This paper proposes a novel decomposition model for high-quality depth recovery (DMDR) from low quality depth measurement accompanied by high-resolution RGB image. We observe that depth patches extracted from the depth map containing smooth regions separated by curves, can be decomposed simultaneously by a low-order polynomial surface and a piece-wise constant signal. In our model, the polynomial surface component is regularized by least-square polynomial smoothing, while the piece-wise constant component is constrained by total variation filtering. The model is effectively solved by the alternating direction method under the augmented Lagrangian multiplier (ALM-ADM) algorithm. Experimental results show that our method is able to handle various types of depth degradation under the designed signal decomposition model, and produces high-quality depth recovery results.