Representation theorems for the Mexican hat wavelet transform

2020 ◽  
Author(s):  
Abhishek Singh ◽  
Nikhila Raghuthaman ◽  
Aparna Rawat ◽  
Jagdev Singh
Keyword(s):  
Wavelet Transform ◽  
Representation Theorems ◽  
Mexican Hat Wavelet ◽  
Mexican Hat

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

scholarly journals The De-Noising of Sonic Echo Test Data through Wavelet Transform Reconstruction

1999 ◽  
Vol 6 (5-6) ◽  
pp. 267-272 ◽  
Author(s):  
J.N. Watson ◽  
P.S. Addison ◽  
A. Sibbald
Keyword(s):  
Wavelet Transform ◽  
Test Data ◽  
Discrete Wavelet ◽  
Non Destructive Testing ◽  
Destructive Testing ◽  
Transform Method ◽  
Mexican Hat Wavelet ◽  
Mexican Hat ◽  
Non Destructive

This paper presents the results of feasibility study into the application of the wavelet transform signal processing method to sonic based non-destructive testing techniques. Finite element generated data from cast in situ foundation piles were collated and processed using both continuous and discrete wavelet transform techniques. Results were compared with conventional Fourier based methods. The discrete Daubechies wavelets and the continuous Mexican hat wavelet were used and their relative merits investigated. It was found that both the continuous Mexican hat and discrete Daubechies D8 wavelets were significantly better at locating the pile toe compared than the Fourier filtered case. The wavelet transform method was then applied to field test data and found to be successful in facilitating the detection of the pile toe.

Mexican Hat Wavelet Transform and Its Applications

2021 ◽  
pp. 299-317
Author(s):  
Abhishek Singh ◽  
Aparna Rawat ◽  
Nikhila Raghuthaman
Keyword(s):  
Wavelet Transform ◽  
Mexican Hat Wavelet ◽  
Mexican Hat

Mexican hat wavelet transform of distributions

2016 ◽  
Vol 27 (6) ◽  
pp. 468-483 ◽  
Author(s):  
R. S. Pathak ◽  
Abhishek Singh
Keyword(s):  
Wavelet Transform ◽  
Mexican Hat Wavelet ◽  
Mexican Hat

scholarly journals An asymptotic expansion of continuous Wavelet transform for large dilation parameter

2018 ◽  
Vol 36 (3) ◽  
pp. 27-39
Author(s):  
Ashish Pathak ◽  
Prabhat Yadav ◽  
M. M. Dixit
Keyword(s):  
Asymptotic Expansion ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Morlet Wavelet ◽  
Continuous Wavelet ◽  
Mexican Hat Wavelet ◽  
Mexican Hat ◽  
Special Cases ◽  
Morlet Wavelet Transform

In this paper , we derive asymptotic expansion of the wavelet transform for large values of the dilation parameter a by using Lopez and Pagola technique. Asymptotic expansion of Mexican Hat wavelet and Morlet wavelet transform are obtained as a special cases.

scholarly journals Object Shape Recognition Using Wavelet Descriptors

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Adnan Abou Nabout
Keyword(s):  
Wavelet Transform ◽  
Image Coding ◽  
Shape Recognition ◽  
Distance Matrix ◽  
Object Shape ◽  
Contour Shape ◽  
Angle Function ◽  
Mexican Hat Wavelet ◽  
Mexican Hat ◽  
Starting Point

The wavelet transform is a well-known signal analysis method in several engineering disciplines. In image processing and pattern recognition, the wavelet transform is used in many applications for image coding as well as feature extraction purposes. It can be used to describe a given object shape by wavelet descriptors (WD). Thus, it is used to recognize objects according to their contour shape by deriving a number of WD and comparing them with the WD of stored contour patterns. For our method, we use a periodical angle function derived from an extracted object contour. In order to apply the WD, the Mexican Hat can be used as the mother wavelet. In this paper, the method of object shape recognition using wavelet descriptors is described coherently and includes details relating to the method of applying the periodical angle function and the derivation of the formulas for the Haar as well as Mexican Hat wavelet descriptors. To evaluate the results of object recognition when using wavelet descriptors taking into account the dependence on the starting point, the paper describes a sufficient method for the comparison of wavelet descriptors using the minimum distance matrix.

Wavelet analysis of the breakdown of a pulsed vortex flow

1999 ◽  
Vol 213 (3) ◽  
pp. 217-229 ◽  
Author(s):  
P. S. Addison
Keyword(s):  
Wavelet Transform ◽  
Wavelet Analysis ◽  
Vortex Flow ◽  
Time Series Data ◽  
Power Spectra ◽  
Low Frequency ◽  
Series Data ◽  
Mexican Hat Wavelet ◽  
Breakdown Region ◽  
Mexican Hat

The paper provides an introduction to the properties and use of the continuous wavelet transform. It then describes the wavelet analysis of the breakdown of a confined vortex flow where time series data of the centre-line velocities from a pulsed vortex flow at a pipe orifice are examined using the Mexican hat wavelet transform. The development of the signal from the periodic, vortex flow via an energetic turbulent breakdown region to a flow composed of low-frequency coherent structures at intermittent temporal scales is monitored using wavelet transform plots, wavelet energy plots and wavelet power spectra.

scholarly journals Video Coding of Various Decomposition with Encoding Techniques

2019 ◽  
Vol 8 (2S6) ◽  
pp. 556-560
Keyword(s):  
Wavelet Transform ◽  
Video Coding ◽  
Compression Ratio ◽  
Curvelet Transform ◽  
Vital Role ◽  
Mexican Hat Wavelet ◽  
Mexican Hat ◽  
Empirical Wavelet Transform ◽  
Total Communication ◽  
Fractional Transform

In a period of past ten years, Compression or coding of video has been elaborated as a vital role in the part of total communication. Multi resolutions techniques play a vital part in the coding of image and video. Wavelet and curve let transform are one of the popular and efficient technique in video coding. In my paper, I am operate to implement various coding based methods with (EWT)empirical wavelet transform, different wavelets ,curvelets with various encoding techniques. They are video coding with EWT and H.264(VEWH), video coding with EWT and LZW(VEWL), video coding with EWT and Huffman with SPIHT(VEWHS), video coding with mexican hat wavelet transform and SPIHT(VMWS), video coding with dual tree wavelet and SPIHT(VDTS), video coding with 3D dual tree wavelet transform and SPIHT(V3DTS), video coding with curvelet transform and SPIHT(VCTS) and video coding with dual tree complex wavelet fractional transform and modified SPIHT(VDTCWFS). Next we implement these methods with the assist of matlab 2014 and 2015, and then analyze these techniques by using PSNR and compression ratio

Abelian theorems for fractional wavelet transform

2017 ◽  
Vol 10 (01) ◽  
pp. 1750019
Author(s):  
Akhilesh Prasad ◽  
Praveen Kumar
Keyword(s):  
Wavelet Transform ◽  
Wavelet Function ◽  
Tempered Distributions ◽  
Final Value ◽  
Mexican Hat Wavelet ◽  
Mexican Hat ◽  
Fractional Wavelet Transform ◽  
Abelian Theorems

In this paper, initial and final value Abelian theorems for fractional wavelet transform of function and tempered distributions are obtained. Using Mexican hat wavelet function, an application for Abelian theorems is investigated.

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