An effective approach for wavelet lifting based on filter optimization and median operator

2010 ◽  
Vol 20 (4) ◽  
pp. 359-366 ◽  
Author(s):  
Do Quan ◽  
Yo-Sung Ho
Keyword(s):  
Wavelet Lifting ◽  
Median Operator

scholarly journals Coarse median algebras: the intrinsic geometry of coarse median spaces and their intervals

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Graham A. Niblo ◽  
Nick Wright ◽  
Jiawen Zhang
Keyword(s):  
Finite Rank ◽  
Intrinsic Geometry ◽  
Bounded Geometry ◽  
Higher Dimensional ◽  
Median Algebra ◽  
Asymptotic Geometry ◽  
Median Operator

AbstractThis paper establishes a new combinatorial framework for the study of coarse median spaces, bridging the worlds of asymptotic geometry, algebra and combinatorics. We introduce a simple and entirely algebraic notion of coarse median algebra which simultaneously generalises the concepts of bounded geometry coarse median spaces and classical discrete median algebras. We study the coarse median universe from the perspective of intervals, with a particular focus on cardinality as a proxy for distance. In particular we prove that the metric on a quasi-geodesic coarse median space of bounded geometry can be constructed up to quasi-isometry using only the coarse median operator. Finally we develop a concept of rank for coarse median algebras in terms of the geometry of intervals and show that the notion of finite rank coarse median algebra provides a natural higher dimensional analogue of Gromov’s concept of $$\delta $$ δ -hyperbolicity.

Wavelet Lifting Scheme for the Numerical Solution of Dynamic Reynolds Equation for Micropolar Fluid Lubrication

2021 ◽  
pp. 2150033
Author(s):  
S. C. Shiralashetti ◽  
M. H. Kantli ◽  
A. B. Deshi
Keyword(s):  
Numerical Solution ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Lifting Scheme ◽  
Computational Time ◽  
Biorthogonal Wavelets ◽  
Wavelet Theory ◽  
Science And Engineering ◽  
Promising Tool ◽  
Wavelet Lifting

Recently, wavelet theory has become a well recognized promising tool in science and engineering field; especially, wavelets are successfully used in fast algorithms for easy execution. In this paper, we developed wavelet lifting scheme using orthogonal and biorthogonal wavelets for the numerical solution of dynamic Reynolds equation for micropolar fluid lubrication. The numerical results gained through proposed scheme are compared with the exact solution to expose the accuracy with speed of convergence in lesser computational time as compared with the existing methods. The examples are given to demonstrate the applicability and attractiveness of proposed method.

Relative time seislet transform

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. V223-V232 ◽  
Author(s):  
Zhicheng Geng ◽  
Xinming Wu ◽  
Sergey Fomel ◽  
Yangkang Chen
Keyword(s):  
Seismic Data ◽  
Computational Cost ◽  
Lifting Scheme ◽  
Real Data ◽  
Data Sets ◽  
Relative Time ◽  
New Approach ◽  
New Formulation ◽  
Wavelet Lifting ◽  
Seismic Images

The seislet transform uses the wavelet-lifting scheme and local slopes to analyze the seismic data. In its definition, the designing of prediction operators specifically for seismic images and data is an important issue. We have developed a new formulation of the seislet transform based on the relative time (RT) attribute. This method uses the RT volume to construct multiscale prediction operators. With the new prediction operators, the seislet transform gets accelerated because distant traces get predicted directly. We apply our method to synthetic and real data to demonstrate that the new approach reduces computational cost and obtains excellent sparse representation on test data sets.

Motion Compensated Temporal Filtering in Scalable Video Coding Algorithm

2014 ◽  
Vol 687-691 ◽  
pp. 4097-4100
Author(s):  
Shun Xing Hu ◽  
Hong Tao Zhang
Keyword(s):  
Video Coding ◽  
Scalable Video Coding ◽  
Temporal Correlation ◽  
Haar Wavelet ◽  
Scalable Video ◽  
Temporal Filtering ◽  
Filtering Method ◽  
Coding Efficiency ◽  
Wavelet Lifting ◽  
Lifting Techniques

the temporal correlation exists between the frame and the frame in a video message, in order to solve temporal redundancy.This paper adopts motion-compensated temporal filtering method for removing temporal correlation, motion-compensated temporal filtering and Haar wavelet lifting techniques are studied and discussed; finally presented the improved motion compensated temporal filtering methods. Results show the new method improves coding efficiency and scalability.

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