用改进的傅里叶变换实现非视域成像的稀疏采样,提升效率并降低存储压力。
Optimized Sampling for Non-Line-of-Sight Imaging Using Modified Fast Fourier Transforms
- 引入NUFFT和SFFT,支持不规则采样与任意位置重建。
- 实测表明可大幅减少采样点数而不损失重建质量。
- 适合需要高速、低存储的非视域成像实际应用。
非视域(NLOS)成像系统通过采集漫反射表面的光信号,利用计算算法重建三维场景。现有方法依赖快速傅里叶变换(FFT),要求输入输出均在均匀网格上采样,但多像素探测阵列会导致继发表面非均匀采样,且显著提高数据读出速率,限制实际部署。本文基于相位场框架,证明当前设置普遍过采样,因此可压缩测量而不明显影响重建质量。由此我们采用非均匀快速傅里叶变换(NUFFT),从任意形状的不规则采样继发面中进行稀疏重建,并支持隐藏空间任意位置的灵活采样。进一步结合缩放快速傅里叶变换(SFFT),可在不增加内存存储的情况下重建更大体积。所有算法保持与FFT相当的计算复杂度,确保实际应用的可扩展性。
原文摘要 · Abstract (English)
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.
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