A variational approach to intensity approximation for remote sensing images using dynamic neural networks

In remote sensing image processing, image approximation, or obtaining a high‐resolution image from a corresponding low‐resolution image, is an ill‐posed inverse problem. In this paper, the regularization method is used to convert the image approximation problem into a solvable variational problem. In regularization, the constraints on smoothness and discontinuity are considered, and the original ill‐posed problem is thereby converted to a well‐posed optimization problem. In order to solve the variational problem, a Hopfield‐type dynamic neural network is developed. This neural network possesses two states that describe the discrepancy between a pixel and adjacent pixels, the intensity evolution of a pixel and two kinds of corresponding weights. Based on the experiment in this study with a Landsat TM image free of added noise and a noisy image, the proposed approach provides better results than other methods. The comparison shows the feasibility of the proposed approach.