• Title/Summary/Keyword: Wavelet

Search Result 3,571, Processing Time 0.039 seconds

On Normalized Tight Frame Wavelet Sets

  • Srivastava, Swati
    • Kyungpook Mathematical Journal
    • /
    • v.55 no.1
    • /
    • pp.127-135
    • /
    • 2015
  • We determine two-interval normalized tight frame wavelet sets for real dilation $d{\in}(1,{\infty})$, and characterize all symmetric normalized tight frame wavelet sets. We also construct a normalized tight frame wavelet set which has an infinite number of components accumulating at the origin. These normalized tight frame wavelet sets and their closures possess the same measure. Finally an example of a normalized tight frame wavelet set is provided whose measure is strictly less than the measure of its closure.

Wavelet Algorithms for Remote Sensing

  • CHAE Gee Ju;CHOI Kyoung Ho
    • Proceedings of the KSRS Conference
    • /
    • 2004.10a
    • /
    • pp.224-227
    • /
    • 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.

  • PDF

A Study on the Application of Wavelet Transform to Faults Current Discrimination (Wavelet 변환을 이용한 고장전류의 판별에 관한 연구)

  • 조현우;정종원;윤기영;김태우;이준탁
    • Proceedings of the Korean Society of Marine Engineers Conference
    • /
    • 2002.05a
    • /
    • pp.213-217
    • /
    • 2002
  • Recently the subject of "wavelet analysis" has be drawn by both mathematical and engineering application fields such as Signal Processing, Compression/Decomposition, Wavelet-Neural Network, Statistics and etc. Even though its similar to courier analysis, wavelet is a versatile tool with much mathematical content and great potential for applications. Especially, wavelet transform uses localizable various mother wavelet functions in time-frequency domain. Therefore, wavelet transform has good time-analysis ability for high frequency component, and has good frequency-analysis ability for low frequency component. Using the discriminative ability is more easy method than other conventional techniques. In this paper, Morlet wavelet transform was applied to discriminate the kind of line fault by acquired data from real power transformation network. The experimental result presented that Morlet wavelet transform is easier, and more useful method than the FFW (Fast courier Transform).ransform).

  • PDF

IMAGE QUALITY OPTIMIZATION BASED ON WAVELET FILTER DESIGN AND WAVELET DECOMPOSITION IN JPEG2000

  • Quan, Do;Ho, Yo-Sung
    • Proceedings of the Korean Society of Broadcast Engineers Conference
    • /
    • 2009.01a
    • /
    • pp.7-12
    • /
    • 2009
  • In JPEG2000, the Cohen-Daubechies-Feauveau (CDF) 9/7-tap wavelet filter adopted in lossy compression is implemented by the lifting scheme or by the convolution scheme while the LeGall 5/3-tap wavelet filter adopted in lossless compression is implemented just by the lifting scheme. However, these filters are not optimal in terms of Peak Signal-to-Noise Ratio (PSNR) values, and irrational coefficients of wavelet filters are complicated. In this paper, we proposed a method to optimize image quality based on wavelet filter design and on wavelet decomposition. First, we propose a design of wavelet filters by selecting the most appropriate rational coefficients of wavelet filters. These filters are shown to have better performance than previous wavelet ones. Then, we choose the most appropriate wavelet decomposition to get the optimal PSNR values of images.

  • PDF

HIGH ACCURACY POINTS OF WAVELET APPROXIMATION

  • Kwon, Soon-Geol
    • Journal of applied mathematics & informatics
    • /
    • v.27 no.1_2
    • /
    • pp.69-78
    • /
    • 2009
  • The accuracy of wavelet approximation at resolution h = $2^{-k}$ to a smooth function f is limited by O($h^M$), where M is the number of vanishing moments of the mother wavelet ${\psi}$; that is, the approximation order of wavelet approximation is M - 1. High accuracy points of wavelet approximation are of interest in some applications such as signal processing and numerical approximation. In this paper, we prove the scaling and translating properties of high accuracy points of wavelet approximation. To illustrate the results in this paper, we also present two examples of high accuracy points of wavelet approximation.

