A novel wavelet based no-search fractal image compression algorithm: How to use the landscape properties

Fractal Image Compression (FIC) problem is a combinatorial optimization problem which has recently become one of the most promising encoding technologies in the generation of compressed images. In order to exploit the information laid in Discrete Wavelet Transform (DWT) coefficients of the images, this paper proposes a novel wavelet based FIC method to both speed up the compression process and retain the quality of the retrieved images. In the proposed algorithm at first the wavelet coefficients of the image are extracted. Then according to the wavelet coefficients of the range blocks the search strategy for each range block is determined. For smooth blocks a no-search algorithm is applied. For the horizontal and vertical edges, if the no-search algorithm does not provide an appropriate result, the wavelet based search algorithm starts its search process. For vertical range blocks, just the vertical domain blocks and for horizontal range blocks, just the horizontal and for orthogonal range blocks just the orthogonal domain blocks are considered for the search process. In order to explain how such an algorithm works, some statistical analysis on the landscape of fractal image compression problem is performed on 8 different pictures with different textures. The proposed algorithm is compared with the GA-based and original version of fractal image compression algorithms and experimental results show improvement both in speed and the quality of the decoded images.