In recent years, computational Time-of-Flight (ToF) imaging has emerged as an exciting and a novel imaging modality that offers new and powerful interpretations of natural scenes, with applications extending to 3D, light-in-flight, and non-line-of-sight imaging. Mathematically, ToF imaging relies on algorithmic super-resolution, as the back-scattered sparse light echoes lie on a finer time resolution than what digital devices can capture. Traditional methods necessitate knowledge of the emitted light pulses or kernels and employ sparse deconvolution to recover scenes. Unlike previous approaches, this paper introduces a novel, blind ToF imaging technique that does not require kernel calibration and recovers sparse spikes on a continuum, rather than a discrete grid. By studying the shared characteristics of various ToF modalities, we capitalize on the fact that most physical pulses approximately satisfy the Strang-Fix conditions from approximation theory. This leads to a new mathematical formulation for sparse super-resolution. Our recovery approach uses an optimization method that is pivoted on an alternating minimization strategy. We benchmark our blind ToF method against traditional kernel calibration methods, which serve as the baseline. Extensive hardware experiments across different ToF modalities demonstrate the algorithmic advantages, flexibility and empirical robustness of our approach. We show that our work facilitates super-resolution in scenarios where distinguishing between closely spaced objects is challenging, while maintaining performance comparable to known kernel situations. Examples of light-in-flight imaging and light-sweep videos highlight the practical benefits of our blind super-resolution method in enhancing the understanding of natural scenes.

翻译：近年来，计算时间飞行（ToF）成像已成为一种新颖且令人兴奋的成像模式，为自然场景提供了全新而强大的解释能力，其应用范围涵盖三维成像、光飞行过程成像以及非视距成像等领域。从数学角度而言，ToF成像依赖于算法超分辨率技术，因为后向散射的稀疏光回波所对应的时间分辨率高于数字设备能够捕获的精度。传统方法需要已知发射光脉冲或核函数，并采用稀疏反卷积技术来重建场景。与先前方法不同，本文提出了一种新颖的盲ToF成像技术，该技术无需核函数校准，并能在连续域而非离散网格上恢复稀疏尖峰信号。通过研究多种ToF模式的共同特性，我们利用大多数物理脉冲近似满足逼近理论中Strang-Fix条件这一事实，从而建立了稀疏超分辨率的新数学框架。我们的恢复方法采用以交替最小化策略为核心的优化算法。我们将所提出的盲ToF方法与作为基准的传统核函数校准方法进行比较评估。跨不同ToF模式的广泛硬件实验证明了该方法在算法优势、灵活性和实证鲁棒性方面的优越性。研究表明，我们的方法能够在难以区分紧密相邻物体的场景中实现超分辨率，同时保持与已知核函数情况相当的性能。光飞行过程成像和光扫描视频的实例凸显了所提出的盲超分辨率方法在增强对自然场景理解方面的实际价值。