Solving Trigonometric Moment Problems for Fast Transient Imaging
Solving Trigonometric Moment Problems for Fast Transient Imaging
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DOI：
10.1145/2816795.2818103
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发表时间：
2015-11-01
影响因子：
6.2
通讯作者：
Klein, Reinhard
中科院分区：
文献类型：
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作者：
Peters, Christoph;Klein, Jonathan;Klein, Reinhard
瞬态图像有助于分析场景中的光传输。除了两个空间维度之外，它们还在飞行时间中被解决。用于捕获它们的具有成本效益的方法使用调幅连续波激光雷达系统，但通常需要超过一分钟的捕获时间。我们提出了新的技术测量和重建的瞬态图像，这大大减少了捕获时间。为此，我们提出了一个三角矩问题的重建问题。大量的数学文献为这些问题提供了强有力的解决方案。特别是，最大熵谱估计和Pisarenko估计提供了两个封闭形式的解决方案重建使用连续密度或稀疏分布，分别。这两种方法都可以使用m个调制频率下的测量来分离m个不同的回波。对于m = 3，我们用测量数据进行的实验证实了这一点。我们的GPU加速实现每秒可以重建超过100000帧的瞬态图像。此外，我们建议修改捕获例程，以实现所需的正弦调制，而不增加捕获时间。这使我们能够每秒捕获高达18.6个瞬态图像，从而生成瞬态视频。一个重要的副产品是一种消除距离成像中多径干扰的方法。
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.