Image Super-Resolution via Adaptive Regularization Term of Compressed Sensing

Compressed sensing theory is widely used to accurately reconstruct the original signal from a small number of random observations, i.e., obtain high-dimensional information from low-dimensional information. This feature has shown effectiveness in image super-resolution. In this paper, based on the compressed sensing theory, the ARSR (Adaptive Regularization term Super Resolution) algorithm is proposed to achieve super-resolution reconstruction of images. The algorithm models on the basis of exploiting the image local sparsity prior. On the one hand, by using adaptive regularization coefficients to weight the elements in the norm, we obtain more accurate sparse representation coefficients. On the other hand, we also add an adaptive regularization term behind the optimization model, which is able to take the correlation of the image into account as well. By generating a suitable coefficient, it can adaptively reconcile the relationship between sparsity and correlation. In addition, we derived an approximation to solve the model iteratively using the alternating direction method of multipliers (ADMM). In this paper, the sparse transform domain is trained by the K-SVD algorithm and the accuracy evaluation indexes of the experiments use peak signal-to-noise ratio (PSNR) and structural similarity (SSIM). Compared with existing classical sparse representation-based image super-resolution algorithms, our ARSR algorithm obtains the highest PSNR and SSIM values in different regions of the image with better subjective visual effects.