arXiv subjects

Vivek K Goyal

Publications and source records attributed to Vivek K Goyal.

At least 37 records · Page 2Linked to original sources

arXiv2019

Source Shot Noise Mitigation in Focused Ion Beam Microscopy by Time-Resolved Measurement

Focused ion beam (FIB) microscopy suffers from source shot noise - random variation in the number of incident ions in any fixed dwell time - along with random variation in the number of detected secondary electrons per incident ion. This multiplicity of sources of randomness increases the variance of the measurements and thus worsens the trade-off between incident ion dose and image accuracy. Time-resolved sensing combined with maximum likelihood estimation from the resulting sets of measurements greatly reduces the effect of source shot noise. Through Fisher information analysis and Monte Carlo simulations, the reduction in mean-squared error or reduction in required dose is shown to be by a factor approximately equal to the secondary electron yield. Experiments with a helium ion microscope (HIM) are consistent with the analyses and suggest accuracy improvement for a fixed source dose, or reduced source dose for a desired imaging accuracy, by a factor of about 3.

cond-mat.mtrl-sci↗

arXiv2019

Beyond Binomial and Negative Binomial: Adaptation in Bernoulli Parameter Estimation

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.

stat.AP↗

arXiv2019

Dead Time Compensation for High-Flux Ranging

Dead time effects have been considered a major limitation for fast data acquisition in various time-correlated single photon counting applications, since a commonly adopted approach for dead time mitigation is to operate in the low-flux regime where dead time effects can be ignored. Through the application of lidar ranging, this work explores the empirical distribution of detection times in the presence of dead time and demonstrates that an accurate statistical model can result in reduced ranging error with shorter data acquisition time when operating in the high-flux regime. Specifically, we show that the empirical distribution of detection times converges to the stationary distribution of a Markov chain. Depth estimation can then be performed by passing the empirical distribution through a filter matched to the stationary distribution. Moreover, based on the Markov chain model, we formulate the recovery of arrival distribution from detection distribution as a nonlinear inverse problem and solve it via provably convergent mathematical optimization. By comparing per-detection Fisher information for depth estimation from high- and low-flux detection time distributions, we provide an analytical basis for possible improvement of ranging performance resulting from the presence of dead time. Finally, we demonstrate the effectiveness of our formulation and algorithm via simulations of lidar ranging.

eess.SP↗

arXiv2019

Estimation from Quantized Gaussian Measurements: When and How to Use Dither

Subtractive dither is a powerful method for removing the signal dependence of quantization noise for coarsely-quantized signals. However, estimation from dithered measurements often naively applies the sample mean or midrange, even when the total noise is not well described with a Gaussian or uniform distribution. We show that the generalized Gaussian distribution approximately describes subtractively-dithered, quantized samples of a Gaussian signal. Furthermore, a generalized Gaussian fit leads to simple estimators based on order statistics that match the performance of more complicated maximum likelihood estimators requiring iterative solvers. The order statistics-based estimators outperform both the sample mean and midrange for nontrivial sums of Gaussian and uniform noise. Additional analysis of the generalized Gaussian approximation yields rules of thumb for determining when and how to apply dither to quantized measurements. Specifically, we find subtractive dither to be beneficial when the ratio between the Gaussian standard deviation and quantization interval length is roughly less than 1/3. If that ratio is also greater than 0.822/$K^{0.930}$ for the number of measurements $K>20$, we present estimators more efficient than the midrange.

stat.AP↗

arXiv2016

A Few Photons Among Many: Unmixing Signal and Noise for Photon-Efficient Active Imaging

