A family of Mexican hat wavelet transforms associated with an isometry in the heat equation

2021 ◽  
Author(s):  
Hari M. Srivastava ◽  
Abhishek Singh ◽  
Aparna Rawat ◽  
Shubha Singh
Keyword(s):  
Heat Equation ◽  
Wavelet Transforms ◽  
Mexican Hat Wavelet ◽  
Mexican Hat

scholarly journals A Relative Method of Video Coding using Different Wavelets with SPIHT

2019 ◽  
Vol 8 (2S10) ◽  
pp. 539-543
Keyword(s):  
Video Coding ◽  
Video Compression ◽  
Wavelet Transforms ◽  
Transmission Rate ◽  
Haar Wavelet ◽  
Mexican Hat Wavelet ◽  
Mexican Hat ◽  
Different Types ◽  
Lossless Data Compression ◽  
The Ideal

Lossy or lossless data compression is needed to Bring down the storage size and greater transmission rate. Wavelet transform is one of the ideal methods used for video compression. Different types of wavelet transforms are now available. In this paper, video is compressed by different wavelets and modified version of SPIHT. Totally seven types of wavelets are used here to compress the video, MSPIHT is used as encoding technique. They are (i) Video coding using duabechies wavelet and MSPIHT (VDM) (ii) Video coding using haar wavelet and MSPIHT (VHM) (iii) video coding using bi orthogonal wavelet and MSPIHT (VBM) (iv) video coding using symlet wavelet and MSPIHT (VSM) (v) video coding using coiflet wavelet and MSPIHT (VCM) (vi) video coding using demeyer wavelet and MSPIHT (VDMM) and (vii) video coding using Mexican hat wavelet and MSPIHT (VMHM). Then we calculate the PSNR and compression ratio for knowing the performance of the system.

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.

Three-Dimensional Profilometry Based on Mexican Hat Wavelet Transform

2009 ◽  
Vol 29 (1) ◽  
pp. 197-202 ◽  
Author(s):  
周翔 Zhou Xiang ◽  
赵宏 Zhao Hong
Keyword(s):  
Wavelet Transform ◽  
Three Dimensional ◽  
Mexican Hat Wavelet ◽  
Mexican Hat

Foreground Separation Methods for Satellite and Balloon Experiments

2005 ◽  
Vol 201 ◽  
pp. 71-74
Author(s):  
R. Belén Barreiro ◽  
Michael P. Hobson ◽  
Anthony N. Lasenby ◽  
Patricio Vielva ◽  
Enrique Martínez-González ◽  
...  
Keyword(s):  
Point Source ◽  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Mexican Hat Wavelet ◽  
Mexican Hat ◽  
Balloon Experiments ◽  
Combined Technique ◽  
Physical Components ◽  
Planck Satellite

A combined technique using the maximum-entropy method (MEM) and the mexican hat wavelet (MHW) to separate and reconstruct the physical components of the microwave sky is presented. We apply this method to simulated observations by the ESA Planck satellite in small patches of the sky. The reconstructed maps of the CMB and foregrounds are improved as compared to those obtained with MEM on its own. Moreover, more accurate point source catalogues are produced at each observing frequency. This technique may also be extended to deal with other multifrequency CMB experiments, including all-sky data.

scholarly journals Combining maximum-entropy and the Mexican hat wavelet to reconstruct the microwave sky

2001 ◽  
Vol 328 (1) ◽  
pp. 1-16 ◽  
Author(s):  
P. Vielva ◽  
R.B. Barreiro ◽  
M.P. Hobson ◽  
E. Martínez-González ◽  
A.N. Lasenby ◽  
...  
Keyword(s):  
Maximum Entropy ◽  
Mexican Hat Wavelet ◽  
Mexican Hat

Continuous quaternion fourier and wavelet transforms

2014 ◽  
Vol 12 (04) ◽  
pp. 1460003 ◽  
Author(s):  
Mawardi Bahri ◽  
Ryuichi Ashino ◽  
Rémi Vaillancourt
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Heat Equation ◽  
Wavelet Transforms ◽  
Quaternion Algebra ◽  
Two Dimensional ◽  
Quaternion Fourier Transform ◽  
Fundamental Properties

A two-dimensional (2D) quaternion Fourier transform (QFT) defined with the kernel [Formula: see text] is proposed. Some fundamental properties, such as convolution, Plancherel and vector differential theorems, are established. The heat equation in quaternion algebra is presented as an example of the application of the QFT to partial differential equations. The wavelet transform is extended to quaternion algebra using the kernel of the QFT.

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