Abstract: The framework for image singularity analysis based on multifractal theory is presented in this paper. The measure is defined which gives the local distribution of the gradient of the image. The exponential formalism between the projection of fast decreasing functions of the defined measure and scale is proved. According to the exponential formalism, the paper also presented an algorithm, in which the nature image can be decomposed in a serial fractal sets with different singularity exponent and fractal dimension. Finally, some basic theoretical results of the choice for the fast decreasing functions are proposed. Also an investigation of how to reconstruct the different fractal image components with derivative information contained in the different fractal sets is made. Experiments show that the multifractal formalism has significance in image singularity analysis and detection.