标题： 基于改进快速傅里叶变换的非视距成像优化采样 显示英文标题

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

摘要： 非视距（NLOS）成像系统在漫反射中继表面上收集光，并将此测量输入到计算算法中，该算法输出三维体积重建。 这些算法利用快速傅里叶变换（FFT）来加速重建过程，但要求输入和输出都以均匀网格进行空间采样。 然而，使用多像素探测器阵列时，NLOS成像的几何结构会导致中继表面上的非均匀采样，尽管此类阵列显著减少了采集时间。 此外，使用这些阵列会增加传感器读出的数据率，这对实际部署构成挑战。 在本工作中，我们利用相位场框架证明，现有的NLOS成像设置通常在空间上过度采样中继表面，解释了为什么可以在不显著牺牲重建质量的情况下压缩测量值。 这使我们能够利用非均匀快速傅里叶变换（NUFFT）从任意形状的不规则采样中继表面上获取的稀疏测量值进行重建。 此外，我们利用NUFFT在隐藏体积中的任意位置进行重建，确保输入和输出的灵活采样方案。 最后，我们利用缩放快速傅里叶变换（SFFT）在不增加内存中存储样本数量的情况下重建更大的体积。 本文介绍的所有算法都保持了基于FFT方法的计算复杂度，确保了实际NLOS成像应用的可扩展性。 显示英文摘要

摘要： 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.