In　this　paper,　a　novel　image　blocky　artifact　removal　scheme　based　on　low-rank　matrix　recovery　is　proposed.　The　problem　of　suppressing　blocky　artifacts　is　formulated　as　recovering　a　low-rank　matrix　from　corrupted　observations.　During　the　deblocking　processing,　we　do　not　directly　recover　the　whole　clean　image　but　only　its　high-frequency　component　and　then　synthesize　the　clean　image　by　incorporating　the　low-frequency　component　of　blocky　image.　To　take　advantage　of　the　low-rank　matrix　recovery　paradigm,　we　first　cluster　the　similar　patches　of　the　high-frequency　component　of　image　via　local　pixel　clustering,　then　the　clean　high-frequency　component　of　image　is　recovered　by　formulating　an　optimization　problem　of　the　nuclear　norm　and　l(1)-norm.　The　experimental　results　show　that　the　proposed　algorithm　can　achieve　competitive　performance　in　terms　of　both　quantitative　and　subjective　quality.