Affine Shear Tight Frames with Two-Layer Structure

被引：0

作者：

Che, Zhihua ^{[1
]}

Zhuang, Xiaosheng ^{[1
]}

机构：

[1] City Univ Hong Kong, Dept Math, Tat Chee Ave, Kowloon, Hong Kong, Peoples R China

来源：

WAVELETS AND SPARSITY XVII | 2017年 / 10394卷

关键词：

directional multiscale representation systems; affine shear tight frames; digital affine shear transforms; 2-layer filter banks; directional filter banks; image/video processing; high-dimensional data analysis; denoising/inpainting; tensor product complex tight framelets; shearlets; curvelets; contourlets; surfacelets; TRANSFORM; DESIGN;

D O I：

10.1117/12.2272398

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

Affine shear tight frames with 2-layer structure in arbitrary dimensions are constructed. Affine shear filter banks with 2-layer structure associated with affine shear tight frames with 2-layer structure are designed and show to be with the perfect reconstruction property. The redundancy rate and computational complexity of affine shear filter banks are discussed. Applications to video denoising are conducted to demonstrate the effectiveness of the affine shear filter banks with 2-layer structure.

引用

页数：8

共 23 条

[1] Gabor shearlets
Bodmann, Bernhard G.
Kutyniok, Gitta
Zhuang, Xiaosheng
[J]. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2015, 38 (01) : 87 - 114
[2] New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities
Candès, EJ
Donoho, DL
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2004, 57 (02) : 219 - 266
[3] Fast discrete curvelet transforms
Candes, Emmanuel
Demanet, Laurent
Donoho, David
Ying, Lexing
[J]. MULTISCALE MODELING & SIMULATION, 2006, 5 (03) : 861 - 899
[4] Che Z., 2017, DIGITAL AFFINE UNPUB
[5] Chui C. K., APPL COMPUT HARMON A, DOI [10.1016/j.acha.2016.12.005, DOI 10.1016/J.ACHA.2016.12.005.]
[6] The nonsubsampled contourlet transform: Theory, design, and applications
da Cunha, Arthur L.
Zhou, Jianping
Do, Minh N.
[J]. IEEE TRANSACTIONS ON IMAGE PROCESSING, 2006, 15 (10) : 3089 - 3101
[7] Daubechies, 1992, CBMS NSF REGIONAL C, DOI [DOI 10.1137/1.9781611970104, 10.1137/1.9781611970104]
[8] The Construction of Smooth Parseval Frames of Shearlets
Guo, K.
Labate, D.
[J]. MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2013, 8 (01) : 82 - 105
[9] GUO K., 2006, Wavelets and Splines: Athens 2005, P189
[10] Optimally sparse multidimensional representation using shearlets
Guo, Kanghui
Labate, Demetrio
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2007, 39 (01) : 298 - 318

← 1 2 3 →