Local Wavelet Transform-based Fractal Image Compression Algorithm

Fractal Theory is a kind of new theory in image compression. It has been acknowledged and developed well because of its high compression ration and fast decoding. Based on fractal theory and wavelet transform, the paper proposes a new fractal coding algorithm based on wavelet transform, which differs from the traditional method of fractal coding in the wavelet domain. The experiments show the algorithm assures image quality, makes the coding speed faster and improves compression ration.The paper discusses the principle of image compression and mathematics base of fractal image coding. And the paper analyses important fractal image compression method, which is proposed earliest by Jacquin. The impossibility and advantage of mergence of the two methods is discussed based on the analysis of wavelet image compression and fractal image compression.The paper puts forward a new fractal coding algorithm based on local wavelet which has been named as LWFC algorithm. It differs from the traditional method of fractal coding in the wavelet domain. The algorithm introduces part wavelet transformation on the basis of Jacquin's fractal coding algorithm and replaces the original image with its low-frequency image to compute the matching process between domain blocks and range blocks, which speeds the searching process between the range block and its matching domain block and quickens the process of encoding. Neighborhood search method is adapted which limits matching domain blocks in part of low-frequency domain bases and reduces compute times greatly. In addition, the coding time has been shorted because four kinds of affine transform replace original eight kinds. In the end, new Huffman algorithm realizes lossless compression of fractal codes which brings satisfied compression ration.In a word, the LWFC is proved an effective image coding algorithm from the results of the experiments.