Learning Non-Local Spatial Correlations To Restore Sparse 3D Single-Photon Data

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30 Citations (Scopus)
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This paper presents a new algorithm for the learning of spatial correlation and non-local restoration of single-photon 3D Lidar images acquired in the photon starved regime (fewer or less than one photon per pixel) or with a reduced number of scanned spatial points (pixels). The algorithm alternates between three steps: (i) extract multi-scale information, (ii) build a robust graph of non-local spatial correlations between pixels, and (iii) the restoration of depth and reflectivity images. A non-uniform sampling approach, which assigns larger patches to homogeneous regions and smaller ones to heterogeneous regions, is adopted to reduce the computational cost associated with the graph. The restoration of the 3D images is achieved by minimizing a cost function accounting for the multi-scale information and the non-local spatial correlation between patches. This minimization problem is efficiently solved using the alternating direction method of multipliers (ADMM) that presents fast convergence properties. Various results based on simulated and real Lidar data show the benefits of the proposed algorithm that improves the quality of the estimated depth and reflectivity images, especially in the photon-starved regime or when containing a reduced number of spatial points.

Original languageEnglish
Pages (from-to)3119-3131
Number of pages13
JournalIEEE Transactions on Image Processing
Early online date11 Dec 2019
Publication statusPublished - 2020


  • 3D Lidar imaging
  • ADMM
  • Laplacian regularization
  • Poisson statistics
  • Single photon
  • graph
  • image restoration
  • multi-scale analysis
  • non-uniform sampling

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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