Conventional LIDAR systems require hundreds or thousands of photon detections to form accurate depth and reflectivity images. Recent photon-efficient computational imaging methods are remarkably effective with only 1.0 to 3.0 detected photons per pixel, but they are not demonstrated at signal-to-background ratio (SBR) below 1.0 because their imaging accuracies degrade significantly in the presence of high background noise. We introduce a new approach to depth and reflectivity estimation that focuses on unmixing contributions from signal and noise sources. At each pixel in an image, short-duration range gates are adaptively determined and applied to remove detections likely to be due to noise. For pixels with too few detections to perform this censoring accurately, we borrow data from neighboring pixels to improve depth estimates, where the neighborhood formation is also adaptive to scene content. Algorithm performance is demonstrated on experimental data at varying levels of noise. Results show improved performance of both reflectivity and depth estimates over state-of-the-art methods, especially at low signal-to-background ratios. In particular, accurate imaging is demonstrated with SBR as low as 0.04. This validation of a photon-efficient, noise-tolerant method demonstrates the viability of rapid, long-range, and low-power LIDAR imaging.

stat.AP↗

arXiv2015

Single-Photon Depth Imaging Using a Union-of-Subspaces Model

Light detection and ranging systems reconstruct scene depth from time-of-flight measurements. For low light-level depth imaging applications, such as remote sensing and robot vision, these systems use single-photon detectors that resolve individual photon arrivals. Even so, they must detect a large number of photons to mitigate Poisson shot noise and reject anomalous photon detections from background light. We introduce a novel framework for accurate depth imaging using a small number of detected photons in the presence of an unknown amount of background light that may vary spatially. It employs a Poisson observation model for the photon detections plus a union-of-subspaces constraint on the discrete-time flux from the scene at any single pixel. Together, they enable a greedy signal-pursuit algorithm to rapidly and simultaneously converge on accurate estimates of scene depth and background flux, without any assumptions on spatial correlations of the depth or background flux. Using experimental single-photon data, we demonstrate that our proposed framework recovers depth features with 1.7 cm absolute error, using 15 photons per image pixel and an illumination pulse with 6.7-cm scaled root-mean-square length. We also show that our framework outperforms the conventional pixelwise log-matched filtering, which is a computationally-efficient approximation to the maximum-likelihood solution, by a factor of 6.1 in absolute depth error.

stat.AP↗

arXiv2014

Photon-Efficient Computational 3D and Reflectivity Imaging with Single-Photon Detectors

Capturing depth and reflectivity images at low light levels from active illumination of a scene has wide-ranging applications. Conventionally, even with single-photon detectors, hundreds of photon detections are needed at each pixel to mitigate Poisson noise. We develop a robust method for estimating depth and reflectivity using on the order of 1 detected photon per pixel averaged over the scene. Our computational imager combines physically accurate single-photon counting statistics with exploitation of the spatial correlations present in real-world reflectivity and 3D structure. Experiments conducted in the presence of strong background light demonstrate that our computational imager is able to accurately recover scene depth and reflectivity, while traditional maximum-likelihood based imaging methods lead to estimates that are highly noisy. Our framework increases photon efficiency 100-fold over traditional processing and also improves, somewhat, upon first-photon imaging under a total acquisition time constraint in raster-scanned operation. Thus our new imager will be useful for rapid, low-power, and noise-tolerant active optical imaging, and its fixed dwell time will facilitate parallelization through use of a detector array.

stat.AP↗

arXiv2014

Distributed Hypothesis Testing with Social Learning and Symmetric Fusion

We study the utility of social learning in a distributed detection model with agents sharing the same goal: a collective decision that optimizes an agreed upon criterion. We show that social learning is helpful in some cases but is provably futile (and thus essentially a distraction) in other cases. Specifically, we consider Bayesian binary hypothesis testing performed by a distributed detection and fusion system, where all decision-making agents have binary votes that carry equal weight. Decision-making agents in the team sequentially make local decisions based on their own private signals and all precedent local decisions. It is shown that the optimal decision rule is not affected by precedent local decisions when all agents observe conditionally independent and identically distributed private signals. Perfect Bayesian reasoning will cancel out all effects of social learning. When the agents observe private signals with different signal-to-noise ratios, social learning is again futile if the team decision is only approved by unanimity. Otherwise, social learning can strictly improve the team performance. Furthermore, the order in which agents make their decisions affects the team decision.

