College of Engineering
https://hdl.handle.net/2144/971
2021-06-11T21:16:24ZQuantization of prior probabilities for collaborative distributed hypothesis testing
https://hdl.handle.net/2144/42552
Quantization of prior probabilities for collaborative distributed hypothesis testing
Rhim, Joong Bum; Varshney, Lav R.; Goyal, Vivek K.
This paper studies the quantization of prior probabilities, drawn from an ensemble, in distributed detection with data fusion by combination of binary local decisions. Design and performance equivalences between a team of N agents and a more powerful single agent are obtained. Effects of identical quantization and diverse quantization on mean Bayes risk are compared. It is shown that when agents using diverse quantizers interact to agree on a perceived common risk, the effective number quantization levels is increased. With this collaboration, optimal diverse regular 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 the maximum Bayes risk error criterion.
2012-09-01T00:00:00ZComputational nanosensing from defocus in single particle interferometric reflectance microscopy
https://hdl.handle.net/2144/42545
Computational nanosensing from defocus in single particle interferometric reflectance microscopy
Yurdakul, Celalettin; Ünlü, M. Selim
Single particle interferometric reflectance (SPIR) microscopy has been studied as a powerful imaging platform for label-free and highly sensitive biological nanoparticle detection and characterization. SPIR's interferometric nature yields a unique 3D defocus intensity profile of the nanoparticles over a large field of view. Here, we utilize this defocus information to recover high signal-to-noise ratio nanoparticle images with a computationally and memory efficient reconstruction framework. Our direct inversion approach recovers this image from a 3D defocus intensity stack using the vectorial-optics-based forward model developed for sub-diffraction-limited dielectric nanoparticles captured on a layered substrate. We demonstrate proof-of-concept experiments on silica beads with a 50 nm nominal diameter.
2020-12-01T00:00:00ZTime-stampless adaptive nonuniform sampling for stochastic signals
https://hdl.handle.net/2144/42544
Time-stampless adaptive nonuniform sampling for stochastic signals
Feizi, Soheil; Goyal, Vivek K.; Medard, Muriel
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.
2012-10-01T00:00:00ZRanked sparse signal support detection
https://hdl.handle.net/2144/42543
Ranked sparse signal support detection
Fletcher, A.K.; Rangan, S.; Goyal, V.K.
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.
2012-11-01T00:00:00ZDistributed functional scalar quantization simplified
https://hdl.handle.net/2144/42542
Distributed functional scalar quantization simplified
Sun, John Z.; Misra, Vinith; Goyal, Vivek K.
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 source distributions with bounded support. We show that a much simpler decoder has equivalent asymptotic performance to the conditional expectation estimator studied previously, thus reducing decoder design complexity. The simpler decoder features decoupled communication and computation blocks. Moreover, we extend the DFSQ framework with the simpler decoder to source distributions with unbounded support. 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.
2013-07-01T00:00:00ZIntersensor collaboration in distributed quantization networks
https://hdl.handle.net/2144/42541
Intersensor collaboration in distributed quantization networks
Sun, John Z.; Goyal, Vivek K.
Several key results in distributed source coding offer the intuition that little improvement in compression can be gained from intersensor communication when the information is coded in long blocks. However, when sensors are restricted to code their observations in small blocks (e.g., one) or desire fidelity of a computation applied to source realizations, intelligent collaboration between sensors can greatly reduce distortion. For networks where sensors are allowed to "chat" using a side channel that is unobservable at the fusion center, we provide asymptotically-exact characterization of distortion performance and optimal quantizer design in the high-resolution (low-distortion) regime using a framework called distributed functional scalar quantization (DFSQ). The key result is that chatting can dramatically improve performance even when intersensor communication is at very low rate. We also solve the rate allocation problem when communication links have heterogeneous costs and provide a detailed example to demonstrate the theoretical and practical gains from chatting. This example for maximum computation gives insight on the gap between chatting and distributed networks, and how to optimize the intersensor communication.
2013-09-01T00:00:00ZDistributed scalar quantization for computing: high-resolution analysis and extensions
https://hdl.handle.net/2144/42540
Distributed scalar quantization for computing: high-resolution analysis and extensions
Misra, Vinith; Goyal, Vivek K.; Varshney, Lav R.
