Total variable-order variation as a regularizer applied on multi-frame image super-resolution

Multi-frame image super-resolution reconstruction focuses on obtaining a high-resolution (HR) image from a low-resolution image. Since the super-resolution problem is ill-posed, it is frequent to use regularization techniques. However, the choice of these regularization terms is not always direct. Generally, every term should contain some prior knowledge over the image, that is why it plays an important role in increasing the quality of the restored HR image. In this paper, we propose a total variable-order variation based-regularization to provide a natural-looking and an effective reconstruction of the desired HR image. We also present some existence and uniqueness results of our proposed model. The alternating direction method of multipliers algorithm is employed to implement the numerical simulations. Experimental results reveal that the proposed approach can reconstruct and recover high-quality results visually and quantitatively.