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**Chapter 10**

**Abstract**

*Abdesselam Bassou*

Packet Transform

standard at a bit rate of 0*:*50 *bpp* for a satellite image.

details; this applies the use of image compression process.

parameters, reduction factor, JPEG standard

**1. Introduction**

compression.

**205**

**Keywords:** quincunx wavelet transform, wavelet packet, quality evaluation

Wavelet is defined as a small wave that can be the base of all physical phenomena; which means that a time and/or space variation of a phenomenon is a sum of multiple wavelets. As examples, the wavelet transform was applied on an electrocardiogram (ECG) signal in order to extract the QRS complex [1] (time variation), on a video sequence in order to implement a hidden watermark [2] (time and space variation) and on a 2D image in order to reduce its size (compression) [3, 4] (space variation). In this chapter, one considers the application of the wavelet on 2D image

An image is one of the most important sources of information; it provides a visual comprehension of a phenomenon. The image can take several natures as medical, natural, textural or satellite image, each nature is characterized by a proper amount of details. For a digital image, the size in bytes is as bigger as the amount of

In other words, if one considers a gray-scale image of size 512 � 512, that means a bit rate of 8 bits per pixel (*Rc* ¼ 8 *bpp*) and a file size of 512 � 512 � 8 bits (256 Kbytes). Compressing this image leads to reduce its file size (without changing the

The Discrete Quincunx Wavelet

This chapter aims to present an efficient compression algorithm based on quincunx wavelet packet transform that can be applied on any image of size 128 � 128 or bigger. Therefore, a division process into sub-images of size 128 � 128 was applied on three gray-scale image databases, then pass each sub-image through the wavelet transform and a bit-level encoder, to finally compress the sub-image with respect to a fixed bit rate. The quality of the reconstructed image is evaluated using several parameters at a given bit rate. In order to improve the quality in sense of the evaluation quality, an exhaustive search has led to the best packet decomposition base. Two versions of the proposed compression scheme were performed; the optimal version is able to decrease the effect of block boundary artifacts (caused by the image division process) by 27*:*70% considering a natural image. This optimal version of the compression scheme was compared with JPEG standard using the quality evaluation parameters and visual observation. As a result, the proposed compression scheme presents a competitive performance to JPEG standard; where the proposed scheme performs a peak signal to noise ratio of 0*:*88 *dB* over JPEG

#### **Chapter 10**
