A nonconvex fractional order variational model for multi-frame image super-resolution

The multi-frame super-resolution(SR) aims to recover a high-resolution (HR) image from a degraded low-resolution (LR) sequence. Since the SR problem is considered as an ill-posed one, the regularization techniques are then inevitable. However, the choice of the fidelity and regularization terms is not easy and plays a major role in the quality of the desired HR image. In this paper, we propose a new nonconvex data fitting term and a fractional total variation regularization term for image super-resolution. The proposed model differs from existing image variational SR models where the fidelity term is always derived from the L1 or L2- norm, and the regularization term is based on a widely choice of convex and nonconvex functions. The use of the nonconvex data fitting term can efficiently reduce complex noises such as impulse noise while the fractional order regularization term preserves image features like edges and texture much better. Numerical experiments show that the proposed model can produce competitive results, visually and quantitatively, compared to some available variational SR models.