Simultaneous Methods of Image Registration and Super-Resolution Using Analytical Combinational Jacobian Matrix

In this paper we propose two simultaneous image registration (IR) and super-resolution (SR) methods using a novel approach in calculating the Jacobian matrix. SR is the process of fusing several low resolution (LR) images to reconstruct a high resolution (HR) image; however, as an inverse problem, it consists of three principal operations of warping, blurring and down-sampling that should be applied sequentially to the desired HR image to produce the existing LR images. Unlike the previous methods, we neither calculate the Jacobian matrix numerically nor derive it by treating the three principal operations separately. We develop a new approach to derive the Jacobian matrix analytically from the combination of the three principal operations. In this approach, a Gaussian kernel (as it is more realistic in a wide range of applications) is considered for blurring, which can be adaptively resized for each LR image. The main intended method is established by applying the aforementioned ideas to the joint methods, a class of simultaneous iterative methods in which the incremental values for both registration parameters and HR image are obtained by solving one linear system of equations per iteration. Our second proposed method is formed by applying these ideas to the alternating minimization (AM) methods, a class of simultaneous iterative methods in which the incremental values of registration parameters are obtained after calculating the HR image at each iteration. The results show that our proposed joint and AM methods are superior to the recently proposed methods such as Tianʹs joint and Hardieʹs AM methods respectively.