A Novel PDE-Based Single Image Super-Resolution Reconstruction Method

For applications such as remote sensing imaging and medical imaging, high-resolution (HR) images are urgently required. Image Super-Resolution (SR) reconstruction has great application prospects in optical imaging. In this paper, we propose a novel unified Partial Differential Equation (PDE)-based method to single image SR reconstruction. Firstly, two directional diffusion terms calculated by Anisotropic Nonlinear Structure Tensor (ANLST) are constructed, combing information of all channels to prevent singular results, making full use of its directional diffusion feature. Secondly, by introducing multiple orientations estimation using high order matrix-valued tensor instead of gradient, orientations can be estimated more precisely for junctions or corners. As a unique descriptor of orientations, mixed orientation parameter (MOP) is separated into two orientations by finding roots of a second-order polynomial in the nonlinear part. Then, we synthesize a Gradient Vector Flow (GVF) shock filter to balance edge enhancement and de-noising process. Experimental results confirm the validity of the method and show that the method enhances image edges, restores corners or junctions, and suppresses noise robustness, which is competitive with the existing methods.