**12. References**

Adelson, E. H.; Simoncelli E. & Hingorani, R. (1987). Orthogonal pyramid transforms for image coding, *SPIE Visual Communication and Image Processing II,* Vol. 845, pp. 50-58 Angelopoulou, M. E.; Cheung, P. Y. K ; Masselos, K. & Andreopoulos, Y. (2008).

Implementation and comparison of the 5/3 lifting 2D discrete wavelet transform

algorithms are inherently multi levels, requiring complex computation schedule in hardware, a comparison of different computation schedule algorithms is presented in (Angelopoulou et al., 2008). The most widely used schedule algorithms such as the row column based algorithm (Mallat, 1989), the line based algorithm (Chrysafis & Ortega, 2000) and the block based algorithm (Lafruit et al., 2000) are implemented in FPGA using the lifting scheme and 2D DWT architecture. The 2D DWT FPGA implementation is fully parameterised. Based on the lifting scheme, Lande et al. in (Lande et al., 2010) introduce a robust invisible watermarking method to be used with still images. The scheme is incorporated in the JPEG 2000 lossless algorithm, featuring an integer to integer biorthogonal 5/3 CDF wavelet filters. The proposed algorithm targets the consumer electronics market. The objectives of the proposed FPGA implementation of this wavelet based watermarking scheme include low power usage, real time performance, robustness

Denoising still images and video sequences is another field of predilection of the wavelet transform (see section 9). Katona et al. (Katona et al., 2006) suggest a real time wavelet based video denoising system and its implementation in FPGA. The method adopts a parallel approach to implement an advanced wavelet domain noise filtering algorithm, which uses a non-decimated wavelet transform. The approach relies on the wavelet "a trous" algorithm and the Daubechies minimum phase wavelet (Daub4). The proposed implementation is decentralised and distributed over two FPGAs. As a proof of concept, digitised television

Since the late 80s, the wavelet transform has been widely used in different scientific applications including signal and image processing. This ongoing growing success, which has been characterised by the adoption of some wavelet-based schemes, is due to features inherent to the transform, such as time-scale localisation and multiresolution capabilities. In this chapter, the basic concepts of the wavelet transform have been introduced. First, the historical development of the wavelet transform and its advent to the field of signal and image processing were reviewed. Then, its features and the mathematical foundations behind it were reviewed. To ease the understanding of the wavelet theory, the related notations and terms, such as the scaling function, multiresolution, filter bank and others

Depending on the application at hand, different algorithms for implementing the wavelet transform have been developed. Four of these algorithms, namely, Burt's pyramid, Mallat algorithm, Feauveau's scheme and the lifting scheme were briefly described. Finally, some

Adelson, E. H.; Simoncelli E. & Hingorani, R. (1987). Orthogonal pyramid transforms for

Angelopoulou, M. E.; Cheung, P. Y. K ; Masselos, K. & Andreopoulos, Y. (2008).

image coding, *SPIE Visual Communication and Image Processing II,* Vol. 845, pp. 50-58

Implementation and comparison of the 5/3 lifting 2D discrete wavelet transform

and ease of integration.

**11. Conclusion** 

**12. References** 

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**18** 

*UK* 

**Wavelet Based** 

*1Staffordshire University,* 

*2Glasgow Caledonian University* 

**Image Compression Techniques** 

Pooneh Bagheri Zadeh1, Akbar Sheikh Akbari2 and Tom Buggy2

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;

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

**1. Introduction**

Shapiro, 1993).

investigated in this chapter.

