On the implementation of nonseparable two-dimensional Haar wavelet transforms

1999 ◽  
Vol 47 (11) ◽  
pp. 3137-3139
Author(s):  
P. Lenders ◽  
A. Sjostrom
Keyword(s):  
Wavelet Transforms ◽  
Haar Wavelet ◽  
Two Dimensional

scholarly journals Investigation of the basic Haar wavelet-transformations in the problem of decryption of space images on detection of waste disposal fields

2018 ◽  
Vol 30 ◽  
pp. 103-122
Author(s):  
Maretta Kazaryan ◽  
Mikhail Shahramanian ◽  
Svetoslav Zabunov
Keyword(s):  
Remote Sensing ◽  
Waste Disposal ◽  
Wavelet Transforms ◽  
Experimental Studies ◽  
Haar Wavelet ◽  
Wavelet Expansion ◽  
Two Dimensional ◽  
Space Images ◽  
The Earth ◽  
Wavelet Transformations

In this paper, we study the use of orthogonal transformations, namely, the basic Haar wavelet transforms, for data processing of the Earth remote sensing. The internal structure of orthogonal Haar transforms is considered. The Haar matrix is divided into blocks of the same type, so that parallelization of the computations is possible. The expediency of replacing the spectral components corresponding to the whole block (or several blocks) of the original matrix with zeros is asserted. Theoretical and experimental studies are carried out to improve the results of image classification (on the example of cluster analysis). The Haar wavelet expansion coefficients are used as indicators when decoding space images for the presence of waste disposal sites. The aim of this paper is to describe the approach, on the basis of which an optimal method is established on a class of vectors with real components, application of two-dimensional discrete Haar wavelet transformations in the problem of recognition of space images for the presence of waste disposal sites. General methodology of research. The paper uses elements of mathematical analysis, wavelet analysis, the theory of discrete orthogonal transformations, and methods for decoding cosmic images. Scientific novelty. Encoding by means of conversion is an indirect method, especially effective in processing of two-dimensional signals, in particular, space images used for remote sensing of the Earth. We propose the approach that takes into account the structure of the wavelet-Haar matrix, while recognizing waste disposal fields by means of space images. The article comprises the result of the experimental application of wavelet-Haar transformations for decoding of space images. We consider this case, both with and without the technique of taking into account the structure of the wavelet-Haar matrices.

Optical Haar Wavelet Transforms with Liquid Crystal Elements

1995 ◽  
Vol 34 (Part 1, No. 12A) ◽  
pp. 6433-6438 ◽  
Author(s):  
Zhan He ◽  
Michinori Honma ◽  
Shin Masuda ◽  
ToshiakiNose ◽  
Susumu Sato
Keyword(s):  
Liquid Crystal ◽  
Wavelet Transforms ◽  
Haar Wavelet

STUDY ON RELATIONSHIP BETWEEN CONDENSED PARTICLES AND STRUCTURE OF CONDENSATION JET USING 2D IMAGE AND DISCRETE WAVELETS MULTIRESOLUTION

2006 ◽  
Vol 04 (02) ◽  
pp. 227-238
Author(s):  
MOTOAKI KIMURA ◽  
MASAHIRO TAKEI ◽  
YOSHIFURU SAITO ◽  
KIYOSHI HORII
Keyword(s):  
Wavelet Transforms ◽  
Large Scale ◽  
Particle Density ◽  
Small Scale ◽  
Discrete Wavelet ◽  
Discrete Wavelet Transforms ◽  
Two Dimensional ◽  
Condensation Zone ◽  
Two Dimensional Image ◽  
Discrete Wavelets

This paper describes the application of discrete wavelet transforms to the analysis of condensation jets in order to clarify the associated fluid and heat transfer phenomena. An experimentally-obtained, two-dimensional image of the condensation particle density around the jet was decomposed into 7 levels of resolution with their respective wavelengths. Based on the known physical characteristics of turbulent flow around the jet, levels 0 and 1 were shown to represent the large-scale components of the condensation particle density and the higher levels represent the small-scale components. From the wavelet-analyzed images, the width of the condensation zone was obtained and this compared well with the width inferred from temperature measurements. Thus, the method was verified and also provided data not available experimentally.

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