A Joint Image Registration and Superresolution Method Using a Combinational Continuous Generative Model

In the superresolution (SR) technique, as an inverse problem, the generative model forms low-resolution images from a high-resolution image. This process consists of three principal operations, namely, warping, blurring, and down-sampling. Unlike the traditional SR methods in which a discrete generative model is used, in this paper, a continuous generative model has been proposed for the SR technique. Rather than using a bilinear interpolation for warping operation, we use a Gaussian kernel for interpolation, as it has lower aliasing effect. Within the framework of the proposed continuous generative model, the three principal operations are combined into a unified operation and hence performed simultaneously. According to this combinational operation, a simultaneous image registration and SR method is proposed. Unlike previous simultaneous methods, we neither calculate the Jacobian matrix numerically (to increase the accuracy of calculation) nor derive it treating the three principal operations separately (to reduce the error propagation). We develop a new approach to derive the Jacobian matrix analytically by combining the three principal operations. The results show that our proposed method is more efficient than the recently proposed simultaneous methods.