• Journal of Positioning, Navigation, and Timing
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• 제8권4호
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• pp.165-173
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• 2019

In this paper, we apply a discrete wavelet packet transform (DWPT) to reduce the influence of interference in global positioning system (GPS) signals and compare the interference mitigation performance of various wavelets. By applying DWPT to the received signal, we can gradually divide the received signal band into low-pass and high-pass bands. After calculating the average power for the separate bands, we can determine whether there is interference by comparing the value with the given threshold. For a band that includes interference, we can reconstruct the whole band signal using inverse DWPT (IDWPT) after applying a nulling method that sets all of the wavelet coefficients to 0. The reconstructed signals are correlated with the pseudorandom noise (PRN) codes to acquire GPS signals. The performance evaluation is based on the number of satellite signals whose peak ratio (defined as the ratio of the first and second correlation peak values in the acquisition stage) exceeds the threshold. In this paper, we compare and evaluate the performance of 6 wavelets including Haar, Daubechies, Symlets, Coiflets, Biorthogonal Splines, and Discrete Meyer.

• KIEE International Transactions on Power Engineering
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• 제3A권3호
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• pp.130-138
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• 2003

This paper presents a discrete wavelet transform approach for determining the beginning and end times of voltage sags. Firstly, investigations in the use of some typical mother wavelets, namely Daubechies, Symlets, Coiflets and Biorthogonal are carried out and the most appropriate mother wavelet is selected. The proposed technique is based on utilizing the maximum value of Dl (at scale 1) coefficients in multiresolution analysis (MRA) based on the discrete wavelet transform. The results are compared with other methods for determining voltage sag duration, such as the Root Mean Square (RMS) voltage and Short Time Fourier Transform (STFT) methods. It is shown that the voltage sag detection technique based on the wavelet transform is a satisfactory and reliable method for detecting voltage sags in power quality disturbance analysis.

• 대한원격탐사학회:학술대회논문집
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• 대한원격탐사학회 2004년도 Proceedings of ISRS 2004
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• pp.224-227
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• 2004

From 1980's, the DWT(Discrete Wavelet Transform) is applied to the data/image processing. Many people use the DWT in remote sensing for diversity purposes and they are satisfied with the wavelet theory. Though the algorithm for wavelet is very diverse, many people use the standard wavelet such as Daubechies D4 wavelet and biorthogonal 9/7 wavelet. We will overview the wavelet theory for discrete form which can be applied to the image processing. First, we will introduce the basic DWT algorithm and review the wavelet algorithm: EZW (Embedded Zerotree Wavelet), SPIHT(Set Partitioning in Hierarchical Trees), Lifting scheme, Curvelet, etc. Finally, we will suggest the properties of wavelet algorithm; and wavelet filter for each image processing in remote sensing.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권4호
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• pp.279-294
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• 2013

We are interested in an adaptive grid method for hyperbolic equations. A multiresolution analysis, based on a biorthogonal family of interpolating scaling functions and lifted interpolating wavelets, is used to dynamically adapt grid points according to the physical field profile in each time step. Traditional finite-difference schemes with fixed stencils produce high oscillations around sharp discontinuities. In this paper, we hybridize high-resolution schemes, which are suitable for capturing singularities, and apply a finite-difference approach to the scaling functions at non-singular points. We use a total variation diminishing Runge-Kutta method for the time integration. The computational cost is proportional to the number of points present after compression. We provide several numerical examples to verify our approach.

