Windowed Fourier Transform for Non-Line-of-Sight Imaging Algorithms

Non-line-of-sight (NLOS) imaging has been a hot research field recently. Time-of-flight-based (ToF-based) active algorithms are one of the bases for NLOS, which is also the focus of this paper. In the preliminary experiments, Filtered-back-projection (FBP), Light-cone-transformation (LCT), and F-K migration algorithms have shown some shortcomings. For instance, the performance of FBP is poor when it is applied to datasets with low spatial resolution. For objects dominated by specular reflections, LCT generates a significant amount of noise. Similarly, F-K migration produces noisy results when it is employed with low spatial resolution data. To overcome the limitations of these algorithms, we study windowed Fourier transform for NLOS imaging. Experiments are used to analyze the performance of different windowing techniques. From 2D to 3D, and from time to frequency domain, we apply Hanning windows with FBP, LCT, and F-K algorithms. The results demonstrate that, compared to time domain, the performance of an algorithm using windows in frequency domain is significantly enhanced. The reconstructions become significantly clearer. Previously unrecoverable contours are revealed. Image noise is greatly reduced. Then, we employ a set of 3D Kaiser windows with various coefficients in the frequency domain for reconstruction, as a comparison to Hanning windows. We find that the Hanning window function and Kaiser windows with β in the range from 4 to 9 best suits the NLOS imaging problem.