This paper proposes a robust single-image super-resolution method for enlarging low quality web image/video degraded by downsampling and compression. To simultaneously improve the resolution and perceptual quality of such web image/video, we bring forward a practical solution which combines adaptive regularization and learning-based super-resolution. The contribution of this work is twofold. First, we propose to analyze the image energy change characteristics during the iterative regularization process, i.e., the energy change ratio between primitive (e.g., edges, ridges and corners) and nonprimitive fields. Based on the revealed convergence property of the energy change ratio, appropriate regularization strength can then be determined to well balance compression artifacts removal and primitive components preservation. Second, we verify that this adaptive regularization can steadily and greatly improve the pair matching accuracy in learning-based super-resolution. Consequently, their combination effectively eliminates the quantization noise and meanwhile faithfully compensates the missing high-frequency details, yielding robust super-resolution performance in the compression scenario. Experimental results demonstrate that our solution produces visually pleasing enlargements for various web images/videos.