Abstract This paper proposes a novel image decomposition model for scene depth recovery from low-quality depth measurements and its corresponding high resolution color image. Through our observation, the depth map mainly contains smooth regions separated by additive step discontinuities, and can be simultaneously decomposed into a local smooth surface and an approximately piecewise constant component. Therefore, the proposed unified model combines the least square polynomial approximation (for smooth surface) and a sparsity-promoting prior (for piecewise constant) to better portray the 2D depth signal intrinsically. As we know, the representation of the piecewise constant signal in gradient domain is extremely sparse. Previous researches using total variation filter based on L1-norm or Lp-norm (0

中文翻译：

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用于深度恢复的稀疏促进图像分解模型

摘要 本文提出了一种新的图像分解模型，用于从低质量深度测量及其相应的高分辨率彩色图像中恢复场景深度。通过我们的观察，深度图主要包含由加性台阶不连续性分隔的平滑区域，并且可以同时分解为局部平滑表面和近似分段常数分量。因此，所提出的统一模型结合了最小二乘多项式近似（对于光滑表面）和稀疏促进先验（对于分段常数），以更好地本质上描绘 2D 深度信号。众所周知，梯度域中分段常数信号的表示非常稀疏。以前的研究使用基于 L1-norm 或 Lp-norm (0