Phasor Field Diffraction Based Reconstruction
for Fast Non-Line-of-Sight Imaging Systems

Xiaochun Liu
Sebastian Bauer
Andreas Velten
Computational Optics Group, University of Wisconsin - Madison

Supplementary Materials
Data archive (spatial-temporal cube format)

* What is Non-Line-of-Sight Imaging?

Non-Line-of-Sight Imaging (NLOS) is a new imaging method that makes it possible to see around corners. Previously, we have shown that we can turn walls into cameras in our Nature work using knowledge from classical optics.

* What is new about this paper?

In this work, we follow our previous work to design a fast computational camera for real-time hidden reconstructions. This enables reconstructing room-sized scenes from non-confocal, parallel multi-pixel measurements in seconds with less memory usage. We also anticipate our method stimulates real-time video-rate reconstruction of hidden scenes using emerging Single-Photon Avalanche Diode array (SPAD arrays) detectors.

Turning walls into a video camera is around the corner. We anticipate huge applications for this technology to make a difference in security, surveillance, biomedical and LiDAR imaging as well as many others.


Non-line-of-sight (NLOS) imaging recovers objects using diffusely reflected indirect light using transient illumination devices in combination with a computational inverse method. While capture systems capable of collecting signal from the entire NLOS relay surface can be much more light efficient than single pixel point scanning detection, current reconstruction algorithms for such systems have computational and memory requirements that prevent real-time NLOS imaging. Existing real-time demonstrations, also, use retroreflecting targets and reconstruct at resolutions far below the hardware limits. Our method enables reconstructing non-confocal, parallel multi-pixel, room-sized measurements in seconds with less memory usage. We anticipate that our method will enable real time NLOS imaging when used with emerging Single-photon avalanche diode array detectors with resolutions only limited by the temporal resolution of the sensor.

Phasor Field Virtual Lens

Faster. Better.

For non-confocal, parallel multi-pixel, SPAD array, fast Non-Line-of-Sight Imaging System

Algorithm complexity Our proposed method is computationally bounded by the Fast Fourier transform (FFT). Compared to previous methodd, our proposed method is much faster with reconstruction in seconds. These GIFs above are for visualization only; the true run time improvement is in factors of 300 to 400. Our unoptimized Matlab code is run on an Intel Core i7-7700 CPU, 3.6GHz x 8 with 32 GB memory.

How it works?

Framework of proposed method. a. Non-line-of-sight imaging measurement sketch. b. Virtual illumination design: these parameters are used for sampling the phasor field wavefront on the relay Wall. c. Our proposed method behaves like a virtual lens which creates a virtual image of hidden objects using fast diffraction algorithm. d. Illustration of the proposed method in a signal processing flowchart.


Results. We compare all existing fast algorithms with N*log(N) algorithm complexity. Overall, we can require room-sized hidden scene in seconds and achieve lateral imaging quality comparable to evaluating the diffraction integral analytically. We also found that all existing approximated methods can not meet the highest reconstructed imaging quality than our proposed method. For more details, please refers to our paper.


This work was funded by DARPA through the DARPA REVEAL project (HR0011-16-C-0025), and the DURIP program (FA9550-18-1-0409). We thank Jeffrey H. Shapiro for the insights about the phasor field broad-band model. We also appreciate the help of Marco La Manna, Ji-Hyun Nam, Toan Le and Atul Ingle on the hardware setup and helpful discussion during calibrations. Xiaochun Liu would like to acknowledge the helpful discussion with David B. Lindell about his approximate non-confocal method and with Ibon Guillen and Miguel J. Galindo at the Graphics and Imaging Lab about volume rendering methods and simulated datasets.

Related Work

Non-Line-of-Sight Imaging:
Non-Line-of-Sight Imaging using Phasor Field Virtual Wave Optics, Nature. [Website]
Phasor Field Diffraction Based Reconstruction for Fast Non-Line-of-Sight Imaging Systems, Nature Communications. [Website]
The role of Wigner Distribution Function in Non-Line-of-Sight Imaging, ICCP. [Website]
Analysis of Feature Visibility in Non-Line-of-Sight Measurements, CVPR. [Website]
On the effect of BRDFs on Phasor Field NLOS imaging, ICASSP. [Website]
A dataset for benchmarking time-resolved non-line-of-sight imaging, SIGGRAPH. [Website]
Phasor field waves: A Huygens-like light transport model for non-line-of-sight imaging applications, Optics Express. [Paper]
Paraxial theory of phasor-field imaging, Optics Express. [Paper]
Phasor field waves: a mathematical treatment, Optics Express. [Paper]
Non-line-of-sight-imaging using dynamic relay surfaces, Optics Express. [Paper]

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