Fast and Memory-efficient Non-line-of-sight Imaging with Quasi-Fresnel Transform

Non-line-of-sight (NLOS) imaging seeks to reconstruct hidden objects by analyzing reflections from intermediary surfaces. Existing methods typically model both the measurement data and the hidden scene in three dimensions, overlooking the inherently two-dimensional nature of most hidden objects. This oversight leads to high computational costs and substantial memory consumption, limiting practical applications and making real-time, high-resolution NLOS imaging on lightweight devices challenging. In this paper, we introduce a novel approach that represents the hidden scene using two-dimensional functions and employs a Quasi-Fresnel transform to establish a direct inversion formula between the measurement data and the hidden scene. This transformation leverages the two-dimensional characteristics of the problem to significantly reduce computational complexity and memory requirements. Our algorithm efficiently performs fast transformations between these two-dimensional aggregated data, enabling rapid reconstruction of hidden objects with minimal memory usage. Compared to existing methods, our approach reduces runtime and memory demands by several orders of magnitude while maintaining imaging quality. The substantial reduction in memory usage not only enhances computational efficiency but also enables NLOS imaging on lightweight devices such as mobile and embedded systems. We anticipate that this method will facilitate real-time, high-resolution NLOS imaging and broaden its applicability across a wider range of platforms.