• Title, Summary, Keyword: multiwavelets

### Thresholding for CFD data compression based on Supercompact Multiwavelets (Supercompact Multiwavelets 을 이용한 CFD 데이터 압축의 Thresholding)

• Kwon, Do-Hoon;Lee, Do-Hyung
• Proceedings of the KSME Conference
• /
• /
• pp.962-967
• /
• 2003
• CFD data compression method based on supercompact multiwavelets is presented. High data compression can be achieved when taking advantage of the compact nature of multiwavelets. Thresholding technique is also a matter of primary concern in determining pressure ratio. In this paper, we apply thresholding for multiwavelets that considers the coefficient vector as a whole rather than thresholding individual elements. Various thresholding methods are described briefly. CFD data compression suggests that the multivariate thresholding method is suitable for supercompact multiwavelets.

### CHARACTERIZATION OF ORTHONORMAL HIGH-ORDER BALANCED MULTIWAVELETS IN TERMS OF MOMENTS

• Kwon, Soon-Geol
• Bulletin of the Korean Mathematical Society
• /
• v.46 no.1
• /
• pp.183-198
• /
• 2009
• In this paper, we derive a characterization of orthonormal balanced multiwavelets of order p in terms of the continuous moments of the multiscaling function $\phi$. As a result, the continuous moments satisfy the discrete polynomial preserving properties of order p (or degree p - 1) for orthonormal balanced multiwavelets. We derive polynomial reproduction formula of degree p - 1 in terms of continuous moments for orthonormal balanced multiwavelets of order p. Balancing of order p implies that the series of scaling functions with the discrete-time monomials as expansion coefficients is a polynomial of degree p - 1. We derive an algorithm for computing the polynomial of degree p - 1.

### ORTHOGONAL TWO-DIRECTION WAVELETS OF ORDER 2 FROM ORTHOGONAL SYMMETRIC/ANTISYMMETRIC MULTIWAVELETS

• KWON, SOON-GEOL
• Journal of applied mathematics & informatics
• /
• v.35 no.1_2
• /
• pp.181-189
• /
• 2017
• A method for recovering Chui-Lian's orthogonal symmetric/antisymmetric multiwavelets of order 2 from orthogonal two-direction wavelets of order 2 was proposed by Yang and Xie. In this paper we pursue the converse, that is, we propose a method for constructing orthogonal two-direction wavelets of order 2 from orthogonal symmetric/antisymmetric multiwavelets of order 2.

### LEGENDRE MULTIWAVELET GALERKIN METHODS FOR DIFFERENTIAL EQUATIONS

• Zhou, Xiaolin
• Journal of applied mathematics & informatics
• /
• v.32 no.1_2
• /
• pp.267-284
• /
• 2014
• The multiresolution analysis for Legendre multiwavelets are given, anti-derivatives of Legendre multiwavelets are used for the numerical solution of differential equations, a special form of multilevel augmentation method algorithm is proposed to solve the disrete linear system efficiently, convergence rate of the Galerkin methods is given and numerical examples are presented.

### A NOTE ON THE PARAMETRIZATION OF MULTIWAVELETS OF DGHM TYPE

• Hwang, Seok-Yoon
• Journal of applied mathematics & informatics
• /
• v.29 no.3_4
• /
• pp.1037-1042
• /
• 2011
• Multiwavelet coefficients can be constructed from the multi-scaling coefficients by using the factorization for paraunitary matrices. In this paper we present a procedure for parametrizing all possible multi-wavelet coefficients corresponding to the multiscaling coefficients of DGHM type.

