Application of Haar Wavelets on Medical Images

Application of Haar Wavelets on Medical Images

R. El Ayachi (Faculty of Science and Technology, Université Sultan Moulay Slimane, Beni Mellal, Morocco), M. Gouskir (Faculty of Science and Technology, Université Sultan Moulay Slimane, Beni Mellal, Morocco) and M. Baslam (Faculty of Science and Technology, Université Sultan Moulay Slimane, Beni Mellal, Morocco)
Copyright: © 2015 |Pages: 9
DOI: 10.4018/JECO.2015040104

Abstract

Recently, the information processing approaches are increased. These methods can be used for several purposes: compressing, restoring, and information encoding. The raw data are less presented and are gradually replaced by others formats in terms of space or speed of access. This paper is interested in compression, precisely, the image compression using the Haar wavelets. The latter allows the application of compression at several levels. The subject is to analyze the compression levels to find the optimal level. This study is conducted on medical images.
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2. Principle Of Haar Wavelets

In 1909, ALFRED HAAR was created a special function called « Haar wavelets » (Figure 1) (Myung-Sin Song, 1991, Ronald A. DeVore & all, 1992, Kamrul Hasan Talukder & all, 2007). This type of waveletallows a decomposition of data. Specifically, in image processing, it is used for compressing.

Figure 1.

Haar wavelet

JECO.2015040104.f01

Consider the image M to be compressed. For a compression level h, Haar wavelets divide the compressed imageMh-1 at the level h-1 into four blocks (Figure 2): The left upper block representing the compressed image Mh and the other containing the details ((horizontal DHh, vertical DVh and diagonal DDh).

Figure 2.

Compressing using Haar wavelets

JECO.2015040104.f02

Obtaining the compressed image at level h is based on the compressed image at level h-1.

The compressed image is computedas follows:

JECO.2015040104.m01
(1) where

  • JECO.2015040104.m02: Compressed image for a level h

  • JECO.2015040104.m03:Haar wavelets coefficients for a level h

  • JECO.2015040104.m04: Transposed of JECO.2015040104.m05

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