Passive Scene Reconstruction in Non-line-of-sight Scenarios

Locating and identifying hidden objects can prove critical in applications ranging from military reconnaissance to emergency rescue. Although non-line-of-sight (NLOS) reconstruction and imaging have received much attention recently, state-of-the-art methods often use coherent sources (lasers) or require control of the scene. This dissertation focuses on passive NLOS scene reconstruction using the light reflected off a diffusive wall. No control over the light illuminating the scene is assumed, and the method is compatible with the partially coherent fields ubiquitous in both indoor and outdoor environments. In order to counteract the detrimental effects of the wall, rather than measuring the 2-dimensional intensity of the reflected light, we exploit the full 4-dimensional spatial coherence function to reconstruct the scene. As a step towards the NLOS problem, we first consider the line-of-sight (LOS) problem. Numerical simulations using Fresnel propagation operators show that our forward model has good agreement with experimental results. We show that numerically back-propagating the measured coherence function enables a visual estimation of the objects\u27 sizes and locations. To facilitate efficient, systematic and explicit detection of object parameters in the inverse problem, we propose a closed-form approximation of the propagated coherence function. Using this analytic solution we formulate a minimum residue optimization problem which is solved using a gradient descent algorithm. Then, for the NLOS problem, we derive an analytic model based on experimentally-verified scattering models. This model is used to study the information retained in the coherence function after the field interacts with the wall, and this insight is used to classify and estimate simple objects. Finally, we consider imaging in more complicated settings with larger objects. We formulate a multi-criteria convex optimization problem, which fuses the reflected field\u27s intensity and spatial coherence information at different scales, along with an algorithm to efficiently solve the proposed problem

Scalable and Robust Community Detection with Randomized Sketching

This paper explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is first applied to a sub-matrix of the graph's adjacency matrix associated with a reduced graph sketch constructed using random sampling. Then, the clusters of the full graph are inferred based on the clusters extracted from the sketch using a correlation-based retrieval step. Uniform random node sampling is shown to improve the computational complexity over clustering of the full graph when the cluster sizes are balanced. A new random degree-based node sampling algorithm is presented which significantly improves upon the performance of the clustering algorithm even when clusters are unbalanced. This algorithm improves the phase transitions for matrix-decomposition-based clustering with regard to computational complexity and minimum cluster size, which are shown to be nearly dimension-free in the low inter-cluster connectivity regime. A third sampling technique is shown to improve balance by randomly sampling nodes based on spatial distribution. We provide analysis and numerical results using a convex clustering algorithm based on matrix completion

Spatial coherence of fields from generalized sources in the Fresnel regime

Analytic expressions of the spatial coherence of partially coherent fields propagating in the Fresnel regime in all but the simplest of scenarios are largely lacking and calculation of the Fresnel transform typically entails tedious numerical integration. Here, we provide a closed-form approximation formula for the case of a generalized source obtained by modulating the field produced by a Gauss-Shell source model with a piecewise constant transmission function, which may be used to model the field's interaction with objects and apertures. The formula characterizes the coherence function in terms of the coherence of the Gauss-Schell beam propagated in free space and a multiplicative term capturing the interaction with the transmission function. This approximation holds in the regime where the intensity width of the beam is much larger than the coherence width under mild assumptions on the modulating transmission function. The formula derived for generalized sources lays the foundation for the study of the inverse problem of scene reconstruction from coherence measurements.Comment: Accepted for publication in JOSA

On the inverse problem of source reconstruction from coherence measurements

We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which uses the authors' recent closed-form approximation formula for the coherence of the propagated field. The developed algorithms require a small data sample for convergence and yield stable inversion by exploiting information in the coherence as opposed to intensity-only measurements. Examples with both simulated and experimental data demonstrate the ability of the proposed approach to simultaneously recover complex sources in different planes transverse to the direction of propagation

Multi-modal Non-line-of-sight Passive Imaging

We consider the non-line-of-sight (NLOS) imaging of an object using the light reflected off a diffusive wall. The wall scatters incident light such that a lens is no longer useful to form an image. Instead, we exploit the 4D spatial coherence function to reconstruct a 2D projection of the obscured object. The approach is completely passive in the sense that no control over the light illuminating the object is assumed and is compatible with the partially coherent fields ubiquitous in both the indoor and outdoor environments. We formulate a multi-criteria convex optimization problem for reconstruction, which fuses the reflected field's intensity and spatial coherence information at different scales. Our formulation leverages established optics models of light propagation and scattering and exploits the sparsity common to many images in different bases. We also develop an algorithm based on the alternating direction method of multipliers to efficiently solve the convex program proposed. A means for analyzing the null space of the measurement matrices is provided as well as a means for weighting the contribution of individual measurements to the reconstruction. This paper holds promise to advance passive imaging in the challenging NLOS regimes in which the intensity does not necessarily retain distinguishable features and provides a framework for multi-modal information fusion for efficient scene reconstruction

Automaton Distillation: Neuro-Symbolic Transfer Learning for Deep Reinforcement Learning

Reinforcement learning (RL) is a powerful tool for finding optimal policies in sequential decision processes. However, deep RL methods suffer from two weaknesses: collecting the amount of agent experience required for practical RL problems is prohibitively expensive, and the learned policies exhibit poor generalization on tasks outside of the training distribution. To mitigate these issues, we introduce automaton distillation, a form of neuro-symbolic transfer learning in which Q-value estimates from a teacher are distilled into a low-dimensional representation in the form of an automaton. We then propose two methods for generating Q-value estimates: static transfer, which reasons over an abstract Markov Decision Process constructed based on prior knowledge, and dynamic transfer, where symbolic information is extracted from a teacher Deep Q-Network (DQN). The resulting Q-value estimates from either method are used to bootstrap learning in the target environment via a modified DQN loss function. We list several failure modes of existing automaton-based transfer methods and demonstrate that both static and dynamic automaton distillation decrease the time required to find optimal policies for various decision tasks

Passive Non-Line-Of-Sight Source Classification From Coherence Measurements

We demonstrate a passive imaging approach for identifying the shape and size of a secondary source using non-line-of-sight spatial coherence measurements