexity. A solution to this problem is a the double-density discrete wavelet transform using 3 direction separable processing method. The proposed wavelet transformation services good performance in image and video processing fields.

• 디지털산업정보학회논문지
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• 제7권4호
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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.

• 한국인터넷방송통신학회논문지
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• 제14권1호
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• pp.77-83
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• 2014

과표본화된 이산 웨이브렛 변환은 입력 데이터보다 더 많은 양의 부대역 데이터들이 생성되지만 기존의 웨이브렛 변환의 이동 불변 불만족의 단점을 극복할 수 있다. 비분리 표본화를 기반으로 하는 이산 웨이브렛 변환은 이동 불변의 특징의 만족과 방향 선택성 등에서 더 많은 부대역 영상을 통하지만 더 효율적이다. 본 논문에서는 보다 많은 부대역 영상을 생성하는 2차원 영상처리 과표본화 된 웨이브렛 변환의 효율적인 처리를 가능하게 하여 디지털 영상의 품질 향상 및 잡음제거 응용 분야에 적용시킬 수 있음을 제안하였다.

• 디지털산업정보학회논문지
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• 제9권1호
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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.

• 디지털산업정보학회논문지
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• 제8권3호
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• pp.133-145
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• 2012

This paper describes the high density discrete wavelet transformation which is one that expands an N point signal to M transform coefficients with M > N. The double-density discrete wavelet transform is one of the high density discrete wavelet transformation. This transformation employs one scaling function and two distinct wavelets, which are designed to be offset from one another by one half. And it is nearly shift-invariant. Similarly, triple-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. Specifically, the spectrum of the first wavelet is concentrated halfway between the spectrum of the second wavelet and the spectrum of its dilated version. In addition, the second wavelet is translated by half-integers rather than whole-integers in the frame construction. This arrangement leads to high density wavelet transformation. But this new transform is approximately shift-invariant and has intermediate scales. In two dimensions, this transform outperforms the standard and double-density discrete wavelet transformation in terms of multiple directions. Resultingly, the proposed wavelet transformation services good performance in image and video processing fields.

• 전기학회논문지
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• 제59권9호
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• pp.1680-1685
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• 2010

In this note, a proof of Utkin's theorem is presented for a MI(Multi Input) uncertain linear case. The invariance theorem with respect to the two transformation methods so called the two diagonalization methods are proved clearly and comparatively for MI uncertain linear systems. With respect to the sliding surface transformation and the control input transformation, the equation of the sliding mode i.e., the sliding surface is invariant. Both control inputs have the same gains. By means of the two transformation methods the same results can be obtained. Through an illustrative example and simulation study, the usefulness of the main results is verified.