arXiv subjects

Vivek K Goyal

Publications and source records attributed to Vivek K Goyal.

At least 19 recordsLinked to original sources

arXiv2026

High-Flux Count-Free Single-Photon 3D Cameras

Single-photon cameras based on single-photon avalanche diode (SPAD) technology are gaining popularity for 3D sensing, thanks to their extreme sensitivity and time resolution. There are two key challenges with single-photon cameras that limit their widespread use: (i) they suffer from non-linear distortions called ''pile-up'' when operated in high-photon-flux conditions, and (ii) they generate a large volume of raw photon data, creating a severe data bottleneck at each sensor pixel. In this work, we show that while compressive capture techniques successfully mitigate data transfer challenges, they exacerbate the effects of dead-time distortion because they fail to retain sufficient information about the photon detection history to allow post-processing pile-up correction via existing methods. We propose a new computational-imaging method that combines free-running capture with an analysis-by-synthesis software pipeline to mitigate pile-up distortions. Our results with hardware emulations and full-scene and single-pixel simulations show that our method can reliably capture scene distance and reflectance over a wide range of illumination conditions. Our work will enable high-resolution SPAD cameras that are severely bandwidth-constrained to operate in real-world high-flux scenarios.

cs.CV↗

arXiv2026

FMCW Lidar Beyond Nyquist by Instantaneous Frequency Fitting

Frequency-modulated continuous-wave (FMCW) lidar conventionally estimates distance and velocity from constant beat frequencies generated through interferometry. Existing FMCW implementations emphasize simple signal processing -- e.g., beat frequency estimation via a fast Fourier transform (FFT) algorithm plus peak-finding -- which results in hardware-focused solutions requiring linear swept-frequency laser sources or linearized resampling. However, the maximum achievable distance by this method is limited by the need to sample the interference signal without aliasing. In this work, we propose two signal processing methods: matched filtering and instantaneous frequency fitting. These two methods can recover larger ranges of distance and velocity by considering the full waveform despite aliasing in the frequency domain. Furthermore, the FMCW lidar signal is often corrupted by phase noise, and we show that the instantaneous frequency fitting approach is more robust than matched filtering by considering the deviation in the phase. We present comprehensive simulation studies along with theoretical analysis using the misspecified Cramér--Rao bound. As these methods are flexible to arbitrary frequency modulation, we also show results for non-linear modulations that could yield better sensitivity to distance and velocity compared to the popular triangular modulation.

eess.SP↗

arXiv2026

Beam Cross Sections Create Mixtures: Improving Feature Localization in Secondary Electron Imaging

Secondary electron (SE) imaging techniques, such as scanning electron microscopy and helium ion microscopy (HIM), use electrons emitted by a sample in response to a focused beam of charged particles incident at a grid of raster scan positions. Spot size -- the diameter of the incident beam's spatial profile -- is one of the limiting factors for resolution, along with various sources of noise in the SE signal. The effect of the beam spatial profile is commonly understood as convolutional. We show that under a simple and plausible physical abstraction for the beam, though convolution describes the mean of the SE counts, the full distribution of SE counts is a mixture. We demonstrate that this more detailed modeling can enable resolution improvements over conventional estimators through a stylized application inspired by semiconductor inspection: localizing the edge in a two-valued sample. We derive Fisher information about edge location in conventional and time-resolved measurements (TRM) and also derive the maximum likelihood estimate (MLE) from the latter. Empirically, the MLE computed from TRM is approximately efficient except at very low beam diameter, so Fisher information comparisons are predictive of performance and can be used to optimize the beam diameter relative to the raster scan spacing. Monte Carlo simulations provide an example of the MLE giving a 5-fold reduction in root mean-squared error (RMSE) of edge localization as compared to conventional interpolation-based estimation. The RMSE is substantially below both the beam diameter and the raster scan spacing and thus sub-pixel localization is demonstrated. Applied to three real HIM datasets, the average RMSE reduction factor is 5.4.

eess.SP↗

arXiv2026

Ozone Cues Mitigate Reflected Downwelling Radiance in LWIR Absorption-Based Ranging

Passive long-wave infrared (LWIR) absorption-based ranging relies on atmospheric absorption to estimate distances to objects from their emitted thermal radiation. First demonstrated decades ago for objects much hotter than the air and recently extended to scenes with low temperature variations, this ranging has depended on reflected radiance being negligible. Downwelling radiance is especially problematic, sometimes causing large inaccuracies. In two new ranging methods, we use characteristic features from ozone absorption to estimate the contribution of reflected downwelling radiance. The quadspectral method gives a simple closed-form range estimate from four narrowband measurements, two at a water vapor absorption line and two at an ozone absorption line. The hyperspectral method uses a broader spectral range to improve accuracy while also providing estimates of temperature, emissivity profiles, and contributions of downwelling from a collection of zenith angles. Experimental results demonstrate improved ranging accuracy, in one case reducing error from over 100 m when reflected light is not modeled to 6.8 m with the quadspectral method and 1.2 m with the hyperspectral method.

