Vivek K Goyal

Sheila Seidel, Hoover Rueda-Chacon, Iris Cusini et al.

The ability to form non-line-of-sight (NLOS) images of changing scenes could be transformative in a variety of fields, including search and rescue, autonomous vehicle navigation, and reconnaissance. Most existing active NLOS methods illuminate the hidden scene using a pulsed laser directed at a relay surface and collect time-resolved measurements of returning light. The prevailing approaches include raster scanning of a rectangular grid on a vertical wall opposite the volume of interest to generate a collection of confocal measurements. These are inherently limited by the need for laser scanning. Methods that avoid laser scanning track the moving parts of the hidden scene as one or two point targets. In this work, based on more complete optical response modeling yet still without multiple illumination positions, we demonstrate accurate reconstructions of objects in motion and a 'map' of the stationary scenery behind them. The ability to count, localize, and characterize the sizes of hidden objects in motion, combined with mapping of the stationary hidden scene, could greatly improve indoor situational awareness in a variety of applications.

Unay Dorken Gallastegi, Hoover Rueda-Chacon, Martin J. Stevens et al.

Passive hyperspectral longwave infrared measurements are remarkably informative about the surroundings. Remote object material and temperature determine the spectrum of thermal radiance, and range, air temperature, and gas concentrations determine how this spectrum is modified by propagation to the sensor. We introduce a passive range imaging method based on computationally separating these phenomena. Previous methods assume hot and highly emitting objects; ranging is more challenging when objects' temperatures do not deviate greatly from air temperature. Our method jointly estimates range and intrinsic object properties, with explicit consideration of air emission, though reflected light is assumed negligible. Inversion being underdetermined is mitigated by using a parametric model of atmospheric absorption and regularizing for smooth emissivity estimates. To assess where our estimate is likely accurate, we introduce a technique to detect which scene pixels are significantly influenced by reflected downwelling. Monte Carlo simulations demonstrate the importance of regularization, temperature differentials, and availability of many spectral bands. We apply our method to longwave infrared (8--13 $μ$m) hyperspectral image data acquired from natural scenes with no active illumination. Range features from 15m to 150m are recovered, with good qualitative match to lidar data for pixels classified as having negligible reflected downwelling.

Alexander Mehta, Ruangrawee Kitichotkul, Vivek K Goyal et al.

Equivariant imaging (EI) enables training signal reconstruction models without requiring ground truth data by leveraging signal symmetries. Deep equilibrium models (DEQs) are a powerful class of neural networks where the output is a fixed point of a learned operator. However, training DEQs with complex EI losses requires implicit differentiation through fixed-point computations, whose implementation can be challenging. We show that backpropagation can be implemented modularly, simplifying training. Experiments demonstrate that DEQs trained with implicit differentiation outperform those trained with Jacobian-free backpropagation and other baseline methods. Additionally, we find evidence that EI-trained DEQs approximate the proximal map of an invariant prior.

Sheila W. Seidel, John Murray-Bruce, Yanting Ma et al.

Passive non-line-of-sight imaging methods are often faster and stealthier than their active counterparts, requiring less complex and costly equipment. However, many of these methods exploit motion of an occluder or the hidden scene, or require knowledge or calibration of complicated occluders. The edge of a wall is a known and ubiquitous occluding structure that may be used as an aperture to image the region hidden behind it. Light from around the corner is cast onto the floor forming a fan-like penumbra rather than a sharp shadow. Subtle variations in the penumbra contain a remarkable amount of information about the hidden scene. Previous work has leveraged the vertical nature of the edge to demonstrate 1D (in angle measured around the corner) reconstructions of moving and stationary hidden scenery from as little as a single photograph of the penumbra. In this work, we introduce a second reconstruction dimension: range measured from the edge. We derive a new forward model, accounting for radial falloff, and propose two inversion algorithms to form 2D reconstructions from a single photograph of the penumbra. Performances of both algorithms are demonstrated on experimental data corresponding to several different hidden scene configurations. A Cramer-Rao bound analysis further demonstrates the feasibility (and utility) of the 2D corner camera.

