An hybrid method for image decomposition problem

We use an hybrid approach based on a genetic algorithm and on the gradient descent method for image decomposition problem. We adopt an iterative gradient descent method, already used in a previous paper and here improved, in order to reconstruct an image by using an optimization task based on the minimization of a cost function. By normalizing the values of its pixels with respect to the grey scale used, an image R is interpreted as a fuzzy relation. In order to obtain better results in terms of quality of the reconstructed image, we use a pre-processing genetic algorithm for determining two initial families of fuzzy sets that compose R in accordance to the concept of Schein rank of R. The experiments are executed on some images extracted from the SIDBA standard image database.