Image super-resolution reconstruction via L1/2 and S1/2 regularizations

Compressed sensing (CS) theory has attracted much attention in the field of signal and image processing. In this paper, the ideas and methods of the image super-resolution (SR) reconstruction combined with CS is studied. The challenge is how to reconstruct a SR image when only one low-resolution (LR) image is available. Regularization methods are the important image SR techniques. Recently, the transform-invariant directional total variation approach with transform-invariant low-rank textures based on Schatten(p=1) and L-1-norm penalties (TI-DTV+ TILT1) has capability of achieving high-quality SR at up-sampling factors. In this paper, we investigate a novel TI-DTV model with TILT based on Schatten(p=1/2) (S-1/2-norm) and L-1/2-norm penalties (TILT1/2). Moreover, inspired by the alternating direction method of multipliers (ADMM), we propose the alternating threshold iterative algorithm for the new model. Numerous experiments show the proposed method can identity more important information of image, make edges align mostly horizontally and vertically following the low-rank structure and decrease the jagged artifacts along the diagonal line and arcs of high quality SR.