Joshua Rapp, Charles Saunders, Julián Tachella et al.

Non-line-of-sight (NLOS) imaging is a rapidly growing field seeking to form images of objects outside the field of view, with potential applications in search and rescue, reconnaissance, and even medical imaging. The critical challenge of NLOS imaging is that diffuse reflections scatter light in all directions, resulting in weak signals and a loss of directional information. To address this problem, we propose a method for seeing around corners that derives angular resolution from vertical edges and longitudinal resolution from the temporal response to a pulsed light source. We introduce an acquisition strategy, scene response model, and reconstruction algorithm that enable the formation of 2.5-dimensional representations -- a plan view plus heights -- and a 180$^{\circ}$ field of view (FOV) for large-scale scenes. Our experiments demonstrate accurate reconstructions of hidden rooms up to 3 meters in each dimension.

Daewon Seo, Ravi Kiran Raman, Joong Bum Rhim et al.

This work explores a social learning problem with agents having nonidentical noise variances and mismatched beliefs. We consider an $N$-agent binary hypothesis test in which each agent sequentially makes a decision based not only on a private observation, but also on preceding agents' decisions. In addition, the agents have their own beliefs instead of the true prior, and have nonidentical noise variances in the private signal. We focus on the Bayes risk of the last agent, where preceding agents are selfish. We first derive the optimal decision rule by recursive belief update and conclude, counterintuitively, that beliefs deviating from the true prior could be optimal in this setting. The effect of nonidentical noise levels in the two-agent case is also considered and analytical properties of the optimal belief curves are given. Next, we consider a predecessor selection problem wherein the subsequent agent of a certain belief chooses a predecessor from a set of candidates with varying beliefs. We characterize the decision region for choosing such a predecessor and argue that a subsequent agent with beliefs varying from the true prior often ends up selecting a suboptimal predecessor, indicating the need for a social planner. Lastly, we discuss an augmented intelligence design problem that uses a model of human behavior from cumulative prospect theory and investigate its near-optimality and suboptimality.

Safa C. Medin, John Murray-Bruce, David Castañón et al.

Estimating the parameter of a Bernoulli process arises in many applications, including photon-efficient active imaging where each illumination period is regarded as a single Bernoulli trial. Motivated by acquisition efficiency when multiple Bernoulli processes are of interest, we formulate the allocation of trials under a constraint on the mean as an optimal resource allocation problem. An oracle-aided trial allocation demonstrates that there can be a significant advantage from varying the allocation for different processes and inspires a simple trial allocation gain quantity. Motivated by realizing this gain without an oracle, we present a trellis-based framework for representing and optimizing stopping rules. Considering the convenient case of Beta priors, three implementable stopping rules with similar performances are explored, and the simplest of these is shown to asymptotically achieve the oracle-aided trial allocation. These approaches are further extended to estimating functions of a Bernoulli parameter. In simulations inspired by realistic active imaging scenarios, we demonstrate significant mean-squared error improvements: up to 4.36 dB for the estimation of p and up to 1.80 dB for the estimation of log p.

Adam C. Zelinski, Vivek K Goyal, Elfar Adalsteinsson

A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the matrices and lone observation, the objective is to find a simultaneously sparse set of unknown vectors that solves the system. We will refer to this as the multiple-system single-output (MSSO) simultaneous sparsity problem. This manuscript contrasts the MSSO problem with other simultaneous sparsity problems and conducts a thorough initial exploration of algorithms with which to solve it. Seven algorithms are formulated that approximately solve this NP-Hard problem. Three greedy techniques are developed (matching pursuit, orthogonal matching pursuit, and least squares matching pursuit) along with four methods based on a convex relaxation (iteratively reweighted least squares, two forms of iterative shrinkage, and formulation as a second-order cone program). The algorithms are evaluated across three experiments: the first and second involve sparsity profile recovery in noiseless and noisy scenarios, respectively, while the third deals with magnetic resonance imaging radio-frequency excitation pulse design.