  • PDF

Damage Detection of Frame Structure Using Wavelet Transform (골조의 손상부위 추정에 웨이블렛 변환의 이용)

  • 박종열;이의택;박진호;박형기
    • Proceedings of the Earthquake Engineering Society of Korea Conference
    • /
    • 2002.09a
    • /
    • pp.173-180
    • /
    • 2002
  • This paper presents a signal processing procedure to detect damage locations of frame structures by using continuous wavelet transform. Morlet wavelet is used as a mother wavelet in wavelet transform. Wavelet transform has the characteristics that allows the use of long time intervals at more precise low-frequency information, and shorter regions at high-frequency information. By this wavelet transform characteristics, Morlet wavelet may be used to identify the locations of damages in the structures. The numerical case studies show that this method can be applied to detect the damage location under a controlled sweeping load.

  • PDF

Growing Algorithm of Wavelet Neural Network (웨이블렛 신경망의 성장 알고리즘)

  • 서재용;김성주;김성현;김용민;전홍태
    • Proceedings of the Korean Institute of Intelligent Systems Conference
    • /
    • 2001.05a
    • /
    • pp.57-60
    • /
    • 2001
  • In this paper, we propose growing algorithm of wavelet neural network. It is growing algorithm that adds hidden nodes using wavelet frame which approximately supports orthogonality in wavelet neural network based on wavelet theory. The result of this processing can be reduced global error and progresses performance efficiency of wavelet neural network. We apply the proposed algorithm to approximation problem and evaluate effectiveness of proposed algorithm.

  • PDF

The Digital Image Processing Method Using Triple-Density Discrete Wavelet Transformation (3중 밀도 이산 웨이브렛 변환을 이용한 디지털 영상처리 기법)

  • Shin, Jong Hong
    • Journal of Korea Society of Digital Industry and Information Management
    • /
    • v.8 no.3
    • /
    • pp.133-145
    • /
    • 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.

Retrieving Phase from Single Interferogram with Spatial Carrier Frequency by Using Morlet Wavelet

  • Hongxin Zhang;Mengyuan Cui
    • Current Optics and Photonics
    • /
    • v.7 no.5
    • /
    • pp.529-536
    • /
    • 2023
  • The Morlet wavelet transform method is proposed to analyze a single interferogram with spatial carrier frequency that is captured by an optical interferometer. The method can retain low frequency components that contain the phase information of a measured optical surface, and remove high frequency disturbances by wavelet decomposition and reconstruction. The key to retrieving the phases from the low-frequency wavelet components is to extract wavelet ridges by calculating the maximum value of the wavelet transform amplitude. Afterwards, the wrapped phases can be accurately solved by multiple iterative calculations on wavelet ridges. Finally, we can reconstruct the wave-front of the measured optical element by applying two-dimensional discrete cosine transform to those wrapped phases. Morlet wavelet transform does not need to remove the spatial carrier frequency components manually in the processing of interferogram analysis, but the step is necessary in the Fourier transform algorithm. So, the Morlet wavelet simplifies the process of the analysis of interference fringe patterns compared to Fourier transform. Consequently, wavelet transform is more suitable for automated programming analysis of interference fringes and avoiding the introduction of additional errors compared with Fourier transform.

Faults Current Discrimination of Power System Using Wavelet Transform (웨이블렛 변환을 이용한 전력시스템 고장전류의 판별)

  • Lee, Joon-Tark;Jeong, Jong-Won
    • Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
    • /
    • v.21 no.3
    • /
    • pp.75-81
    • /
    • 2007
  • Recently the subject of "wavelet analysis" has be drawn by both mathematical and engineering application fields such as Signal Processing, Compression/Decomposition, Wavelet-Neural Network, Statistics and etc. Even though its similar to Fourier analysis, wavelet is a versatile tool with much mathematical content and great potential for applications. Especially, wavelet transform uses localizable various mother wavelet functions in time-frequency domain. Therefore, wavelet transform has good time-analysis ability for high frequency component, and has good frequency-analysis ability for low frequency component. Using the discriminative ability is more easy method than other conventional techniques. In this paper, Morlet wavelet transform was applied to discriminate the kind of line fault by acquired data from real power transformation network. The experimental result presented that Morlet wavelet transform is easier, and more useful method than the Fast Fourier Transform(FFT).