scholarly journals A Variation on Uncertainty Principle and Logarithmic Uncertainty Principle for Continuous Quaternion Wavelet Transforms

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Mawardi Bahri ◽  
Ryuichi Ashino
Keyword(s):  
Wavelet Transform ◽  
Uncertainty Principle ◽  
Wavelet Transforms ◽  
Quaternion Algebra ◽  
Uncertainty Principles ◽  
Quaternion Fourier Transform ◽  
Coordinate Form ◽  
Quaternion Wavelet Transform ◽  
Polar Coordinate ◽  
Extended Uncertainty

The continuous quaternion wavelet transform (CQWT) is a generalization of the classical continuous wavelet transform within the context of quaternion algebra. First of all, we show that the directional quaternion Fourier transform (QFT) uncertainty principle can be obtained using the component-wise QFT uncertainty principle. Based on this method, the directional QFT uncertainty principle using representation of polar coordinate form is easily derived. We derive a variation on uncertainty principle related to the QFT. We state that the CQWT of a quaternion function can be written in terms of the QFT and obtain a variation on uncertainty principle related to the CQWT. Finally, we apply the extended uncertainty principles and properties of the CQWT to establish logarithmic uncertainty principles related to generalized transform.

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.

scholarly journals The generalized and extended uncertainty principles and their implications on the Jeans mass

2019 ◽  
Vol 488 (1) ◽  
pp. L69-L74 ◽  
Author(s):  
H Moradpour ◽  
A H Ziaie ◽  
S Ghaffari ◽  
F Feleppa
Keyword(s):  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Ideal Gas ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Newtonian Gravity ◽  
Uncertainty Principles ◽  
Temperature Relation ◽  
Heisenberg Uncertainty Principle ◽  
Extended Uncertainty

ABSTRACT The generalized and extended uncertainty principles affect the Newtonian gravity and also the geometry of the thermodynamic phase space. Under the influence of the latter, the energy–temperature relation of ideal gas may change. Moreover, it seems that the Newtonian gravity is modified in the framework of the Rényi entropy formalism motivated by both the long-range nature of gravity and the extended uncertainty principle. Here, the consequences of employing the generalized and extended uncertainty principles, instead of the Heisenberg uncertainty principle, on the Jeans mass are studied. The results of working in the Rényi entropy formalism are also addressed. It is shown that unlike the extended uncertainty principle and the Rényi entropy formalism that lead to the same increase in the Jeans mass, the generalized uncertainty principle can decrease it. The latter means that a cloud with mass smaller than the standard Jeans mass, obtained in the framework of the Newtonian gravity, may also undergo the gravitational collapse process.

Medical Image Feature Matching Based on Wavelet Transform and SIFT Algorithm

2011 ◽  
Vol 65 ◽  
pp. 497-502
Author(s):  
Yan Wei Wang ◽  
Hui Li Yu
Keyword(s):  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Medical Image ◽  
Feature Matching ◽  
Image Feature ◽  
Scale Invariant ◽  
Sift Algorithm ◽  
Matching Algorithm ◽  
Invariant Feature ◽  
Scale Invariant Feature

A feature matching algorithm based on wavelet transform and SIFT is proposed in this paper, Firstly, Biorthogonal wavelet transforms algorithm is used for medical image to delaminating, and restoration the processed image. Then the SIFT (Scale Invariant Feature Transform) applied in this paper to abstracting key point. Experimental results show that our algorithm compares favorably in high-compressive ratio, the rapid matching speed and low storage of the image, especially for the tilt and rotation conditions.

Evaluation of Crowd Motion Direction Based on Wavelet Transform

2013 ◽  
Vol 846-847 ◽  
pp. 1106-1110
Author(s):  
Guo Qing Yang ◽  
Rong Yi Cui
Keyword(s):  
Wavelet Decomposition ◽  
Estimation Method ◽  
Motion Vectors ◽  
Motion Direction ◽  
Main Research ◽  
Object A ◽  
Coordinate Form ◽  
Direction Estimation ◽  
Polar Coordinate ◽  
Crowd Motion

Taking the wavelet decomposed approximate image as the main research object, a direction estimation method for moving object was proposed in this paper. Firstly, the approximate image for the frame of the video was obtained via wavelet decomposition; and furthermore, the motion estimation on the approximate image was achieved to obtain the motion vectors. Finally, the motion vectors were described as polar coordinate form to compute the number of motion vectors in specified angles and the information entropy of the motion directions. The experiment results show that the proposed method can remove the effect of noise and the results of direction estimation are consistent with the actual motion directions.

Wavelet transform to quantify heart rate variability and to assess its instantaneous changes

1999 ◽  
Vol 86 (3) ◽  
pp. 1081-1091 ◽  
Author(s):  
Vincent Pichot ◽  
Jean-Michel Gaspoz ◽  
Serge Molliex ◽  
Anestis Antoniadis ◽  
Thierry Busso ◽  
...  
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Nervous System ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Autonomous Nervous System ◽  
Dynamic Changes ◽  
Nonstationary Signals ◽  
Higher Doses

Heart rate variability is a recognized parameter for assessing autonomous nervous system activity. Fourier transform, the most commonly used method to analyze variability, does not offer an easy assessment of its dynamics because of limitations inherent in its stationary hypothesis. Conversely, wavelet transform allows analysis of nonstationary signals. We compared the respective yields of Fourier and wavelet transforms in analyzing heart rate variability during dynamic changes in autonomous nervous system balance induced by atropine and propranolol. Fourier and wavelet transforms were applied to sequences of heart rate intervals in six subjects receiving increasing doses of atropine and propranolol. At the lowest doses of atropine administered, heart rate variability increased, followed by a progressive decrease with higher doses. With the first dose of propranolol, there was a significant increase in heart rate variability, which progressively disappeared after the last dose. Wavelet transform gave significantly better quantitative analysis of heart rate variability than did Fourier transform during autonomous nervous system adaptations induced by both agents and provided novel temporally localized information.

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