Optimized Sampling for Non-Line-of-Sight Imaging Using Modified Fast Fourier Transforms

Non-line-of-Sight (NLOS) imaging systems collect light at a diffuse relay surface and input this measurement into computational algorithms that output a 3D volumetric reconstruction. These algorithms utilize the Fast Fourier Transform (FFT) to accelerate the reconstruction process but require both input and output to be sampled spatially with uniform grids. However, the geometry of NLOS imaging inherently results in non-uniform sampling on the relay surface when using multi-pixel detector arrays, even though such arrays significantly reduce acquisition times. Furthermore, using these arrays increases the data rate required for sensor readout, posing challenges for real-world deployment. In this work, we utilize the phasor field framework to demonstrate that existing NLOS imaging setups typically oversample the relay surface spatially, explaining why the measurement can be compressed without significantly sacrificing reconstruction quality. This enables us to utilize the Non-Uniform Fast Fourier Transform (NUFFT) to reconstruct from sparse measurements acquired from irregularly sampled relay surfaces of arbitrary shapes. Furthermore, we utilize the NUFFT to reconstruct at arbitrary locations in the hidden volume, ensuring flexible sampling schemes for both the input and output. Finally, we utilize the Scaled Fast Fourier Transform (SFFT) to reconstruct larger volumes without increasing the number of samples stored in memory. All algorithms introduced in this paper preserve the computational complexity of FFT-based methods, ensuring scalability for practical NLOS imaging applications.

Iterating the Transient Light Transport Matrix for Non-Line-of-Sight Imaging

Active imaging systems sample the Transient Light Transport Matrix (TLTM) for a scene by sequentially illuminating various positions in this scene using a controllable light source, and then measuring the resulting spatiotemporal light transport with time of flight (ToF) sensors. Time-resolved Non-line-of-sight (NLOS) imaging employs an active imaging system that measures part of the TLTM of an intermediary relay surface, and uses the indirect reflections of light encoded within this TLTM to "see around corners". Such imaging systems have applications in diverse areas such as disaster response, remote surveillance, and autonomous navigation. While existing NLOS imaging systems usually measure a subset of the full TLTM, development of customized gated Single Photon Avalanche Diode (SPAD) arrays \cite{riccardo_fast-gated_2022} has made it feasible to probe the full measurement space. In this work, we demonstrate that the full TLTM on the relay surface can be processed with efficient algorithms to computationally focus and detect our illumination in different parts of the hidden scene, turning the relay surface into a second-order active imaging system. These algorithms allow us to iterate on the measured, first-order TLTM, and extract a \textbf{second order TLTM for surfaces in the hidden scene}. We showcase three applications of TLTMs in NLOS imaging: (1) Scene Relighting with novel illumination, (2) Separation of direct and indirect components of light transport in the hidden scene, and (3) Dual Photography. Additionally, we empirically demonstrate that SPAD arrays enable parallel acquisition of photons, effectively mitigating long acquisition times.