非视域目标重构技术旨在对视域外物体进行成像。为此，观察者向中介面发射激光脉冲，并通过测量到的光子事件标记重构非视域目标的反射率及法向。该技术在灾难救援，自动驾驶，遥感成像，医疗成像等领域具备广阔应用前景。 本文提出一般场景的非视域目标探测数学模型，并通过圆盘中心投影面积比的几何模型，解释光强平方衰减与余弦调制的经验公式。基于简化后的线性模型，本文证明了共焦探测场景下目标反射率及法向的唯一性。 实际应用中，针对正演模型偏差难以估计及探测数据信噪比低的困难，本文提出信号与物体联合先验的非视域目标重构框架。该方法融合并推广稀疏优化，字典学习，区块匹配，维纳滤波等多种方法，在共焦及非共焦探测场合均可重构目标的反射率及法向，所得结果边界清晰，背景噪音低。 此外，本文将该方法与水平集函数结合，提出基于水平集函数的信号与物体联合先验重构方法，更加准确地刻画了物体法向。为求解水平集函数，本文提出无穷拉普拉斯插值方法对方向反射率体素的方向角进行插值，将目标表面的方向角全局光滑地插值到整个重构区域，对水平集函数的求解至关重要。 针对中介面大小或形状受限的复杂非视域目标探测场景，本文提出基于虚拟共焦补偿的信号与物体联合先验重构方法，为任意照射及探测模式下的非视域目标重构问题提供了一种解决方案。该方法有效克服了测量矩阵的秩亏性，在共焦探测及非共焦探测场景下均可反演目标反射率及法向，是当前该场景中唯一有效的重构方法。对于中介面完整的场景，测量空间稀疏的信号并用该方法进行目标重构，可显著降低信号采集时间。 针对实时探测的需求，本文提出基于信号与曲面联合先验的非视域目标重构方法，为极少量空间测量数据的非视域目标重构问题提供了一种解决方案。该方法对共焦及非共焦探测场景均适用。本文展示了仅利用公开数据集中5 × 5实测数据对具有复杂几何结构的非视域物体进行重构的实例。在该实例中，探测时间小于原始数据集探测时间的万分之一，满足实时探测的需求。
The technique of non-line-of-sight (NLOS) reconstruction aims at imaging objects out of the direct line of sight. To achieve this, laser pulses are emitted to the relay surface, and the detected photon events are used to reconstruct the albedo and surface normal of the hidden target. Potential applications of this technique include disaster rescuing, autonomous driving, remote sensing and medical imaging. In this work, we introduce the mathematical model of NLOS detection under the general setting. Using the geometric model of the area ratio of the central projected disk, we explain the empirical formula containing square fall-off and cosine attenuation of the photon intensity. We then prove the uniqueness of the directional albedo with a simplified linear model. In real-world applications, the error of the forward model is hard to estimate and the measured data suffer from low signal-to-noise ratio. To overcome these difficulties, we propose the signal-object collaborative regularization (SOCR) framework. This method incorporates and extends several techiniques including sparse optimization, dictionary learning, block matching and Wiener filtering, and is capable of reconstructing the albedo and surface normal in both confocal and non-confocal measurement scenarios. The reconstructed target enjoys clear boundaries with few noise in the background. Besides, for better characterization of the surface normal of the hidden target, we combine the SOCR method with the level set function, and propose the level set based signal-object collaborative regularization framework (L-SOCR). To obtain the level set function, we propose the infinity Laplacian (IL) method, which interoplates the direction angles of the hidden surface normal to the whole reconstruction domain. The IL method provides globally smooth interpolations and is crucial for finding the level set function. For complex NLOS detection scenarios with limitations on the size or shape of the relay surface, we propose the confocal complemented signal-object collaborative regularization (CC-SOCR) method, which is a solution for NLOS reconstruction with arbitrary illumination and detection patterns. The proposed method overcomes the rank deficiency of the measurement matrix and reconstructs both the albedo and surface normal in both confocal and non-confocal measurement scenarios. So far, this is the only method that can reconstruct the hidden targets in these scenarios. For scenarios without limiations on the relay surface, the exposure time can be reduced significantly by applying the CC-SOCR method to spatially sparse measurements. For real-time NLOS detection, we propose the signal-surface collaborative regularization (SSCR) method, which provides NLOS reconstructions with an extreme small number of measurements. This method works under both confocal and non-confocal settings. We report the reconstruction of a hidden target with complex geometric structures with only 5 × 5 confocal measurements from public datasets, indicating an acceleration of the original measurement process by a factor of at least 10,000, so that real-time detection can be realized.