### A Study on the Comparison Between Full-3D and Quasi-1D Supercompact Multiwavelets (Full-3D와 Quasi-1D Supercompact Multiwavelets의 비교 연구)

• Park, June-Pyo;Lee, Do-Hyung;Kwon, Do-Hoon
• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.28 no.12
• /
• pp.1608-1615
• /
• 2004
• CFD data compression methods based on Full-3D and Quasi-1D supercompact multiwavelets are presented. Supercompact wavelets method provide advantageous benefit that it allows higher order accurate representation with compact support. Therefore it avoids unnecessary interaction with remotely located data across singularities such as shock. Full-3D wavelets entails appropriate cross-derivative scaling function & wavelets, hence it can allow highly accurate multi-spatial data representation. Quasi-1D method adopt 1D multiresolution by alternating the directions rather than solving huge transformation matrix in Full-3D method. Hence efficient and relatively handy data processing can be conducted. Several numerical tests show swift data processing as well as high data compression ratio for CFD simulation data.

### SPIHT Image Compression Using Biorthogonal Multiwavelets on [-1,1]

• Yoo Sang-Wook;Kwon Seong-Geun;Kwon Ki-Ryong
• Journal of Korea Multimedia Society
• /
• v.8 no.6
• /
• pp.776-782
• /
• 2005
• This paper presents a SPIHT image compression method using biorthogonal multi wavelets on [-1,1]. A family of biorthogonal scaling vectors is constructed using fractal interpolation function, and the associated biorthogonal multi wavelets are constructed. This paper uses biorthogonal multi wavelets to be supported in [-1,1] associated with biorthogonal scaling vectors to be supported in [-1,1]. The scaling vectors and wavelets remain biorthogonal when restricted to integer intervals, making them well suited for bounded domains. The experiment results of simulation of the proposed image compression using biorthogonal multiwavelets on [-1,1] based on SPIHT were found to be excellent PSNR for LENA and PEPPERS images except for BABOON image than already existing single wavelets and DGHM multi wavelets.

### A Study on CFD Data Compression Using Hybrid Supercompact Wavelets

• Hyungmin Kang;Lee, Dongho;Lee, Dohyung
• Journal of Mechanical Science and Technology
• /
• v.17 no.11
• /
• pp.1784-1792
• /
• 2003
• A hybrid method with supercompact multiwavelets is suggested as an efficient and practical method to compress CFD dataset. Supercompact multiwavelets provide various advantages such as compact support and orthogonality in CFD data compression. The compactness is a crucial condition for approximated representation of CFD data to avoid unnecessary interaction between remotely spaced data across various singularities such as shock and vortices. But the supercompact multiwavelet method has to fit the CFD grid size to a product of integer and power of two, m${\times}$2$^n$. To resolve this problem, the hybrid method with combination of 3, 2 and 1 dimensional version of wavelets is studied. With the hybrid method, any arbitrary size can be handled without any shrinkage or expansion of the original problem. The presented method allows high data compression ratio for fluid simulation data. Several numerical tests substantiate large data compression ratios for flow field simulation successfully.

### ORTHOGONAL TWO-DIRECTION REFINABLE FUNCTION OF ORDER 3

• KWON, SOON-GEOL
• Journal of applied mathematics & informatics
• /
• v.37 no.3_4
• /
• pp.307-315
• /
• 2019
• In this paper we construct orthogonal two-direction scaling function of order 3 and corresponding wavelet function. In this paper we propose a different approach using orthogonal symmetric/antisymmetric multiwavelets of order 3. An example for constructing orthogonal two-direction scaling function of order 3 and corresponding wavelet function is given.

### INFINITUDE OF MINIMALLY SUPPORTED TOTALLY INTERPOLATING BIORTHOGONAL MULTIWAVELET SYSTEMS WITH LOW APPROXIMATION ORDERS

• Choi, Youngwoo;Jung, Jaewon
• Korean Journal of Mathematics
• /
• v.21 no.3
• /
• pp.247-263
• /
• 2013
• By analyzing one-parameter families of totally interpolating multiwavelet systems of minimal total length with low approximation orders, whose explicit formulas were obtained with the aid of well-known relations of filters, we demonstrate the infinitude of such systems.