Abstract. Limitations in imaging systems and the effects of changes in sensing have caused limitation in acquiring high resolution images such as satellite images and magnetic resonance imaging (MRI). Sparsity can reduce the noises and improve the resolution. Super resolution in medical and satellite imagery is essential because low resolution image analysis is very difficult. Sparsity techniques have significant influence on computer vision specially when the main objective is extracting the meaningful information. The success of sparsity is related to the nature of signals such as image and sound which are naturally sparse because they were founded based on Wavelet and Fourier equations. In this research, we proposed a method for restoring a clear image from the related low-resolution parts of both MRI and satellite images. First, we proposed a widespread structure for learning the couple low rank and sparse main characteristic representation. Combined optimization of the nuclear and L1 norms extracts the total low rank formation and the local patterns lodged in the image. In that case the reconstructed image will be more informative and matrix decomposition problem can recover a noisy observation matrix into an approximation of low rank matrix and a second matrix which contains some low dimensional structure. We assumed that by removing the blur and noise from these images, they would be reconstructed in the highest quality. The proposed method was compared with a variety dictionary learning approaches which addressed super resolution problem, such as tensor sparsity, Generative Bayesian and TV based methods. We demonstrated the results of applied method on MRI and satellite images, showing both visual and psnr improvements. Dealing with complex data in best manner shows the robustness of the proposed method.