In super resolution (SR) technique, as an inverse problem, generative model forms low resolution (LR) images from a high resolution (HR) 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 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 (IR) 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.

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