In fractral decoding procedure, the reconstructed image is obtained by iteratively applying the contractive transform to an arbitrary initial image. But this method is not suitable for the fast decoding because convergence speed depends on the selection of initial image. Therefore, the initial image to achieve fast decoding should be selected. In this paper, we propose an initial image estimation that can be applied to various decoding methods. The initial image similar to the original image is estimated by using only the compressed data so that the proposed method does not affect the compression ratio. From the simulation, the PSNR of the proposed initial image is 6dB higher han that of ones iterated output image of conventional decoding with Babaraimage. Computations in addition and multiplication are reduced about 96%. On the other hands, if we apply the proposed initial image to other decoding algorithms, the faster convergence speed is expected.