Single image super-resolution using combined total variation regularization by split Bregman Iteration

• We propose a new regularization item called steering kernel regression total variation (SKRTV).
• A MAP super-resolution framework is presented to assemble the global reconstruction constraint, SKRTV and NLTV terms.
• We solve our model using split Bregman iterations.

This paper addresses the problem of generating a high-resolution (HR) image from a single degraded low-resolution (LR) input image without any external training set. Due to the ill-posed nature of this problem, it is necessary to find an effective prior knowledge to make it well-posed. For this purpose, we propose a novel super-resolution (SR) method based on combined total variation regularization. In the first place, we propose a new regularization term called steering kernel regression total variation (SKRTV), which exploits the local structural regularity properties in natural images. In the second place, another regularization term called non-local total variation (NLTV) is employed as a complementary term in our method, which makes the most of the redundancy of similar patches in natural images. By combining the two complementary regularization terms, we propose a maximum a posteriori probability framework of SR reconstruction. Furthermore, split Bregman iteration is applied to implement the proposed model. Extensive experiments demonstrate the effectiveness of the proposed method.