Parameterizations of masks for 3-band tight wavelet frames by symmetric extension of polyphase matrix

2013 ◽  
Vol 225 ◽  
pp. 461-474
Author(s):  
Jianjun Sun ◽  
Yan Huang ◽  
Shuyao Sun ◽  
Lihong Cui
Keyword(s):  
Wavelet Frames ◽  
Symmetric Extension ◽  
Polyphase Matrix

scholarly journals Symmetry Feature and Construction for the 3-Band Tight Framelets with Prescribed Properties

2012 ◽  
Vol 2012 ◽  
pp. 1-20
Author(s):  
Jianjun Sun ◽  
Bin Huang ◽  
Xiaodong Chen ◽  
Lihong Cui
Keyword(s):  
Wavelet Frames ◽  
Symmetric Extension ◽  
The Matrix ◽  
Polyphase Matrix ◽  
Necessary Constraints ◽  
Sobolev Exponent

A construction approach for the 3-band tight wavelet frames by factorization of paraunitary matrix is developed. Several necessary constraints on the filter lengths and symmetric features of wavelet frames are investigated starting at the constructed paraunitary matrix. The matrix is a symmetric extension of the polyphase matrix corresponding to 3-band tight wavelet frames. Further, the parameterizations of 3-band tight wavelet frames with3N+1filter lengths are established. Examples of framelets with symmetry/antisymmetry and Sobolev exponent are computed by appropriately choosing the parameters in the scheme.

scholarly journals Polyphase matrix characterization of framelets on local fields of positive characteristic

2017 ◽  
Vol 9 (1) ◽  
pp. 248-259
Author(s):  
F. A. Shah ◽  
M. Y. Bhat
Keyword(s):  
Positive Characteristic ◽  
Local Fields ◽  
Extension Principle ◽  
Wavelet Frames ◽  
Unitary Extension ◽  
Polyphase Matrix

AbstractAn important tool for the construction of framelets on local fields of positive characteristic using unitary extension principle was presented by Shah and Debnath [Tight wavelet frames on local fields, Analysis, 33 (2013), 293-307]. In this article, we continue the study of framelets on local fields and present a polyphase matrix characterization of framelets generated by the extension principle.

A PAIR OF ORTHOGONAL WAVELET FRAMES IN L2(ℝd)

2014 ◽  
Vol 12 (02) ◽  
pp. 1450011 ◽  
Author(s):  
GHANSHYAM BHATT
Keyword(s):  
Dimensional Case ◽  
Extension Principle ◽  
Higher Dimension ◽  
Wavelet Frames ◽  
Orthogonal Wavelet ◽  
Extra Condition ◽  
Simple Method ◽  
One Dimensional ◽  
Unitary Extension ◽  
Polyphase Matrix

A simple method of construction of a pair of orthogonal wavelet frames in L2(ℝd) is presented. This is a generalization of one-dimensional case to higher dimension. The construction is based on the well-known Unitary Extension Principle (UEP). The presented method produces the polyphase components of the filters of the wavelet functions, and hence the filters. A pair of orthogonal wavelet frames can be constructed with an extra condition. In the construction, the polyphase matrix is used as opposed to the modulation matrix. This is less restrictive and yields a fewer wavelet functions in the system than in the previously known constructions.

Parameterization of Masks for Tight Wavelet Frames and Multiple Pseudoframes and Applications in Mechanical Engineering

2014 ◽  
Vol 915-916 ◽  
pp. 1448-1451
Author(s):  
Yu Min Yu
Keyword(s):  
Mechanical Engineering ◽  
Materials Science ◽  
Constructive Method ◽  
Sufficient Condition ◽  
Wavelet Frames ◽  
Decomposition Scheme ◽  
Symmetric Extension ◽  
Analysis Design ◽  
Affine Frames ◽  
Resolution Structure

Mechanical engineering is a discipline of engineering that applies the principles of engine ering, physics and materials science for analysis, design, manufacturing, and maintenance of mecha nical systems. In this work, the construction of 4-band tight wavelet frames with symmetric proper-ties using symmetric extension and parameterization of the paraunitary matrix. The notion of an 4-band generalized multiresolution structure of subspace is proposed. The characteristics of affine pseudoframes for subspaces is investigated. The construction of a generalized multiresolution structure of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obta-ined based on such a generalized multiresolution structure and a sufficient condition for its exist-ence is presented. A constructive method for affine frames of based on a generalized multi-resolution structure is presented.

TIGHT FRAME CHARACTERIZATION OF MULTIWAVELET VECTOR FUNCTIONS IN TERMS OF THE POLYPHASE MATRIX

2009 ◽  
Vol 07 (01) ◽  
pp. 9-21 ◽  
Author(s):  
JENS KROMMWEH
Keyword(s):  
Tight Frame ◽  
Extension Principle ◽  
Wavelet Frames ◽  
Unitary Extension ◽  
Directional Wavelets ◽  
Extension Principles ◽  
Polyphase Matrix ◽  
Common Extension ◽  
Polyphase Representation

The extension principles play an important role in characterizing and constructing of wavelet frames. The common extension principles, the unitary extension principle (UEP) or the oblique extension principle (OEP), are based on the unitarity of the modulation matrix. In this paper, we state the UEP and OEP for refinable function vectors in the polyphase representation. Finally, we apply our results to directional wavelets on triangles which we have constructed in a previous work. We will show that the wavelet system generates a tight frame for L2(ℝ2).

scholarly journals Wavelet Frames for Distributions in Anisotropic Besov Spaces

2005 ◽  
Vol 12 (4) ◽  
pp. 637-658
Author(s):  
Dorothee D. Haroske ◽  
Erika Tamási
Keyword(s):  
Large Class ◽  
Besov Spaces ◽  
Studia Math ◽  
Wavelet Frames ◽  
Anisotropic Besov Spaces ◽  
Wavelet Decompositions

Abstract This paper deals with wavelet frames in anisotropic Besov spaces , 𝑠 ∈ ℝ, 0 < 𝑝, 𝑞 ≤ ∞, and 𝑎 = (𝑎1, . . . , 𝑎𝑛) is an anisotropy, with 𝑎𝑖 > 0, 𝑖 = 1, . . . , 𝑛, 𝑎1 + . . . + 𝑎𝑛 = 𝑛. We present sub-atomic and wavelet decompositions for a large class of distributions. To some extent our results can be regarded as anisotropic counterparts of those recently obtained in [Triebel, Studia Math. 154: 59–88, 2003].

A novel approach on micropolar fluid flow in a porous channel with high mass transfer via wavelet frames

2021 ◽  
Vol 10 (1) ◽  
pp. 39-45
Author(s):  
S. Kumbinarasaiah ◽  
K.R. Raghunatha
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Micropolar Fluid ◽  
High Mass ◽  
Porous Channel ◽  
Physical Parameters ◽  
Wavelet Frames ◽  
Parseval Frame ◽  
Highly Nonlinear ◽  
Frame Method

Abstract In this article, we present the Laguerre wavelet exact Parseval frame method (LWPM) for the two-dimensional flow of a rotating micropolar fluid in a porous channel with huge mass transfer. This flow is governed by highly nonlinear coupled partial differential equations (PDEs) are reduced to the nonlinear coupled ordinary differential equations (ODEs) using Berman's similarity transformation before being solved numerically by a Laguerre wavelet exact Parseval frame method. We also compared this work with the other methods in the literature available. Moreover, in the graphs of the velocity distribution and microrotation, we shown that the proposed scheme's solutions are more accurate and applicable than other existing methods in the literature. Numerical results explaining the effects of various physical parameters connected with the flow are discussed.

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