Overcomplete　representation　is　attracting　interest　in　image　restoration　due　to　its　potential　to　generate　sparse　representations　of　signals.　However,　the　problem　of　seeking　sparse　representation　must　be　unstable　in　the　presence　of　noise.　Restricted　Isometry　Property　(RIP),　playing　a　crucial　role　in　providing　stable　sparse　representation,　has　been　ignored　in　the　existing　sparse　models　as　it　is　hard　to　integrate　into　the　conventional　sparse　models　as　a　regularizer.　In　this　paper,　we　propose　a　stable　sparse　model　with　non-tight　frame　(SSM-NTF)　via　applying　the　corresponding　frame　condition　to　approximate　RIP.　Our　SSM-NTF　model　takes　into　account　the　advantage　of　the　traditional　sparse　model,　and　meanwhile　contains　RIP　and　closed-form　expression　of　sparse　coefficients　which　ensure　stable　recovery.　Moreover,　benefitting　from　the　pair-wise　of　the　non-tight　frame　(the　original　frame　and　its　dual　frame),　our　SSM-NTF　model　combines　a　synthesis　sparse　system　and　an　analysis　sparse　system.　By　enforcing　the　frame　bounds　and　applying　a　second-order　truncated　series　to　approximate　the　inverse　frame　operator,　we　formulate　a　dictionary　pair　(frame　pair)　learning　model　along　with　a　two-phase　iterative　algorithm.　Extensive　experimental　results　on　image　restoration　tasks　such　as　denoising,　super　resolution　and　inpainting　show　that　our　proposed　SSM-NTF　achieves　superior　recovery　performance　in　terms　of　both　subjective　and　objective　quality.