cs.IT↗

arXiv2012

Social Teaching: Being Informative vs. Being Right in Sequential Decision Making

We show that it can be suboptimal for Bayesian decision-making agents employing social learning to use correct prior probabilities as their initial beliefs. We consider sequential Bayesian binary hypothesis testing where each individual agent makes a binary decision based on an initial belief, a private signal, and the decisions of all earlier-acting agents---with the actions of precedent agents causing updates of the initial belief. Each agent acts to minimize Bayes risk, with all agents sharing the same Bayes costs for Type I (false alarm) and Type II (missed detection) errors. The effect of the set of initial beliefs on the decision-making performance of the last agent is studied. The last agent makes the best decision when the initial beliefs are inaccurate. When the private signals are described by Gaussian likelihoods, the optimal initial beliefs are not haphazard but rather follow a systematic pattern: the earlier-acting agents should act as if the prior probability is larger than it is in reality when the true prior probability is small, and vice versa. We interpret this as being open minded toward the unlikely hypothesis. The early-acting agents face a trade-off between making a correct decision and being maximally informative to the later-acting agents.

cs.IT↗

arXiv2012

Distributed Functional Scalar Quantization Simplified

Distributed functional scalar quantization (DFSQ) theory provides optimality conditions and predicts performance of data acquisition systems in which a computation on acquired data is desired. We address two limitations of previous works: prohibitively expensive decoder design and a restriction to sources with bounded distributions. We rigorously show that a much simpler decoder has equivalent asymptotic performance as the conditional expectation estimator previously explored, thus reducing decoder design complexity. The simpler decoder has the feature of decoupled communication and computation blocks. Moreover, we extend the DFSQ framework with the simpler decoder to acquire sources with infinite-support distributions such as Gaussian or exponential distributions. Finally, through simulation results we demonstrate that performance at moderate coding rates is well predicted by the asymptotic analysis, and we give new insight on the rate of convergence.

cs.IT↗

arXiv2011

Ranked Sparse Signal Support Detection

This paper considers the problem of detecting the support (sparsity pattern) of a sparse vector from random noisy measurements. Conditional power of a component of the sparse vector is defined as the energy conditioned on the component being nonzero. Analysis of a simplified version of orthogonal matching pursuit (OMP) called sequential OMP (SequOMP) demonstrates the importance of knowledge of the rankings of conditional powers. When the simple SequOMP algorithm is applied to components in nonincreasing order of conditional power, the detrimental effect of dynamic range on thresholding performance is eliminated. Furthermore, under the most favorable conditional powers, the performance of SequOMP approaches maximum likelihood performance at high signal-to-noise ratio.

cs.IT↗

arXiv2011

Time-Stampless Adaptive Nonuniform Sampling for Stochastic Signals

In this paper, we introduce a time-stampless adaptive nonuniform sampling (TANS) framework, in which time increments between samples are determined by a function of the $m$ most recent increments and sample values. Since only past samples are used in computing time increments, it is not necessary to save sampling times (time stamps) for use in the reconstruction process. We focus on two TANS schemes for discrete-time stochastic signals: a greedy method, and a method based on dynamic programming. We analyze the performances of these schemes by computing (or bounding) their trade-offs between sampling rate and expected reconstruction distortion for autoregressive and Markovian signals. Simulation results support the analysis of the sampling schemes. We show that, by opportunistically adapting to local signal characteristics, TANS may lead to improved power efficiency in some applications.

cs.IT↗

arXiv2011

Asymptotic Analysis of MAP Estimation via the Replica Method and Applications to Compressed Sensing

The replica method is a non-rigorous but well-known technique from statistical physics used in the asymptotic analysis of large, random, nonlinear problems. This paper applies the replica method, under the assumption of replica symmetry, to study estimators that are maximum a posteriori (MAP) under a postulated prior distribution. It is shown that with random linear measurements and Gaussian noise, the replica-symmetric prediction of the asymptotic behavior of the postulated MAP estimate of an n-dimensional vector "decouples" as n scalar postulated MAP estimators. The result is based on applying a hardening argument to the replica analysis of postulated posterior mean estimators of Tanaka and of Guo and Verdu. The replica-symmetric postulated MAP analysis can be readily applied to many estimators used in compressed sensing, including basis pursuit, lasso, linear estimation with thresholding, and zero norm-regularized estimation. In the case of lasso estimation the scalar estimator reduces to a soft-thresholding operator, and for zero norm-regularized estimation it reduces to a hard-threshold. Among other benefits, the replica method provides a computationally-tractable method for precisely predicting various performance metrics including mean-squared error and sparsity pattern recovery probability.

