3D　depth　cameras　have　become　more　and　more　popular　in　recent　years.　However,　depth　maps　captured　by　these　cameras　can　hardly　be　used　in　3D　reconstruction　directly　because　they　often　suffer　from　low　resolution　and　blurring　depth　discontinuities.　Super　resolution　of　depth　maps　is　necessary.　In　depth　maps,　the　edge　areas　play　more　important　role　and　demonstrate　distinct　geometry　directions　compared　with　natural　images.　However,　most　existing　super-resolution　methods　ignore　this　fact,　and　they　can　not　handle　depth　edges　properly.　Motivated　by　this,　we　propose　a　compound　method　that　combines　multi-direction　dictionary　sparse　representation　and　autoregressive　(AR)　models,　so　that　the　depth　edges　are　presented　precisely　at　different　levels.　In　the　patch　level,　the　depth　edge　patches　with　geometry　directions　are　well　represented　by　the　pre-trained　multi-directional　dictionaries.　Compared　with　a　universal　dictionary,　multiple　dictionaries　trained　from　different　directional　patches　can　represent　the　directional　depth　patch　much　better.　In　the　finer　pixel　level,　we　utilize　an　adaptive　AR　model　to　represent　the　local　correlation　patterns　in　small　areas.　Extensive　experimental　results　on　both　synthetic　and　real　datasets　demonstrate　that,　the　proposed　model　outperforms　state-of-the-art　depth　map　super-resolution　methods　in　terms　of　both　quantitative　metrics　and　subjective　visual　quality.