cs.CV↗

arXiv2025

Equivariant Deep Equilibrium Models for Imaging Inverse Problems

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.

eess.IV↗

arXiv2025

Free-running vs. Synchronous: Single-Photon Lidar for High-flux 3D Imaging

Conventional wisdom suggests that single-photon lidar (SPL) should operate in low-light conditions to minimize dead-time effects. Many methods have been developed to mitigate these effects in synchronous SPL systems. However, solutions for free-running SPL remain limited despite the advantage of reduced histogram distortion from dead times. To improve the accuracy of free-running SPL, we propose a computationally efficient joint maximum likelihood estimator of the signal flux, the background flux, and the depth using only histograms, along with a complementary regularization framework that incorporates a learned point cloud score model as a prior. Simulations and experiments demonstrate that free-running SPL yields lower estimation errors than its synchronous counterpart under identical conditions, with our regularization further improving accuracy.

eess.SP↗

arXiv2025

Image Reconstruction from Readout-Multiplexed Single-Photon Detector Arrays

Readout multiplexing is a promising solution to overcome hardware limitations and data bottlenecks in imaging with single-photon detectors. Conventional multiplexed readout processing creates an upper bound on photon counts at a very fine time scale, where frames with multiple detected photons must either be discarded or allowed to introduce significant bias. We formulate multiphoton coincidence resolution as an inverse imaging problem and introduce a solution framework to probabilistically resolve the spatial locations of photon incidences. Specifically, we develop a theoretical abstraction of row--column multiplexing and a model of photon events that make readouts ambiguous. Using this, we propose a novel estimator that spatially resolves up to four coincident photons. Monte Carlo simulations show that our proposed method increases the peak signal-to-noise ratio (PSNR) of reconstruction by 3 to 4 dB compared to conventional methods under optimal incident flux conditions. Additionally, this method reduces the required number of readout frames to achieve the same mean-squared error as other methods by a factor of ~4. Finally, our method matches the Cramer--Rao bound for detection probability estimation for a wider range of incident flux values compared to conventional methods. While demonstrated for a specific detector type and readout architecture, this method can be extended to more general multiplexing with different detector models.

quant-ph↗

arXiv2025

Absorption-Based, Passive Range Imaging from Hyperspectral Thermal Measurements

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.

cs.CV↗

arXiv2024

Shot noise-mitigated secondary electron imaging with ion count-aided microscopy

Modern science is dependent on imaging on the nanoscale, often achieved through processes that detect secondary electrons created by a highly focused incident charged particle beam. Multiple types of measurement noise limit the ultimate trade-off between the image quality and the incident particle dose, which can preclude useful imaging of dose-sensitive samples. Existing methods to improve image quality do not fundamentally mitigate the noise sources. Furthermore, barriers to assigning a physically meaningful scale make the images qualitative. Here we introduce ion count-aided microscopy (ICAM), which is a quantitative imaging technique that uses statistically principled estimation of the secondary electron yield. With a readily implemented change in data collection, ICAM substantially reduces source shot noise. In helium ion microscopy, we demonstrate 3x dose reduction and a good match between these empirical results and theoretical performance predictions. ICAM facilitates imaging of fragile samples and may make imaging with heavier particles more attractive.

physics.med-ph↗

arXiv2023

Denoising Particle Beam Micrographs with Plug-and-Play Methods

In a particle beam microscope, a raster-scanned focused beam of particles interacts with a sample to generate a secondary electron (SE) signal pixel by pixel. Conventionally formed micrographs are noisy because of limitations on acquisition time and dose. Recent work has shown that estimation methods applicable to a time-resolved measurement paradigm can greatly reduce noise, but these methods apply pixel by pixel without exploiting image structure. Raw SE count data can be modeled with a compound Poisson (Neyman Type A) likelihood, which implies data variance that is signal-dependent and greater than the variation in the underlying particle-sample interaction. These statistical properties make methods that assume additive white Gaussian noise ineffective. This paper introduces methods for particle beam micrograph denoising that use the plug-and-play framework to exploit image structure while being applicable to the unusual data likelihoods of this modality. Approximations of the data likelihood that vary in accuracy and computational complexity are combined with denoising by total variation regularization, BM3D, and DnCNN. Methods are provided for both conventional and time-resolved measurements, assuming SE counts are available. In simulations representative of helium ion microscopy and scanning electron microscopy, significant improvements in root mean-squared error (RMSE), structural similarity index measure (SSIM), and qualitative appearance are obtained. Average reductions in RMSE are by factors ranging from 2.24 to 4.11.

