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.

I. Introduction

Superresolution (SR) is the process of creating a high-resolution (HR) and quality image from single or several low-resolution (LR) images. The methods that use single LR image are known as single-image SR methods. In some of these methods, high-frequency information corresponding to the patches of the LR image is derived from an existing HR image [1], while in others, natural structure of image (e.g., edges [2]) or a prior is used to create an enhanced HR image. The methods that use several LR images are known as multiframe SR methods. In these methods, a sequence of LR images is fused to create an HR image with more detail than each of LR images. This paper is devoted to the multiframe SR techniques. A variety of such SR techniques have been proposed in the literature, including [3]–[5].