Haar Wavelet Expansions of Signals and their Applications in Image Processing

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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2017
Authors:
Shyam Lal, K. K. Shukla, Sarika Keshri
10.5120/ijca2017915317

Shyam Lal, K K Shukla and Sarika Keshri. Haar Wavelet Expansions of Signals and their Applications in Image Processing. International Journal of Computer Applications 173(9):1-23, September 2017. BibTeX

@article{10.5120/ijca2017915317,
	author = {Shyam Lal and K. K. Shukla and Sarika Keshri},
	title = {Haar Wavelet Expansions of Signals and their Applications in Image Processing},
	journal = {International Journal of Computer Applications},
	issue_date = {September 2017},
	volume = {173},
	number = {9},
	month = {Sep},
	year = {2017},
	issn = {0975-8887},
	pages = {1-23},
	numpages = {23},
	url = {http://www.ijcaonline.org/archives/volume173/number9/28360-2017915317},
	doi = {10.5120/ijca2017915317},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}
}

Abstract

In this paper, double wavelet series of a signal f of two variables t1 and t2 using Haar Scaling function Φ(t1, t2) = φ(t1)φ(t2) and Haar Wavelet function Ψ(t1, t2) = ψ(t1) ψ(t2) has been introduced and it has been verified by a number of examples. Several properties of this signal and it’s image have been studied.The significient result of this paper are the decomposition and reconstruction of signals of a single variable t1 and signals of two variables t1and t2 using Haar Scaling signal as well as Haar Wavelets.

References

  1. Haar A., Zurtheorie der orthogonalen funktionen systeme, Math. Ann., Vol. 69, pp. 331-371, 1910.
  2. Tichmarsh.,E.C., The Theory of Functions, Second Edition, Oxford University Press, (1939).

Keywords

Haar Wavelet, Signal Processing, Image Processing, Double Wavelet Series, Signals of Lip Class