• The Journal of the Acoustical Society of Korea
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• 제18권1E호
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• pp.13-19
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• 1999

This paper introduces an adaptive wavelet transform based on the lifting scheme, which is applied to signal denoising. The wavelet representation using orthogonal wavelet bases has received widespread attention. Recently the lifting scheme has been developed for the construction of biorthogonal wavelets in the spatial domain. Wavelet transforms are performed through three stages: the first stage or Lazy wavelet splits the data into two subsets, even and odd, the second stage calculates the wavelet coefficients (highpass) as the failure to interpolate or predict the odd set using the even, and the third stage updates the even set using neighboring odd points (wavelet coefficients) to compute the scaling function coefficients (lowpass). In this paper, we adaptively find some of the prediction coefficients for better representation of signals and this customizes wavelet transforms to provide an efficient framework for denoising. Special care has been given to the boundaries, where we design a set of different prediction coefficients to reduce the prediction error.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1999년도 하계학술대회 논문집 G
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• pp.3224-3226
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• 1999

This paper introduces a nonlinear wavelet transform based on the lifting scheme, which is applied to signal denoising through the translation invariant wavelet transform. The wavelet representation using orthogonal wavelet bases has received widespread attention. Recently the lifting scheme has been developed for the construction of biorthogonal wavelets in the spatial domain. In this paper, we adaptively reduce the vanishing moments in the discontinuities to suppress the ringing artifacts and this customizes wavelet transforms providing an efficient framework for the translation invariant denoising. Special care has been given to the boundaries, where we design a set of different prediction coefficients to reduce the prediction error.

• Spatial Information Research
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• 제17권4호
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• pp.455-462
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• 2009

원격탐사 영상에서 압축을 위한 근최적의 PSNR 값을 찾는 방법을 연구하였다. 예상 웨이블릿쌍은 다양한 영상에서 최적의 결과로 나타났다. 영상처리를 위한 최고의 웨이블릿쌍을 찾는 규칙은 없다. 제시된 알고리즘에 따라 예상 웨이블릿쌍이 다양한 종류의 영상에서 최적의 결과를 나타냈다. 먼저 세 개의 웨이블릿 패밀리에서 PSNR 값의 변화를 분석하였다. 직교 웨이블릿 패밀리에서는 많은 경우에 웨이블릿 필터의 길이가 길수록 높은 PSNR 값을 나타내지만, 그 증가 비율이 점차로 작아졌다. 연산비용의 측면에서 중간 필터길이의 웨이블릿을 제안한다. 쌍직교 웨이블릿 패밀리에서는 필터의 길이와 PSNR값의 관계를 예측하기는 어려웠다. 다차원 웨이블릿 분석에서는 세 개의 웨이블릿 패밀리가 3단계까지 처리되었다. 쌍직교 웨이블릿 패밀리는 최대 PSNR 값에서 불규칙한 패턴을 보였지만, 직교 웨이블릿 패밀리는 규칙적 패턴을 나타냈다. 직교 웨이블릿 패밀리는 1단계 결과로부터 근최적의 웨이블릿쌍을 예상할 수 있었다.

• 한국멀티미디어학회논문지
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• 제8권1호
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• pp.19-26
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• 2005

본 논문에서 사용한 웨이블릿 변환의 기저 함수는 일반적인 웨이블릿 변환과 다른 리프팅 스킴을 사용하여 만들어 졌다. 리프팅 스킴은 푸리에 변환을 사용하여 기저 함수를 생성하지 않는 새로운 쌍직교 웨이블릿 기저 함수를 생성하는 방법이다 본 본문은 리프팅 스킴을 이용한 새로운 영상 압축 및 에지 검출 방법을 제안하고 있다. 그리고 이 방법은 부분 복원과 공간 복원을 할 수 있어 데이터 가시화를 향상시킬 수 있다. 다양한 해상도에서의 근사 영상은 원래 영상으로부터 적은 정보만으로 다양한 크기의 특징을 뽑아낼 수 있고, 적은 양의 스케일링 계수를 사용하여 생성된 근사 영상은 빠르게 원래 영상의 대략적인 개요만이 필요할 때 유용하게 사용된다. 본 논문에서 제안한 영상 압축 및 에지 검출 기법은 멀티미디어 데이터베이스에서 데이터 관리와 데이터 가시화를 향상시킬 수 있는 좋은 기틀을 마련해 준다.