To　solve　the　unstable　generic　image　reconstruction　problem,　an　improved　image　super　resolution　algorithm　was　presented　for　exploiting　the　properties　of　sparse　representation　and　matrix　completion.　Over-complete　dictionary　pair　was　established　by　training　natural　images.　According　to　the　local　prior　constraints,　sparse　coefficients　of　each　low　resolution　image　patches　would　be　estimated.　In　multi-frame　images,　the　sparse　coefficients　of　each　frame　were　similar.　Therefore,　the　inexact　augmented　Lagrange　multiplier　method　was　adopted　to　achieve　matrix　completion　and　recovery　in　the　process　of　recurring　global　constraints.　The　final　high　resolution　image　would　be　generated　from　output　low-rank　matrix.　Results　show　that　the　methods　are　effective　in　retaining　the　image　edges　and　details,　and　it　is　of　robustness　to　the　scope　of　dictionary　with　higher　PSNR　value.　This　algorithm　can　be　applied　in　remote　sensing　image　super-resolution　reconstruction　areas.