cs.IT↗

arXiv2011

Quantization of Prior Probabilities for Collaborative Distributed Hypothesis Testing

This paper studies the quantization of prior probabilities, drawn from an ensemble, for distributed detection and data fusion. Design and performance equivalences between a team of N agents tied by a fixed fusion rule and a more powerful single agent are obtained. Effects of identical quantization and diverse quantization are compared. Consideration of perceived common risk enables agents using diverse quantizers to collaborate in hypothesis testing, and it is proven that the minimum mean Bayes risk error is achieved by diverse quantization. The comparison shows that optimal diverse quantization with K cells per quantizer performs as well as optimal identical quantization with N(K-1)+1 cells per quantizer. Similar results are obtained for maximum Bayes risk error as the distortion criterion.

cs.IT↗

arXiv2011

Scalar Quantization with Random Thresholds

The distortion-rate performance of certain randomly-designed scalar quantizers is determined. The central results are the mean-squared error distortion and output entropy for quantizing a uniform random variable with thresholds drawn independently from a uniform distribution. The distortion is at most 6 times that of an optimal (deterministically-designed) quantizer, and for a large number of levels the output entropy is reduced by approximately (1-gamma)/(ln 2) bits, where gamma is the Euler-Mascheroni constant. This shows that the high-rate asymptotic distortion of these quantizers in an entropy-constrained context is worse than the optimal quantizer by at most a factor of 6 exp(-2(1-gamma)).

cs.IT↗

arXiv2011

Channels That Die

Given the possibility of communication systems failing catastrophically, we investigate limits to communicating over channels that fail at random times. These channels are finite-state semi-Markov channels. We show that communication with arbitrarily small probability of error is not possible. Making use of results in finite blocklength channel coding, we determine sequences of blocklengths that optimize transmission volume communicated at fixed maximum message error probabilities. We provide a partial ordering of communication channels. A dynamic programming formulation is used to show the structural result that channel state feedback does not improve performance.

cs.IT↗

arXiv2011

Distributed Scalar Quantization for Computing: High-Resolution Analysis and Extensions

Communication of quantized information is frequently followed by a computation. We consider situations of \emph{distributed functional scalar quantization}: distributed scalar quantization of (possibly correlated) sources followed by centralized computation of a function. Under smoothness conditions on the sources and function, companding scalar quantizer designs are developed to minimize mean-squared error (MSE) of the computed function as the quantizer resolution is allowed to grow. Striking improvements over quantizers designed without consideration of the function are possible and are larger in the entropy-constrained setting than in the fixed-rate setting. As extensions to the basic analysis, we characterize a large class of functions for which regular quantization suffices, consider certain functions for which asymptotic optimality is achieved without arbitrarily fine quantization, and allow limited collaboration between source encoders. In the entropy-constrained setting, a single bit per sample communicated between encoders can have an arbitrarily-large effect on functional distortion. In contrast, such communication has very little effect in the fixed-rate setting.

cs.IT↗

arXiv2011

Malleable Coding with Fixed Reuse

In cloud computing, storage area networks, remote backup storage, and similar settings, stored data is modified with updates from new versions. Representing information and modifying the representation are both expensive. Therefore it is desirable for the data to not only be compressed but to also be easily modified during updates. A malleable coding scheme considers both compression efficiency and ease of alteration, promoting codeword reuse. We examine the trade-off between compression efficiency and malleability cost-the difficulty of synchronizing compressed versions-measured as the length of a reused prefix portion. Through a coding theorem, the region of achievable rates and malleability is expressed as a single-letter optimization. Relationships to common information problems are also described.

cs.IT↗