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.