Dictionary　learning　for　sparse　representation　has　been　an　active　topic　in　the　field　of　image　processing.　Most　existing　dictionary　learning　schemes　focus　on　the　representation　ability　of　the　learned　dictionary.　However,　according　to　the　theory　of　compressive　sensing,　the　mutual　incoherence　of　the　dictionary　is　of　crucial　role　in　the　sparse　coding.　Thus　incoherent　dictionary　is　desirable　to　improve　the　performance　of　sparse　representation　based　image　restoration.　In　this　paper,　we　propose　a　new　incoherent　dictionary　learning　model　that　minimizes　the　representation　error　and　the　mutual　incoherence　by　incorporating　the　constraint　of　mutual　incoherence　into　the　dictionary　update　model.　The　optimal　incoherent　dictionary　is　achieved　by　seeking　an　optimization　solution.　An　efficient　algorithm　is　developed　to　solve　the　optimization　problem　iteratively.　Experimental　results　on　image　denoising　demonstrate　that　the　proposed　scheme　achieves　better　recovery　quality　and　converges　faster　than　K-SVD　while　keeping　lower　computation　complexity.　©　2014　IEEE.