Integrating a scale-invariant feature of fractal geometry into the Hopfield neural network for super-resolution mapping

Super-resolution mapping (SRM) is a potential technique to improve image pattern recognition by predicting the spatial distribution of class composition at a sub-pixel scale. A number of SRM techniques have been reported in the past two decades. Most of the techniques are based on the assumption of spatial dependence. In this paper, a scale-invariant concept of fractal geometry is taking into account in the original Hopfield neural network (HNN) algorithm and a self-similar Hopfield neural network (SSHNN) is proposed which based on both spatial dependence and self-similarity in the fractal geometry. Both synthetic and real satellite images are used to test the performance of the SSHNN. The results show that by taking self-similarity into consideration, with a single image and no other additional data needed, the mapping accuracy of the SSHNN increases by up to 20% compared to the HNN.