Blind single-image super resolution based on compressive sensing

• A novel framework is proposed for blind single-image super resolution based on compressive sensing.
• Due to the extremely ill-posed nature of the problem, just a few works have been proposed.
• The proposed method is one of the first works that considers general PSFs.
• The fundamental idea is to use sparsity as regularizer in both the image and blur domains.
• The efficiency of the proposed method is competitive with methods that use multiple LR images.

Blind super resolution is an interesting area in image processing that can restore high resolution (HR) image without requiring prior information of the volatile point spread function (PSF). In this paper, a novel framework is proposed for blind single-image super resolution (SISR) problem based on compressive sensing (CS) framework that is one of the first works that considers general PSFs. The fundamental idea in the proposed approach is to use sparsity on a known sparse transform domain as a powerful regularizer in both the image and blur domains. Therefore, a new cost function with respect to the unknown HR image patch and PSF kernel is presented and minimization is performed based on two subproblems that are modeled similar to that of CS. Simulation results demonstrate the effectiveness of the proposed algorithm that is competitive with methods that use multiple LR images to achieve a single HR image.