International Journal of Computer Engineering Science (IJCES) Volume 2 Issue 5 (May 2012) ISSN : 2250:3439 https://sites.google.com/site/ijcesjournal http://www.ijces.com/ 28 Encoding Time Reduction method for the Wavelet based Fractal Image Compression Jyoti Bhola 1 , Simarpreet Kaur 2 1 Department of Electonics Engg., Shoolini University Solan 1 jyoti1may@gma il.com 2 Department of Electonics Engg., B.B.S.B. Engg. College Fatehgarh simarpreet.kaur@bbsbec.ac.in Abstract —In this paper we show the two implementations of fractal (Pure- fractal and Wavelet fractal image compression algorithms) which have been applied on the images in order to investigate the compression ratio and corresponding quality of the images using peak signal to noise ratio (PSNR). And in this paper we also set the threshold value for reducing the redundancy of domain blocks and range blocks, and then to search and match. By this, we can largely reduce the computing time. In this paper we also try to achieve the best threshold value at which we can achieve optimum encoding time. Keywords : Fractal image coding; Wavelet; Iterated Function System; Wavelet; Mean Square Error; Compression Ratio. 1 Introduction In 1988 M. Barnsley and Jacquin introduced the FRACTAL image compression techniques are the product of the study of iterated function systems (IFS). For recent years, the application of fractal image coding has become more and more popular. These techniques involve an approach to compression quite different from standard transform coder-based methods. Transform coders model images in a very simple fashion, namely, as vectors drawn from a wide-sense stationary random process. They store images as quantized transform coefficients. Fractal block coders, as described by Jacquin, assume that “image redundancy can be ef ficiently exploited through self- transformability on a blockwise basis” [1]. They store images as contraction maps of which the images are approximate fixed points. Images are decoded by iterating these maps to their fixed points. Fractal coding is based on fractal geometry, it has a character of big compression ratio and a fast decoding speed, but it cannot be used for real time processing. It is its blocks searching and matching that makes its long time. As wavelet can get good space frequency multi resolution, the energy mainly concentrated in low frequency sub images, and the images with same directions but different resolutions have self similarity, which is consistent with fractal’s nature properties. The combination of wavelet and fractal is firstly proposed by Pentland and Horowitz. They wanted to find the redundancy of sub images decomposed after wavelet. Later, Rinaldo and Calvagno proposed a new method. First, decompose a image by wavelet, and then code the sub image with minimum resolution, and predict the other sub images.