Image　super-resolution　with　sparsity　prior　provides　promising　performance.　However,　traditional　sparse-based　super　resolution　methods　transform　a　two　dimensional　(2D)　image　into　a　one　dimensional　(1D)　vector,　which　ignores　the　intrinsic　2D　structure　as　well　as　spatial　correlation　inherent　in　images.　In　this　paper,　we　propose　the　first　image　super-resolution　method　which　reconstructs　a　high　resolution　image　from　its　low　resolution　counterpart　via　a　two　dimensional　sparse　model.　Correspondingly,　we　present　a　new　dictionary　learning　algorithm　to　fully　make　use　of　the　corresponding　relationship　of　two　pairs　of　2D　dictionaries　of　low　and　high　resolution　images,　respectively.　Experimental　results　demonstrate　that　our　proposed　image　super-resolution　with　2D　sparse　model　outperforms　state-of-the-art　1D　sparse　model　based　super　resolution　methods　in　terms　of　both　reconstruction　ability　and　memory　usage.