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

2025-01-09

AI Summary

To address the challenges of non-uniform sampling on relay surfaces and high data rates in non-line-of-sight (NLOS) imaging, this paper proposes a sparse reconstruction framework based on phasor-field modeling. Our method systematically integrates non-uniform fast Fourier transform (NUFFT) and sparse fast Fourier transform (SFFT) into NLOS imaging—breaking the strict uniform-grid constraint of conventional FFT. This enables sparse sampling over arbitrarily shaped relay surfaces, flexible voxel placement for reconstruction, and large-volume, memory-efficient reconstruction without explicit memory expansion. By jointly exploiting measurement sparsity and inverse problem optimization, our approach achieves substantial reductions in sampling density and sensor data rate while preserving reconstruction fidelity. Crucially, it maintains an overall computational complexity of *O*(*N* log *N*). The result is high-fidelity, real-time, and scalable 3D reconstruction of hidden scenes.

Technology Category

• Search and Optimization: Non-convex Optimization
• Computer Vision: 3D Computer Vision
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Security and Privacy: Large-scale security measurements

Abstract

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.

Problem

• Non-Line-of-Sight Imaging
• Data Processing Speed
• Image Generation Flexibility

Innovation

• NUFFT
• SFFT
• NLOS Imaging