Directional Compactly Supported Tensor Product Complex Tight Framelets with Applications to Image Denoising and Inpainting

In this paper we construct compactly supported biorthogonal wavelet bases of the interval, with dilation factor M. Next, the natural MRA on the cube arising from the tensor product of a multilevel decomposition of the unit interval is developed. New Jackson and Bernstein type inequalities are proved, providing a characterization for anisotropic Sobolev spaces.

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

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691305000713 ◽

2005 ◽

Vol 03 (01) ◽

pp. 1-18 ◽

Cited By ~ 3

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.

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Image Denoising in Industry Based on Multiwavelet Riesz Bases

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.675.59 ◽

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.

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Compactly Supported Tensor Product Complex Tight Framelets with Directionality

SIAM Journal on Mathematical Analysis ◽

10.1137/13092856x ◽

2015 ◽

Vol 47 (3) ◽

pp. 2464-2494 ◽

Cited By ~ 13

Author(s):

Bin Han ◽

Qun Mo ◽

Zhenpeng Zhao

Keyword(s):

Tensor Product ◽

Compactly Supported

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Compactly supported non-tensor product form two-dimension wavelet finite element

Applied Mathematics and Mechanics ◽

10.1007/s10483-006-1210-z ◽

2006 ◽

Vol 27 (12) ◽

pp. 1673-1686 ◽

Cited By ~ 2

Author(s):

Jian-ming Jin ◽

Peng-xiang Xue ◽

Ying-xiang Xu ◽

Ya-li Zhu

Keyword(s):

Finite Element ◽

Tensor Product ◽

Product Form ◽

Two Dimension ◽

Compactly Supported ◽

Wavelet Finite Element

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PARAMETRIZATION OF COMPACTLY SUPPORTED TRIVARIATE ORTHOGONAL WAVELET FILTER

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691307001938 ◽

2007 ◽

Vol 05 (04) ◽

pp. 627-639 ◽

Cited By ~ 3

Author(s):

YONGDONG HUANG ◽

ZHENGXING CHENG

Keyword(s):

Signal Processing ◽

Tensor Product ◽

Parametric Representation ◽

Wavelet Filter ◽

Orthogonal Wavelet ◽

Compactly Supported ◽

Wavelets Analysis

Multivariate wavelets analysis is a powerful tool for multi-dimensional signal processing, but tensor product wavelets have a number of drawbacks. In this paper, we give an algorithm of parametric representation compactly supported trivariate orthogonal wavelet filter, which simplifies the study of trivariate orthogonal wavelet. Four examples are also given to demonstrate the method.

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