The　sparsity　of　images　in　a　certain　transform　domain　or　dictionary　has　been　exploited　in　many　image　processing　applications.　Both　classic　transforms　and　sparsifying　transforms　reconstruct　images　by　a　linear　combination　of　a　small　basis　of　the　transform.　Both　kinds　of　transform　are　non-redundant.　However,　natural　images　admit　complicated　textures　and　structures,　which　can　hardly　be　sparsely　represented　by　square　transforms.　To　solve　this　issue,　we　propose　a　data-driven　redundant　transform　based　on　Parseval　frames　(DRTPF)　by　applying　the　frame　and　its　dual　frame　as　the　backward　and　forward　transform　operators,　respectively.　Benefitting　from　this　pairwise　use　of　frames,　the　proposed　model　combines　a　synthesis　sparse　system　and　an　analysis　sparse　system.　By　enforcing　the　frame　pair　to　be　Parseval　frames,　the　singular　values　and　condition　number　of　the　learnt　redundant　frames,　which　are　efficient　values　for　measuring　the　quality　of　the　learnt　sparsifying　transforms,　are　forced　to　achieve　an　optimal　state.　We　formulate　a　transform　pair　(i.e.,　frame　pair)　learning　model　and　a　two-phase　iterative　algorithm,　analyze　the　robustness　of　the　proposed　DRTPF　and　the　convergence　of　the　corresponding　algorithm,　and　demonstrate　the　effectiveness　of　our　proposed　DRTPF　by　analyzing　its　robustness　against　noise　and　sparsification　errors.　Extensive　experimental　results　on　image　denoising　show　that　our　proposed　model　achieves　superior　denoising　performance,　in　terms　of　subjective　and　objective　quality,　compared　to　traditional　sparse　models.