This paper presents an existent and constructive proof of image fractal compression mappings and application in fractal image coding. In addition

based on the procedure of the existent and constructive proof of image fractal compression mappings

a new fractal image coding algorithm is presented. Some beneficial theory about these constructive fractal mappings are also discussed. The theoretical result shows that the theory is feasible. The experimental results prove that the new algorithm can improve reconstructing image while reducing encoding time.