High-resolution images have always been in urgent need in the fields of surveying, mapping, military and civilian. In this paper, first, based on anisotropic nonlinear diffusion tensor, a diffusion tensor regularization term which can make full use of direction selection smoothing property was constructed. Based on the improved gradient vector field (GVF), a regularization term which can constrain the continuity of gradient vectors for high-resolution and low-resolution images was constructed. On the basis of these, a multi-frame super-resolution reconstruction algorithm based on double regularization terms was proposed and verified by simulation. Second, combining PCA with adaptive dictionary learning, two constraints of reconstruction regularity based on improved nonlocal means and kernel regression were proposed for experimental verification, and an improved K-means clustering algorithm for initial centre selection of spatial characteristic measure clustering was proposed to enhance the stability of the algorithm. Then high-resolution image generated by learning method was used as the initial input of multi-frame reconstruction of optical remote sensing images. The experimental results show that the reconstruction algorithm based on partial differential equation and unsupervised learning achieves both subjective and objective results for the realization of super-resolution reconstruction of optical remote sensing images.
Periodic orbits for double regularization of piecewise smooth systems with a switching manifold of codimension two
