Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Curvature regularization for Non-line-of-sight Imaging from Under-sampled Data

Rui Ding, Juntian Ye, Qifeng Gao, Feihu Xu, Yuping Duan

TL;DR

Two novel NLOS reconstruction models based on curvature regularization based on the alternating direction method of multipliers with the backtracking stepsize rule are proposed, which achieve state-of-the-art performance, especially in the compressed sensing setting.

Abstract

Non-line-of-sight (NLOS) imaging aims to reconstruct the three-dimensional hidden scenes from the data measured in the line-of-sight, which uses photon time-of-flight information encoded in light after multiple diffuse reflections. The under-sampled scanning data can facilitate fast imaging. However, the resulting reconstruction problem becomes a serious ill-posed inverse problem, the solution of which is highly possibility to be degraded due to noises and distortions. In this paper, we propose novel NLOS reconstruction models based on curvature regularization, i.e., the object-domain curvature regularization model and the dual (signal and object)-domain curvature regularization model. In what follows, we develop efficient optimization algorithms relying on the alternating direction method of multipliers (ADMM) with the backtracking stepsize rule, for which all solvers can be implemented on GPUs. We evaluate the proposed algorithms on both synthetic and real datasets, which achieve state-of-the-art performance, especially in the compressed sensing setting. Based on GPU computing, our algorithm is the most effective among iterative methods, balancing reconstruction quality and computational time. All our codes and data are available at https://github.com/Duanlab123/CurvNLOS.

Curvature regularization for Non-line-of-sight Imaging from Under-sampled Data

TL;DR

Two novel NLOS reconstruction models based on curvature regularization based on the alternating direction method of multipliers with the backtracking stepsize rule are proposed, which achieve state-of-the-art performance, especially in the compressed sensing setting.

Abstract

Non-line-of-sight (NLOS) imaging aims to reconstruct the three-dimensional hidden scenes from the data measured in the line-of-sight, which uses photon time-of-flight information encoded in light after multiple diffuse reflections. The under-sampled scanning data can facilitate fast imaging. However, the resulting reconstruction problem becomes a serious ill-posed inverse problem, the solution of which is highly possibility to be degraded due to noises and distortions. In this paper, we propose novel NLOS reconstruction models based on curvature regularization, i.e., the object-domain curvature regularization model and the dual (signal and object)-domain curvature regularization model. In what follows, we develop efficient optimization algorithms relying on the alternating direction method of multipliers (ADMM) with the backtracking stepsize rule, for which all solvers can be implemented on GPUs. We evaluate the proposed algorithms on both synthetic and real datasets, which achieve state-of-the-art performance, especially in the compressed sensing setting. Based on GPU computing, our algorithm is the most effective among iterative methods, balancing reconstruction quality and computational time. All our codes and data are available at https://github.com/Duanlab123/CurvNLOS.
Paper Structure (23 sections, 24 equations, 12 figures, 4 tables, 2 algorithms)

This paper contains 23 sections, 24 equations, 12 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Forward propagation model
  3. Object-domain curvature method
  4. Numerical minimization
  5. Sub-minimization problem w.r.t. $v$
  6. Sub-minimization problem w.r.t. $u$
  7. Update of Lagrange multipliers
  8. Our algorithm
  9. Dual-domain curvature method and GPU implementation
  10. Dual-domain reconstruction method
  11. GPU implementation
  12. Numerical Results
  13. Parameter discussing
  14. Experiments on synthetic data
  15. Results on Bowling w.r.t. different scanning points
  16. ...and 8 more sections

Figures (12)

  • Figure 1: Overview of NLOS imaging measurements, where (a) The ground truth of hidden objects, (b) The measurements of the wall $\tau$ attenuated along the time axis, and (c) A histogram measured at a selected scanned point on the visible wall.
  • Figure 2: The visual comparison of the comparison reconstruction methods under full sampling on Bowling, where the parameters of our methods are set as: $a = 5\times10^{-5}, b = 5\times10^{-5}$, $\mu$ = 0.1 for Algorithm \ref{['alg1']}; $a_{\tau} = 1\times10^{-4}, b_{\tau} = 3\times10^{-2},a_u = 1\times10^{-4}, b_u = 1\times10^{-4}, \lambda = 400$ for Algorithm \ref{['alg2']}.
  • Figure 3: Reconstruction results using different numbers of scanning points from up to down the scanning points are of $8\times 8$, $6\times 6$, and $4\times4$, respectively, where (a) LCT, (b) SPIRAL w/o smoothing, (c) SPIRAL with smoothing, (d) Algorithm 1 and (e) Algorithm 2. The parameters of our methods are set as: $a = 9\times10^{-5}, b = 2\times10^{-5}$ ($8\times8$ ), $a = 1\times10^{-6}, b = 4\times10^{-5}$ ($6\times6$ ), $a = 1\times10^{-5}, b = 1\times10^{-5}$ ($4\times4$) and $\mu$ = 0.1 for Algorithm \ref{['alg1']}; $\lambda = 235, a_{\tau} = 4\times10^{-4}, b_{\tau} = 3\times10^{-2},a_u = 2\times10^{-4}, b_u = 4.5\times10^{-4}$ ($8\times8$), $\lambda = 270, a_{\tau} = 2\times10^{-4}, b_{\tau} = 4\times10^{-2},a_u = 8\times10^{-4}, b_u = 1\times10^{-4}$ ($6\times6$), $\lambda = 300,a_{\tau} = 1\times10^{-4}, b_{\tau} = 1.2\times10^{-2},a_u = 6\times10^{-4}, b_u = 3\times10^{-4}$($4\times4$) for Algorithm \ref{['alg2']}.
  • Figure 4: The comparison of energy decays between SPIRAL in ye2021compressed and our Algorithm \ref{['alg1']}, Algorithm \ref{['alg2']}.
  • Figure 5: Comparison for the reconstruction results of under-sampled Stanford bunny, where scanning points are of resolution $8\times8$ and $4\times4$, respectively.
  • ...and 7 more figures