Active imaging systems sample the Transient Light Transport Matrix (TLTM) for a scene by sequentially illuminating various positions in this scene using a controllable light source, and then measuring the resulting spatiotemporal light transport with time of flight (ToF) sensors. Time-resolved Non-line-of-sight (NLOS) imaging employs an active imaging system that measures part of the TLTM of an intermediary relay surface, and uses the indirect reflections of light encoded within this TLTM to "see around corners". Such imaging systems have applications in diverse areas such as disaster response, remote surveillance, and autonomous navigation. While existing NLOS imaging systems usually measure a subset of the full TLTM, development of customized gated Single Photon Avalanche Diode (SPAD) arrays \cite{riccardo_fast-gated_2022} has made it feasible to probe the full measurement space. In this work, we demonstrate that the full TLTM on the relay surface can be processed with efficient algorithms to computationally focus and detect our illumination in different parts of the hidden scene, turning the relay surface into a second-order active imaging system. These algorithms allow us to iterate on the measured, first-order TLTM, and extract a \textbf{second order TLTM for surfaces in the hidden scene}. We showcase three applications of TLTMs in NLOS imaging: (1) Scene Relighting with novel illumination, (2) Separation of direct and indirect components of light transport in the hidden scene, and (3) Dual Photography. Additionally, we empirically demonstrate that SPAD arrays enable parallel acquisition of photons, effectively mitigating long acquisition times.

翻译：主动成像系统通过可控光源依次照亮场景中的不同位置，并使用飞行时间传感器测量由此产生的时空光传输，从而对场景的瞬态光传输矩阵进行采样。时间分辨非视距成像采用主动成像系统测量中介中继表面的部分TLTM，并利用该TLTM中编码的光的间接反射实现“拐角成像”。此类成像系统在灾害响应、远程监视和自主导航等多个领域具有应用前景。虽然现有NLOS成像系统通常仅测量完整TLTM的子集，但定制化门控单光子雪崩二极管阵列的发展使得探测完整测量空间成为可能。本研究表明，中继表面的完整TLTM可通过高效算法进行处理，从而在计算上聚焦并检测隐藏场景不同区域的照明，将中继表面转化为二阶主动成像系统。这些算法使我们能够对测量得到的一阶TLTM进行迭代，并提取隐藏场景表面的二阶TLTM。我们展示了TLTM在NLOS成像中的三个应用：(1) 采用新型照明进行场景重光照，(2) 分离隐藏场景中光传输的直接与间接分量，以及(3) 双重摄影。此外，我们通过实验证明SPAD阵列能够实现光子并行采集，有效缓解了长采集时间问题。