The objective of this work is image super-resolution (SR), where the input is specified by a low-resolution image and a consistent higher-resolution image should be returned. We propose a post-processing procedure named iterative fine-tuning and approximation (IFA) for mainstream SR methods. Internal image statistics are complemented by iteratively fine-tuning and performing linear subspace approximation on the outputs of existing external SR methods, helping to better reconstruct missing details and reduce unwanted artifacts. The primary concept of our method is that it first explores and enhances internal image information by grouping similar image patches and then finds their sparse representations by iteratively learning the bases, thereby enhancing the primary structures and some details of the image. Experiment results demonstrate that the proposed IFA can yield substantial improvements for most existing methods via tweaking their outputs, achieving state-of-the-art performance.