Solving Trigonometric Moment Problems for Fast Transient Imaging

In: ACM Trans. Graph. (Proc. SIGGRAPH Asia) (Nov. 2015), 34:6
 

Abstract

Transient images help to analyze light transport in scenes. Besides two spatial dimensions, they are resolved in time of flight. Cost-efficient approaches for their capture use amplitude modulated continuous wave lidar systems but typically take more than a minute of capture time. We propose new techniques for measurement and reconstruction of transient images, which drastically reduce this capture time. To this end, we pose the problem of reconstruction as a trigonometric moment problem. A vast body of mathematical literature provides powerful solutions to such problems. In particular, the maximum entropy spectral estimate and the Pisarenko estimate provide two closed-form solutions for reconstruction using continuous densities or sparse distributions, respectively. Both methods can separate m distinct returns using measurements at m modulation frequencies. For m=3 our experiments with measured data confirm this. Our GPU-accelerated implementation can reconstruct more than 100000 frames of a transient image per second. Additionally, we propose modifications of the capture routine to achieve the required sinusoidal modulation without increasing the capture time. This allows us to capture up to 18.6 transient images per second, leading to transient video. An important byproduct is a method for removal of multipath interference in range imaging.

Here is a link to the publication page in the ACM digital library. The work has also been presented as poster at ICCP 2016. The poster is available for download below.

The supplementary video is also available on YouTube.

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Bibtex

@ARTICLE{peters-2015-fast-transient,
    author = {Peters, Christoph and Klein, Jonathan and Hullin, Matthias B. and Klein, Reinhard},
     title = {Solving Trigonometric Moment Problems for Fast Transient Imaging},
   journal = {ACM Trans. Graph. (Proc. SIGGRAPH Asia)},
    volume = {34},
    number = {6},
      year = {2015},
     month = nov,
  abstract = {Transient images help to analyze light transport in scenes. Besides two spatial dimensions, they are
              resolved in time of flight. Cost-efficient approaches for their capture use amplitude modulated
              continuous wave lidar systems but typically take more than a minute of capture time. We propose new
              techniques for measurement and reconstruction of transient images, which drastically reduce this
              capture time. To this end, we pose the problem of reconstruction as a trigonometric moment problem.
              A vast body of mathematical literature provides powerful solutions to such problems. In particular,
              the maximum entropy spectral estimate and the Pisarenko estimate provide two closed-form solutions
              for reconstruction using continuous densities or sparse distributions, respectively. Both methods
              can separate m distinct returns using measurements at m modulation frequencies. For m=3 our
              experiments with measured data confirm this. Our GPU-accelerated implementation can reconstruct more
              than 100000 frames of a transient image per second. Additionally, we propose modifications of the
              capture routine to achieve the required sinusoidal modulation without increasing the capture time.
              This allows us to capture up to 18.6 transient images per second, leading to transient video. An
              important byproduct is a method for removal of multipath interference in range imaging.},
       doi = {10.1145/2816795.2818103}
}