Image Denoising in Industry Based on Multiwavelet Riesz Bases

2013 ◽  
Vol 675 ◽  
pp. 59-62
Author(s):  
Qi Chao Song ◽  
Zhi Song Liu ◽  
Chao Ping Wang
Keyword(s):  
Image Denoising ◽  
Riesz Bases ◽  
Refinement Equation ◽  
Compactly Supported

Damage testing of components is a key point in many industry fields. In some cases, endoscope is used to inspect the damage part, while the images are often noised. In this paper, we focus on industrial image denoising based on multiwavelet Riesz bases. Starting from compactly supported vector refinement equation, we provide a characterization to form two Riesz bases and an example is given. Based on example Riesz bases, we research industrial endoscope image denoising and get satisfying result.

Characters of Two-Directional Compactly Supported Bivariate Wavelet Packets

2010 ◽  
Vol 439-440 ◽  
pp. 914-919
Author(s):  
Zong Sheng Sheng ◽  
Shu De Du
Keyword(s):  
Frequency Analysis ◽  
Natural Science ◽  
Operator Theory ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Science And Engineering ◽  
Time Frequency ◽  
Compactly Supported ◽  
Engineering Computation ◽  
Algebra Theory

Wavelet analysis has been a powerful tool for exploring and solving many complicated problems in natural science and engineering computation. In this article, the notion of biorthogonal two-direction compactly supported bivariate wavelet packets with polyscale is developed. Their properties is investigated by algebra theory, means of time-frequency analysis methodand, operator theory. The direct decomposition relationship is provided. In the final, new Riesz bases of space are constructed from these wavelet packets. Three biorthogonality formulas regarding these wavelet packets are established.

A Study of a Two-Directional Vector Multivariate Wavelet Wraps and Applications in Engineering Materials

2014 ◽  
Vol 889-890 ◽  
pp. 1270-1274
Author(s):  
Jin Shun Feng ◽  
Qing Jiang Chen
Keyword(s):  
Multiresolution Analysis ◽  
Riesz Bases ◽  
Scaling Functions ◽  
Sufficient Condition ◽  
Analysis Method ◽  
Compactly Supported ◽  
Dilation Matrix ◽  
Engineering Materials ◽  
Vector Valued

The existence of compactly supported orthogonal two-directional vector-valued wavelets associated with a pair of orthogonal shortly supported vector-valued scaling functions is researched. We introduce a class of two-directional vector-valued four-dimensional wavelet wraps according to a dilation matrix, which are generalizations of univariate wavelet wraps. Three orthogonality formulas regarding the wavelet wraps are established. Finally, it is shown how to draw new Riesz bases of space from these wavelet wraps. The sufficient condition for the existence of four-dimensional wavelet wraps is established based on the multiresolution analysis method.

scholarly journals Analysis of Compactly Supported Nonstationary Biorthogonal Wavelet Systems Based on Exponential B-Splines

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Yeon Ju Lee ◽  
Jungho Yoon
Keyword(s):  
Riesz Bases ◽  
Refinable Functions ◽  
Biorthogonal Wavelet ◽  
Wavelet Bases ◽  
Refinable Function ◽  
B Splines ◽  
Compactly Supported ◽  
Mathematical Properties ◽  
The Stability

This paper is concerned with analyzing the mathematical properties, such as the regularity and stability of nonstationary biorthogonal wavelet systems based on exponential B-splines. We first discuss the biorthogonality condition of the nonstationary refinable functions, and then we show that the refinable functions based on exponential B-splines have the same regularities as the ones based on the polynomial B-splines of the corresponding orders. In the context of nonstationary wavelets, the stability of wavelet bases is not implied by the stability of a refinable function. For this reason, we prove that the suggested nonstationary wavelets form Riesz bases for the space that they generate.

Zero-filling Technique in Fresnel Transfrom Image Reconstruction for MR Image Denoising

PIERS Online ◽  
2005 ◽  
Vol 1 (4) ◽  
pp. 473-477
Author(s):  
Bin-Rong Wu ◽  
Satoshi Ito ◽  
Yoshitsugu Kamimura ◽  
Yoshifumi Yamada
Keyword(s):  
Image Reconstruction ◽  
Image Denoising ◽  
Mr Image
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