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.

本研究解决了非视线(NLOS)成像中因几何结构导致的非均匀采样问题，进而影响了重建质量。通过引入相位场框架和非均匀快速傅里叶变换(NUFFT)，实现了对稀疏测量的有效重建，从而在保证计算复杂度的前提下，提升了成像系统的灵活性和实时性，具有显著的实际应用潜力。

使用改进快速傅里叶变换的非视线成像优化采样