This letter proposes a reconstruction-based single image super resolution (SR) method by using joint regularization, where a group-residual-based regularization (GRR) and a ridge-regression-based regularization (3R) are combined. In GRR, non-local similar patches are grouped together, and the group weights are calculated so as to adaptively constrain the residual values in the gradient domain. In 3R, we adopt the ridge-regression-based method to establish the projection matrices from an external high-resolution (HR) training set, so that the external HR information can be utilized. To obtain an estimation of the targeted HR image, an efficient algorithm is designed for solving the joint formulation. Experimental results on different image datasets indicate that the proposed method is able to achieve the state-of-the-art performance.<\/strong><\/p>\n\n\n\n Index Terms\u2014Super Resolution, Non-local Self-similarity, Total Variation, Ridge Regression, Regularization.<\/strong><\/p>\n\n\n\nSource Code<\/h3>\n\n\n\n