Simultaneous Methods of Image Registration and Super-Resolution Using Analytical Combinational Jacobian Matrix
: Image Processing
(Islamic Azad University, Torbat-e-Heydariyeh Branch)
(Ferdowsi University of Mashhad)
Combinational coefficient matrix,
In this paper we propose two new simultaneous image registration (IR) and super-resolution (SR) methods using a novel approach to calculate the Jacobian matrix. SR is the process of fusing several low resolution (LR) images to reconstruct a high resolution (HR) image; however as inverse problem it consists of three principal operations of warping, blurring and down-sampling should be applied to the desired HR image to produce the existing LR images. Unlike the previous methods, we neither calculate the Jacobian matrix numerically nor derive the Jacobian matrix by treating the three principal operations separately. We develop a new approach to derive the Jacobian matrix analytically from combinational form of the three principal operations. In this approach, a Gaussian kernel (as it is more realistic in a wide rang 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 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 high resolution image at each iteration. The results show that our methods are superior to the recently proposed methods such as Tian's joint and Hardie's AM method. Additionally, the computational cost of our proposed methods has also been reduced.