• Korean Journal of Mathematics
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• 제22권2호
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• pp.289-305
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• 2014

In this paper we propose a new approach to the variable selection problem for a primary resolution and wavelet basis functions in wavelet regression. Most wavelet shrinkage methods focus on thresholding the wavelet coefficients, given a primary resolution which is usually determined by the sample size. However, both a primary resolution and the basis functions are affected by the shape of an unknown function rather than the sample size. Unlike existing methods, our method does not depend on the sample size and also takes into account the shape of the unknown function.

• Journal of the Korean Data and Information Science Society
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• 제19권4호
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• pp.1465-1476
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• 2008

In recent years wavelet methods have been focused on block shrinkage or thresholding approaches to accounting for the sparseness of the wavelet representation for an unknown function. The block shrinkage or thresholding methods have been developed in both of classical methods and Bayesian methods. In this paper, we propose a Bayesian approach to selecting wavelet basis functions at each resolution level without MCMC procedure. Simulation study and an application are shown.

• Communications for Statistical Applications and Methods
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• 제15권3호
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• pp.379-386
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• 2008

In this paper, the choice of a primary resolution and wavelet basis functions are introduced under random or irregular design points of which the sample size is free of a power of two. Most wavelet methods have used the number of the points as the primary resolution. However, it turns out that a proper primary resolution is much affected by the shape of an unknown function. The proposed methods are illustrated by some simulations.

• 대한원격탐사학회지
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• 제24권5호
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• pp.437-444
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• 2008

Land-use or land-cover classification of satellite images is one of the important tasks in remote sensing application and many researchers have tried to enhance classification accuracy. Previous studies have shown that the classification technique based on wavelet transform is more effective than traditional techniques based on original pixel values, especially in complicated imagery. Various basis functions such as Haar, daubechies, coiflets and symlets are mainly used in 20 image processing based on wavelet transform. Selecting adequate wavelet is very important because different results could be obtained according to the type of basis function in classification. However, it is not easy to choose the basis function which is effective to improve classification accuracy. In this study, we first computed the wavelet coefficients of satellite image using ten different basis functions, and then classified images. After evaluating classification results, we tried to ascertain which basis function is the most effective for image classification. We also tried to see if the optimum basis function is decided by energy parameter before classifying the image using all basis functions. The energy parameters of wavelet detail bands and overall accuracy are clearly correlated. The decision of optimum basis function using energy parameter in the wavelet based image classification is expected to be helpful for saving time and improving classification accuracy effectively.

• 대한원격탐사학회:학술대회논문집
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• 대한원격탐사학회 2008년도 International Symposium on Remote Sensing
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• pp.169-172
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• 2008

Land-use or land-cover classification of satellite images is one of the important tasks in remote sensing application and many researchers have been tried to enhance classification accuracy. Previous studies show that the classification technique based on wavelet transform is more effective than that of traditional techniques based on original pixel values, especially in complicated imagery. Various wavelets can be used in wavelet transform. Wavelets are used as basis functions in representing other functions, like sinusoidal function in Fourier analysis. In these days, some basis functions such as Haar, Daubechies, Coiflets and Symlets are mainly used in 2D image processing. Selecting adequate wavelet is very important because different results could be obtained according to the type of basis function in classification. However, it is not easy to choose the basis function which is effective to improve classification accuracy. In this study, we computed the wavelet coefficients of satellite image using 10 different basis functions, and then classified test image. After evaluating classification results, we tried to ascertain which basis function is the most effective for image classification. We also tried to see if the optimum basis function is decided by energy parameter before classifying the image using all basis function. The energy parameter of signal is the sum of the squares of wavelet coefficients. The energy parameter is calculated by sub-bands after the wavelet decomposition and the energy parameter of each sub-band can be a favorable feature of texture. The decision of optimum basis function using energy parameter in the wavelet based image classification is expected to be helpful for saving time and improving classification accuracy effectively.

