We present a resolution-invariant image representation (RIIR) framework in this paper. The RIIR framework includes the methods of building a set of multi-resolution bases from training images, estimating the optimal sparse resolution-invariant representation of any image, and reconstructing the missing patches of any resolution level. As the proposed RIIR framework has many potential resolution enhancement applications, we discuss three novel image magnification applications in this paper. In the first application, we apply the RIIR framework to perform Multi-Scale Image Magnification where we also introduced a training strategy to built a compact RIIR set. In the second application, the RIIR framework is extended to conduct Continuous Image Scaling where a new base at any resolution level can be generated using existing RIIR set on the fly. In the third application, we further apply the RIIR framework onto Content-Base Automatic Zooming applications. The experimental results show that in all these applications, our RIIR based method outperforms existing methods in various aspects.