physics.med-ph↗

arXiv2022

Non-Line-of-Sight Tracking and Mapping with an Active Corner Camera

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.

eess.IV↗

arXiv2022

Time-Resolved Focused Ion Beam Microscopy: Modeling, Estimation Methods, and Analyses

In a focused ion beam (FIB) microscope, source particles interact with a small volume of a sample to generate secondary electrons that are detected, pixel by pixel, to produce a micrograph. Randomness of the number of incident particles causes excess variation in the micrograph, beyond the variation in the underlying particle-sample interaction. We recently demonstrated that joint processing of multiple time-resolved measurements from a single pixel can mitigate this effect of source shot noise in helium ion microscopy. This paper is focused on establishing a rigorous framework for understanding the potential for this approach. It introduces idealized continuous- and discrete-time abstractions of FIB microscopy with direct electron detection and estimation-theoretic limits of imaging performance under these measurement models. Novel estimators for use with continuous-time measurements are introduced and analyzed, and estimators for use with discrete-time measurements are analyzed and shown to approach their continuous-time counterparts as time resolution is increased. Simulated FIB microscopy results are consistent with theoretical analyses and demonstrate that substantial improvements over conventional FIB microscopy image formation are made possible by time-resolved measurement.

physics.med-ph↗

arXiv2021

Online Beam Current Estimation in Particle Beam Microscopy

In conventional particle beam microscopy, knowledge of the beam current is essential for accurate micrograph formation and sample milling. This generally necessitates offline calibration of the instrument. In this work, we establish that beam current can be estimated online, from the same secondary electron count data that is used to form micrographs. Our methods depend on the recently introduced time-resolved measurement concept, which combines multiple short measurements at a single pixel and has previously been shown to partially mitigate the effect of beam current variation on micrograph accuracy. We analyze the problem of jointly estimating beam current and secondary electron yield using the Cramer-Rao bound. Joint estimators operating at a single pixel and estimators that exploit models for inter-pixel correlation and Markov beam current variation are proposed and tested on synthetic microscopy data. Our estimates of secondary electron yield that incorporate explicit beam current estimation beat state-of-the-art methods, resulting in micrograph accuracy nearly indistinguishable from what is obtained with perfect beam current knowledge. Our novel beam current estimation could help improve milling outcomes, prevent sample damage, and enable online instrument diagnostics.

physics.med-ph↗

arXiv2020

Compressively sampling the optical transmission matrix of a multimode fibre

Measurement of the optical transmission matrix (TM) of an opaque material is an advanced form of space-variant aberration correction. Beyond imaging, TM-based methods are emerging in a range of fields including optical communications, optical micro-manipulation, and optical computing. In many cases the TM is very sensitive to perturbations in the configuration of the scattering medium it represents. Therefore applications often require an up-to-the-minute characterisation of the fragile TM, typically entailing hundreds to thousands of probe measurements. In this work we explore how these measurement requirements can be relaxed using the framework of compressive sensing: incorporation of prior information enables accurate estimation from fewer measurements than the dimensionality of the TM we aim to reconstruct. Examples of such priors include knowledge of a memory effect linking input and output fields, an approximate model of the optical system, or a recent but degraded TM measurement. We demonstrate this concept by reconstructing a full-size TM of a multimode fibre supporting 754 modes at compression ratios down to ~5% with good fidelity. The level of compression achievable is dependent upon the strength of our priors. We show in this case that imaging is still possible using TMs reconstructed at compression ratios down to ~1% (8 probe measurements). This compressive TM sampling strategy is quite general and may be applied to any form of scattering system about which we have some prior knowledge, including diffusers, thin layers of tissue, fibre optics of any known refractive profile, and reflections from opaque walls. These approaches offer a route to measurement of high-dimensional TMs quickly or with access to limited numbers of measurements.

physics.optics↗

arXiv2020

SWAGGER: Sparsity Within and Across Groups for General Estimation and Recovery

Penalty functions or regularization terms that promote structured solutions to optimization problems are of great interest in many fields. Proposed in this work is a nonconvex structured sparsity penalty that promotes one-sparsity within arbitrary overlapping groups in a vector. This allows one to enforce mutual exclusivity between components within solutions to optimization problems. We show multiple example use cases (including a total variation variant), demonstrate synergy between it and other regularizers, and propose an algorithm to efficiently solve problems regularized or constrained by the proposed penalty.

math.OC↗

arXiv2020

Two-Dimensional Non-Line-of-Sight Scene Estimation from a Single Edge Occluder

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.

eess.IV↗

arXiv2020

Seeing Around Corners with Edge-Resolved Transient Imaging

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.

eess.IV↗

arXiv2019

Beliefs in Decision-Making Cascades

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.

cs.GT↗