Genetic algorithm based on discrete wavelet transformation for fractal image compression

• The DWT method can save seven eighths MSE computations.
• Two DWT coefficients have the information of edge and brightness variation.
• Two DWT coefficients are used to find the optimal Dihedral transformation.
• We embed the DWT into the GA to speedup the fractal encoder further.
• The shorter chromosome is obtained to speedup the GA evolution.

In this paper, a genetic algorithm (GA) based on discrete wavelet transformation (DWT) is proposed to overcome the drawback of the time-consuming for the fractal encoder. First, for each range block, two wavelet coefficients are used to find the fittest Dihedral block of the domain block. The similar match is done only with the fittest block to save seven eighths redundant MSE computations. Second, embedding the DWT into the GA, a GA based on DWT is built to fast evolutionary speed further and maintain good retrieved quality. Experiments show that, under the same number of MSE computations, the PSNR of the proposed GA method is reduced 0.29 to 0.47 dB in comparison with the SGA method. Moreover, at the encoding time, the proposed GA method is 100 times faster than the full search method, while the penalty of retrieved image quality is relatively acceptable.