High-quality　depth　information　is　urgently　required　with　their　increasingly　wide　application　in　many　real-world　multimedia　fields.　However,　due　to　the　limitation　of　depth　sensing　technology,　the　captured　depth　map　in　practice　usually　owns　low　resolution　and　poor　quality,　which　limits　its　practical　application.　As　we　all　know,　consistency　between　high-quality　color　images　and　low-quality　depth　maps　achieves　good　effects　in　depth　super-resolution.　But　the　edge　inconsistency　also　limits　the　recovery　of　depth　map.　Inspired　by　the　geometric　relationship　between　surface　normal　of　a　3D　scene　and　their　distance　from　camera,　we　discover　that　there　are　more　consistency　between　surface　normal　map　and　depth　map　in　the　edge　areas.　Meanwhile,　surface　normal　map　can　provide　more　spatial　geometric　constraints　for　depth　map　reconstruction,　for　both　of　them　are　special　images　with　spatial　information,　which　we　called　2.5D　images.　In　this　paper,　we　propose　a　unified　framework--Normal　Data　Guided　Depth　Map　Restoration　with　Edge-Preserving　Smoothing　Regularization(NDEPS)　method,　via　joint　spatial　domain　and　gradient　domain　regularization-one　characterizing　the　relationship　between　surface　normal　data　and　depth　in　the　spatial　domain　and　another　edge-aware　constraint　in　the　gradient　domain.　The　proposed　NDEPS　method　formulates　a　constrained　optimization　problem　that　can　be　solved　by　an　iterative　conjugate　gradient(CG)　algorithm.　Extensive　quantitative　and　qualitative　evaluations　compared　with　state-of-the-art　depth　recovery　methods　show　the　effectiveness　and　superiority　of　our　method.