• 대한원격탐사학회지
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• 제24권1호
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• pp.57-64
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• 2008

In the previous study, the Haar wavelet was used as the sole basis function for the 3D discrete wavelet transform because the number of bands is too small to decompose a remotely sensed image in band direction with other basis functions. However, it is possible to use other basis functions for wavelet decomposition in horizontal and vertical directions because wavelet decomposition is independently performed in each direction. This study aims to classify a high spatial resolution image with the six types of basis function including the Haar function and to compare those results. The other wavelets are more helpful to classify high resolution imagery than the Haar wavelet. In overall accuracy, the Coif4 wavelet has the best result. The improvement of classification accuracy is different depending on the type of class and the type of wavelet. Using the basis functions with long length could be effective for improving accuracy in classification, especially for the classes of small area. This study is expected to be used as fundamental information for selecting optimal basis function according to the data properties in the 3D DWT based image classification.

• 대한원격탐사학회지
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• 제25권3호
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• pp.215-223
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• 2009

The noise removal as a preprocessing was tried with various kinds of wavelet pairs. Wavelet transform for 2D images generally uses the same wavelets as basis functions in horizontal and vertical directions. A method with different wavelets was tried for each direction separately, which gives more precise interpretation of the classification. Total 486 pairs of wavelets from nine basis functions were tried to remove image noises. The classification accuracies before and after the noise removal were compared. Although all kinds of wavelet pairs showed the increased accuracies in classification, there were best and worst wavelet pairs depending on the data sets. Wavelet pairs with low energy percentage of LL band showed the high classification accuracy. A pattern was found in the results that very similar vertical accuracy was distributed for each horizontal ones. Since Haar is the shortest length filter, Haar could be a predictor wavelet to find the good wavelet pairs.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.419-426
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• 2009

In expansion of function by special basis functions, properties of expansion kernel are very important. In the Fourier series, the series are expressed by the convolution with Dirichlet kernel. We investigate some of properties of kernel in wavelet expansions both in one and higher dimensions.

• 전자공학회논문지CI
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• 제39권6호
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• pp.47-52
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• 2002

웨이블릿 함수의 경우 스케일링 함수에서 비롯되었으며, 스케일과 중심을 결정함으로써 신경회로망의 노드로 구성된다. 본 논문에서는 웨이블릿 함수를 이용하여 망을 구성하는 과정에 스케일링 함수를 은닉층의 노드로 복합 구성한 구조를 제안하고자 한다. 제안한 구조의 특징은 스케일링 함수를 이용하여 대강 근사(rough approximation)를 행한 다음, 웨이블릿 함수를 이용하여 미세 근사(fine approximation)를 행하도록 신경회로망의 은닉층을 복합 구성하는 데 있다. 또한, 복합 신경회로망을 구성하는 과정에서 미세 근사에 필요한 웨이블릿 함수의 개수를 유전 알고리즘을 이용하여 결정하는 초기 구조의 최적화를 도모하고자 한다.

• 한국콘텐츠학회논문지
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• 제8권4호
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• pp.79-85
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• 2008

현재 많은 광대역 전송 시스템의 변복조 방식으로 직교 주파수 분할 다중화(orthogonal frequency division multiplexing: OFDM) 방식이 널리 사용되고 있다. OFDM 방식은 기저파형으로 서로 직교하는 정현파를 사용하는 직교 파형 변조의 하나이다. 이 논문에서는 기저파형으로 정현파 대신 웨이블릿 패킷을 사용하는 웨이블릿 패킷 변조에 대해 살펴보고자 한다. 웨이블릿 패킷은 시간-주파수 2차원 평면에서 서로 다른 모양을 가질 수 있기 때문에 채널환경에 따라 그에 적합한 파형을 쉽게 설계할 수 있다. 이 논문에서는 다중반송파 변조방식의 다른 형태로서 웨이블릿 패킷 변조의 특징에 대해 살펴보고, 협대역 간섭 환경에서 대역폭을 유연하게 조절함으로써 간섭의 영향을 감소시킬 수 있음을 보이고자 한다.