Optimizing hopfield neural network for super-resolution mapping

Remote sensing is a potential source of information of land covers on the surface of the Earth. Different types of remote sensing images offer different spatial resolution quality. High resolution images contain rich information, but they are expensive, while low resolution image are less detail but they are cheap. Super-resolution mapping (SRM) technique is used to enhance the spatial resolution of the low resolution image in order to produce land cover mapping with high accuracy. The mapping technique is crucial to differentiate land cover classes. Hopfield neural network (HNN) is a popular approach in SRM. Currently, numerical implementation of HNN uses ordinary differential equation (ODE) calculated with traditional Euler method. Although producing satisfactory accuracy, Euler method is considered slow especially when dealing with large data like remote sensing image. Therefore, in this paper several advanced numerical methods are applied to the formulation of the ODE in SRM in order to speed up the iterative procedure of SRM. These methods are an improved Euler, Runge-Kutta, and Adams-Moulton. Four classes of land covers such as vegetation, water bodies, roads, and buildings are used in this work. Results of traditional Euler produces mapping accuracy of 85.18% computed in 1000 iterations within 220-1020 seconds. Improved Euler method produces accuracy of 86.63% computed in a range of 60-620 iterations within 20-500 seconds. Runge-Kutta method produces accuracy of 86.63% computed in a range of 70-600 iterations within 20-400 seconds. Adams-Moulton method produces accuracy of 86.64% in a range of 40-320 iterations within 10-150 seconds