A Hopfield-type neural network used for remote sensing images with variational principle

In remote sensing image processing, image approximation, or to obtain a high-resolution image equivalently from a corresponding low-resolution image is an ill-posed inverse problem. In this paper, with the consideration of the constraints on smoothness and discontinuity, the regularization method is used to convert the image approximation problem into a solvable variational problem. Furthermore, a Hopfield-type dynamic neural network is proposed to solve the variational problem. This neural network possesses two kinds of states describing the discrepancy of a pixel with adjacent pixels and the intensity evolution of a pixel and two kinds of corresponding weights. The experimental results obtained in this study under free noise added Landsat TM image and noisy image cases show that the proposed approach is better than those by the three previous ones used for comparison indicating its feasibility.