• Korean Journal of Mathematics
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• v.22 no.2
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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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• v.19 no.4
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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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• v.15 no.3
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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.

• Korean Journal of Remote Sensing
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• v.24 no.5
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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.

• Proceedings of the KSRS Conference
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• 2008.10a
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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.

• Korean Journal of Remote Sensing
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• v.24 no.1
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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.

• Korean Journal of Remote Sensing
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• v.25 no.3
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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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• v.27 no.1_2
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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.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.39 no.6
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• pp.47-52
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• 2002

The wavelet functions are originated from scaling functions and can be used as activation function in the hidden node of the network by deciding two parameters such as scale and center. In this paper, we would like to propose the mixed structure. When we compose the WNN using wavelet functions, we propose to set a single scale function as a node function together. The properties of the proposed structure is that while one scale function approximates the target function roughly, the other wavelet functions approximate it finely. During the determination of the parameters, the wavelet functions can be determined by the global search algorithm such as genetic algorithm to be suitable for the suggested problem. Finally, we use the back-propagation algorithm in the learning of the weights.

• The Journal of the Korea Contents Association
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• v.8 no.4
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• pp.79-85
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• 2008

These days, orthogonal frequency division multiplexing (OFDM) transmission method is widely used for broadband communication systems. The OFDM, which uses sine waves as orthogonal basis functions, is one of the orthogonal waveform modulation techniques. In this paper, we investigate a wavelet packet modulation method which uses wavelet packets instead of sine waves as the basis functions. The wavelet packets may have different patterns in two dimensional time-frequency domain, and we can design the packets appropriate for the channel environments with much flexibility. In this paper, we investigate the characteristics of the wavelet packet modulation as one of the multicarrier modulation methods, And we illustrate by simulations that narrowband interference can be reduced effectively by control the bandwidth of the wavelet packets.