Communication of quantized information is frequently followed by a computation. We consider situations of 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.
2011-08-01T00:00:00ZSimultaneously sparse solutions to linear inverse problems with multiple system matrices and a single observation vector
https://hdl.handle.net/2144/42526
Simultaneously sparse solutions to linear inverse problems with multiple system matrices and a single observation vector
Zelinski, Adam C.; Goyal, Vivek K.; Adalsteinsson, Elfar
A problem that arises in slice-selective magnetic resonance imaging (MRI) radio-frequency (RF) excitation pulse design is abstracted as a novel linear inverse problem with a simultaneous sparsity constraint. Multiple unknown signal vectors are to be determined, where each 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 approximately solves the system. We refer to this as the multiple-system single-output (MSSO) simultaneous sparse approximation problem. This manuscript contrasts the MSSO problem with other simultaneous sparsity problems and conducts an initial exploration of algorithms with which to solve it. Greedy algorithms and techniques based on convex relaxation are derived and compared empirically. Experiments involve sparsity pattern recovery in noiseless and noisy settings and MRI RF pulse design.
2010-01-20T00:00:00ZConcentric permutation source codes
https://hdl.handle.net/2144/42524
Concentric permutation source codes
Nguyen, Ha Q.; Varshney, Lav R.; Goyal, Vivek K.
Permutation codes are a class of structured vector quantizers with a computationally-simple encoding procedure based on sorting the scalar components. Using a codebook comprising several permutation codes as subcodes preserves the simplicity of encoding while increasing the number of rate-distortion operating points, improving the convex hull of operating points, and increasing design complexity. We show that when the subcodes are designed with the same composition, optimization of the codebook reduces to a lower-dimensional vector quantizer design within a single cone. Heuristics for reducing design complexity are presented, including an optimization of the rate allocation in a shape-gain vector quantizer with gain-dependent wrapped spherical shape codebook.
2010-11-01T00:00:00ZFrame permutation quantization
https://hdl.handle.net/2144/42523
Frame permutation quantization
Nguyen, Ha Q.; Goyal, Vivek K.; Varshney, Lav R.
Frame permutation quantization (FPQ) is a new vector quantization technique using finite frames. In FPQ, a vector is encoded using a permutation source code to quantize its frame expansion. This means that the encoding is a partial ordering of the frame expansion coefficients. Compared to ordinary permutation source coding, FPQ produces a greater number of possible quantization rates and a higher maximum rate. Various representations for the partitions induced by FPQ are presented, and reconstruction algorithms based on linear programming, quadratic programming, and recursive orthogonal projection are derived. Implementations of the linear and quadratic programming algorithms for uniform and Gaussian sources show performance improvements over entropy-constrained scalar quantization for certain combinations of vector dimension and coding rate. Monte Carlo evaluation of the recursive algorithm shows that mean-squared error (MSE) decays as for an M-element frame, which is consistent with previous results on optimal decay of MSE. Reconstruction using the canonical dual frame is also studied, and several results relate properties of the analysis frame to whether linear reconstruction techniques provide consistent reconstructions.
2011-07-01T00:00:00ZOn the estimation of nonrandom signal coefficients from jittered samples
https://hdl.handle.net/2144/42522
On the estimation of nonrandom signal coefficients from jittered samples
Weller, Daniel S.; Goyal, Vivek K.
This paper examines the problem of estimating the parameters of a bandlimited signal from samples corrupted by random jitter (timing noise) and additive, independent identically distributed (i.i.d.) Gaussian noise, where the signal lies in the span of a finite basis. For the presented classical estimation problem, the Cramér-Rao lower bound (CRB) is computed, and an Expectation-Maximization (EM) algorithm approximating the maximum likelihood (ML) estimator is developed. Simulations are performed to study the convergence properties of the EM algorithm and compare the performance both against the CRB and a basic linear estimator. These simulations demonstrate that by postprocessing the jittered samples with the proposed EM algorithm, greater jitter can be tolerated, potentially reducing on-chip ADC power consumption substantially.
2011-02-01T00:00:00ZBayesian post-processing methods for jitter mitigation in sampling
https://hdl.handle.net/2144/42519
Bayesian post-processing methods for jitter mitigation in sampling
Weller, Daniel S.; Goyal, Vivek K.
