**1. Introduction**

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With advances in multimedia technologies, demand for transmission and storage of voluminous multimedia data has dramatically increased and, as a consequence, data compression is now essential in reducing the amount of data prior storage or transmission. Compression techniques aim to minimise the number of bits required to represent image data while maintaining an acceptable visual quality. Image compression is achieved by exploiting the spatial and perceptual redundancies present in image data. Image compression techniques are classified into two categories, lossless and lossy. Lossless techniques refer to those that allow recovery of the original input data from its compressed representation without any loss of information, i.e. after decoding, an identical copy of the original data can be restored. Lossy techniques offer higher compression ratios but it is impossible to recover the original data from its compressed data, as some of the input information is lost during the lossy compression. These techniques are designed to minimise the amount of distortion introduced into the image data at certain compression ratios. Compression is usually achieved by transforming the image data into another domain, e.g. frequency or wavelet domains, and then quantizing and losslessy encoding the transformed coefficients (Ghanbari, 1999; Peng & Kieffer, 2004; Wang et al., 2001). In recent years much research has been undertaken to develop efficient image compression techniques. This research has led to the development of two standard image compression techniques called: JPEG and JPEG2000 (JPEG, 1994; JPEG 2000, 2000), and many nonstandard image compression algorithms (Said & Pearlman, 1996; Scargall & Dlay, 2000; Shapiro, 1993).

Statistical parameters of image data have been used in a number of image compression techniques (Chang & Chen, 1993; Lu et al., 2000; Lu et al., 2002; Saryazdi and Jafari, 2002). These techniques offer promising visual quality at low bit rates. However, the application of statistical parameters of the transformed data in image compression techniques has been less reported in the literature. Therefore, the statistical parameters of the transformed image data and their application in developing novel compression algorithms are further investigated in this chapter.

Wavelet Based Image Compression Techniques 425

Differential Pulse code Modulation (DPCM)

Vector Quantization (VQ)

Zero-Tree Coding

Neural Networks Trellis Coding

Fractal

Fig. 1. The CSF curves for the luminance and chrominance channels of the HVS (Nadenau et

Due to the complexity of the human visual processing system, assessments of the performance of HVS-models are based on psychophysical observations. Physiologists have performed many psycho-visual experiments with the goal of understanding how the HVS works. One of the limitations of the HVS, which was found experimentally, is the lower sensitivity of the HVS for patterns with high spatial-frequencies. Exploiting this property of the HVS model, and embedding it into compression algorithms, can significantly improve the visual quality of compressed images. Natural images are composed of small details and

Standard image coding techniques Non standard image coding techniques

Table 1. Standard and non-standard image compression techniques.

DCT-base Wavelet-base

JPEG (1980) JPEG2000 (2000)

al., 2003).

The performance of image compression techniques can also be significantly improved by embedding the properties of the Human Visual System (HVS) in their compression algorithms (Bradley, 1999; Nadenau et al., 2003). Due to the space–frequency localization properties of wavelet transforms, wavelet based image codecs are most suitable for embedding the HVS model in their coding algorithm (Bradley, 1999). The HVS model can be embedded either in the quantization stage (Aili et al., 2006; HSontsch & Karam, 2000; Nadenau et al., 2003), or at the bit allocation stage (Antonini et al., 1992; Sheikh Akbari & Soraghan, 2003; Thornton et al., 2002; Voukelatos & Soraghan, 1997) of the wavelet based encoders. In this chapter, HVS coefficients for wavelet high frequency subbands are calculated and their application in improving the coding performance of the statistical encoder is investigated.
