scholarly journals Construction of orthonormal directional wavelets based on quincunx dilation subsampling

2015 ◽  
Author(s):  
Rujie Yin
Keyword(s):  
Directional Wavelets

THE BACK-PROJECTION METHOD FOR CONSTRUCTING 3D NON-TENSOR PRODUCT MOTHER WAVELETS AND THE APPLICATION IN IMAGE EDGE DETECTION

2012 ◽  
Vol 10 (03) ◽  
pp. 1250026 ◽  
Author(s):  
LI ZENG ◽  
JIQIANG GUO ◽  
CHENCHENG HUANG
Keyword(s):  
Tensor Product ◽  
Computational Cost ◽  
Three Dimension ◽  
Back Projection ◽  
Mother Wavelet ◽  
3D Images ◽  
Mexican Hat Wavelet ◽  
Mexican Hat ◽  
Directional Wavelets ◽  
Mother Wavelets

In this paper, a non-tensor product method for constructing three-dimension (3D) mother wavelets by back-projecting two dimension (2D) mother wavelets is presented. We have proved that if a 2D mother wavelet satisfies certain conditions, the back-projection of the 2D mother wavelet is a 3D mother wavelet. And the construction instances of 3D Mexican-hat wavelet and 3D Meyer wavelet are given. These examples imply that we can get some new 3D mother wavelets from known 1D or 2D mother wavelets by using back-projecting method. This method inaugurates a new approach for constructing non-tensor product 3D wavelet. In addition, the non-tensor product 3D Mexican-hat wavelet is used for detecting the edge of two 3D images in our experimental section. Compared with the Mallat's maximum wavelet module approach which uses 3D directional wavelets, experimental results show it can obtain better outcome especial for the edge which the orientation is not along the coordinate axis. Furthermore, the edge is more fine, and the computational cost is much smaller. The non-tensor product mother wavelets constructed by using the method of this paper also can be widely used for compression, filtering and denoising of 3D images.

Undersampled MRI reconstruction with patch-based directional wavelets

2012 ◽  
Vol 30 (7) ◽  
pp. 964-977 ◽  
Author(s):  
Xiaobo Qu ◽  
Di Guo ◽  
Bende Ning ◽  
Yingkun Hou ◽  
Yulan Lin ◽  
...  
Keyword(s):  
Directional Wavelets ◽  
Mri Reconstruction

Rate-Distortion Analysis of Directional Wavelets

2012 ◽  
Vol 21 (2) ◽  
pp. 588-600 ◽  
Author(s):  
A. Maleki ◽  
B. Rajaei ◽  
H. R. Pourreza
Keyword(s):  
Rate Distortion ◽  
Distortion Analysis ◽  
Directional Wavelets

Directional Wavelets and a Wavelet Variogram for Two-Dimensional Data

2009 ◽  
Vol 41 (6) ◽  
pp. 611-641 ◽  
Author(s):  
E. H. Bosch ◽  
A. P. González ◽  
J. G. Vivas ◽  
G. R. Easley
Keyword(s):  
Two Dimensional ◽  
Directional Wavelets

Accelerating patch-based directional wavelets with multicore parallel computing in compressed sensing MRI

2015 ◽  
Vol 33 (5) ◽  
pp. 649-658 ◽  
Author(s):  
Qiyue Li ◽  
Xiaobo Qu ◽  
Yunsong Liu ◽  
Di Guo ◽  
Zongying Lai ◽  
...  
Keyword(s):  
Parallel Computing ◽  
Compressed Sensing ◽  
Directional Wavelets

Tracking speckle motion with directional wavelets

2001 ◽  
Author(s):  
Igor Patrickeyev ◽  
Sean J. Kirkpatrick ◽  
Donald D. Duncan
Keyword(s):  
Directional Wavelets
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