One of the main disadvantages of fractal image data compression is a loss time in the process of image compression (encoding) and conversion into a system of iterated functions (IFS). In this paper, the idea of the inverse problem of fixed point is introduced. This inverse problem is based on collage theorem which is the cornerstone of the mathematical idea of fractal image compression. Then this idea is applied by iterated function system, iterative system functions and grayscale iterated function system down to general transformation. Mathematical formulation form is also provided on the digital image space, which deals with the computer. Next, this process has been revised to reduce the time required for image compression by excluding some parts of the image that have a specific milestone. The neural network algorithms have been applied on the process of compression (encryption). The experimental results are presented and the performance of the proposed algorithm is discussed. Finally, the comparison between filtered ranges method and self-organizing method is introduced.