A unified framework for wavelet transforms based on the lifting scheme

2002 ◽  
Author(s):  
Hoon Yoo ◽  
Jechang Jeong
Keyword(s):  
Wavelet Transforms ◽  
Lifting Scheme ◽  
Unified Framework

NON-SEPARABLE 2D BIORTHOGONAL WAVELETS WITH TWO-ROW FILTERS

2005 ◽  
Vol 03 (01) ◽  
pp. 1-18 ◽  
Author(s):  
YINWEI ZHAN ◽  
HENK J. A. M. HEIJMANS
Keyword(s):  
Image Processing ◽  
Characteristic Feature ◽  
Tensor Product ◽  
Wavelet Transforms ◽  
Lifting Scheme ◽  
Efficient Implementation ◽  
Biorthogonal Wavelets ◽  
Compactly Supported

In the literature 2D (or bivariate) wavelets are usually constructed as a tensor product of 1D wavelets. Such wavelets are called separable. However, there are various applications, e.g. in image processing, for which non-separable 2D wavelets are prefered. In this paper, we investigate the class of compactly supported orthonormal 2D wavelets that was introduced by Belogay and Wang.2 A characteristic feature of this class of wavelets is that the support of the corresponding filter comprises only two rows. We are concerned with the biorthogonal extension of this kind of wavelets. It turns out that the 2D wavelets in this class are intimately related to some underlying 1D wavelet. We explore this relation in detail, and we explain how the 2D wavelet transforms can be realized by means of a lifting scheme, thus allowing an efficient implementation. We also describe an easy way to construct wavelets with more rows and shorter columns.

Improved Wavelet Algorithm on Image Denoising Processing

2011 ◽  
Vol 128-129 ◽  
pp. 160-163
Author(s):  
Zhen Xian Lin
Keyword(s):  
Image Processing ◽  
Image Denoising ◽  
Fast Algorithm ◽  
Wavelet Transforms ◽  
Simulation Experiment ◽  
Lifting Scheme ◽  
Important Method ◽  
Wavelet Image ◽  
Wavelet Algorithm ◽  
Improved Algorithm

Wavelet image de-noising has been well acknowledged as an important method of de-noising in Image Processing. Lifting scheme is not only a fast algorithm of existing wavelet transforms, but also a tool to produce new wavelet transforms. In this paper, the principle of several wavelet de-noising algorithms are described, and we compares with these algorithm, gives three kinds of improved algorithm. The simulation experiment shows that it is practicable and effective.

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