Super-resolved　reconstruction　of　images　can　yield　poor　results　in　the　absence　of　extensively-trained　dictionaries.　A　superresolution　algorithm　is　presented　which　remedies　this　problem　by　exploiting　recent　results　from　the　work　on　sparse　representation　and　matrix　completion.　An　over-complete　dictionary　pair　is　trained　using　natural　image　data.　Sparse　coefficients　of　low-resolution　image　patches　are　estimated　using　local　prior　constraints.　In　multi-frame　images,　sparse　coefficients　are　similar　across　frames,　and　the　Inexact　Augmented　Lagrange　Multiplier　method　is　employed　to　achieve　matrix　completion　and　recovery　in　the　process　of　imposing　global　constraints.　The　final　high-resolution　image　is　generated　from　the　output　low-rank　matrix.　Experiments　reveal　that　the　method　yields　higher　PSNR　value　than　other　mainstream　SR　algorithms,　produces　perceptibly　superior　edges　and　details,　and　is　more　robust　to　dictionary　insufficiency.　©　2013　IEEE.