Linear　representation　models　are　effective　to　represent　the　correlation　in　image　interpolation.　However,　linear　models　usually　lack　constraints　of　the　representation　coefficient.　In　this　paper,　we　propose　a　low　rank　matrix　recovery　based　image　interpolation　to　reinforce　the　sparsity　of　representation　coefficient　implicitly.　Since　both　the　local　and　nonlocal　correlation　is　pervasive　in　natural　images,　we　exploit　such　correlations　by　incorporating　the　local　and　nonlocal　modeling,　which　fully　utilizes　the　redundancy　in　images　and　improves　the　representation　ability　of　our　model.　By　minimizing　the　sum　of　the　rank　of　data　matrices　which　reflect　the　linear　relationship　among　local　patch　pixels　and　nonlocal　similar　patch　pixels,　a　precise　low　rank　approximation　of　the　missing　pixels　is　obtained　according　to　the　low　rank　matrix　recovery　theory.　A　Split　Bregman　based　minimization　algorithm　is　developed　to　efficiently　solve　the　low　rank　recovery　problem.　Extensive　experimental　results　indicate　the　proposed　method　outperforms　the　traditional　methods　in　both　the　objective　and　subjective　visual　quality.