Minimum mean-square error (MMSE) estimators of signals from samples corrupted by jitter (timing noise) and additive noise are nonlinear, even when the signal parameters and additive noise have normal distributions. This paper develops a stochastic algorithm based on Gibbs sampling and slice sampling to approximate the optimal MMSE estimator in this Bayesian formulation. Simulations demonstrate that this nonlinear algorithm can improve significantly upon the linear MMSE estimator, as well as the EM algorithm approximation to the maximum likelihood (ML) estimator used in classical estimation. Effective off-chip postprocessing to mitigate jitter enables greater jitter to be tolerated, potentially reducing on-chip ADC power consumption.
2011-05-01T00:00:00ZOptimal quantization for compressive sensing under message passing reconstruction
https://hdl.handle.net/2144/42518
Optimal quantization for compressive sensing under message passing reconstruction
Kamilov, Ulugbek; Goyal, Vivek K.; Rangan, Sundeep
We consider the optimal quantization of compressive sensing measurements along with estimation from quantized samples using generalized approximate message passing (GAMP). GAMP is an iterative reconstruction scheme inspired by the belief propagation algorithm on bipartite graphs which generalizes approximate message passing (AMP) for arbitrary measurement channels. Its asymptotic error performance can be accurately predicted and tracked through the state evolution formalism. We utilize these results to design mean-square optimal scalar quantizers for GAMP signal reconstruction and empirically demonstrate the superior error performance of the resulting quantizers.
2011-07-01T00:00:00ZEstimating signals with finite rate of innovation from noisy samples: a stochastic algorithm
https://hdl.handle.net/2144/42517
Estimating signals with finite rate of innovation from noisy samples: a stochastic algorithm
Tan, V.Y.F.; Goyal, V.K.
2008-10-01T00:00:00ZNecessary and sufficient conditions for sparsity pattern recovery
https://hdl.handle.net/2144/42504
Necessary and sufficient conditions for sparsity pattern recovery
Fletcher, Alyson K.; Rangan, Sundeep; Goyal, Vivek K.
The paper considers the problem of detecting the sparsity pattern of a k -sparse vector in \BBR n from m random noisy measurements. A new necessary condition on the number of measurements for asymptotically reliable detection with maximum-likelihood (ML) estimation and Gaussian measurement matrices is derived. This necessary condition for ML detection is compared against a sufficient condition for simple maximum correlation (MC) or thresholding algorithms. The analysis shows that the gap between thresholding and ML can be described by a simple expression in terms of the total signal-to-noise ratio (SNR), with the gap growing with increasing SNR. Thresholding is also compared against the more sophisticated Lasso and orthogonal matching pursuit (OMP) methods. At high SNRs, it is shown that the gap between Lasso and OMP over thresholding is described by the range of powers of the nonzero component values of the unknown signals. Specifically, the key benefit of Lasso and OMP over thresholding is the ability of Lasso and OMP to detect signals with relatively small components.
2009-12-01T00:00:00ZTime-resolved focused ion beam microscopy: modeling, estimation methods, and analyses
https://hdl.handle.net/2144/42502
Time-resolved focused ion beam microscopy: modeling, estimation methods, and analyses
Peng, Minxu; Murray-Bruce, John; Goyal, Vivek K.
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.
2021-01-01T00:00:00ZSWAGGER: sparsity within and across groups for general estimation and recovery
https://hdl.handle.net/2144/42501
SWAGGER: sparsity within and across groups for general estimation and recovery
Saunders, Charles; Goyal, Vivek K.
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.
2020-01-01T00:00:00ZOn-off random access channels: a compressed sensing framework
https://hdl.handle.net/2144/42500
On-off random access channels: a compressed sensing framework
Fletcher, Alyson K.; Rangan, Sundeep; Goyal, Vivek K.
This paper considers a simple on-off random multiple access channel, where n users communicate simultaneously to a single receiver over m degrees of freedom. Each user transmits with probability 𝛌, where typically 𝛌n < m << n, and the receiver must detect which users transmitted. We show that when the codebook has i.i.d. Gaussian entries, detecting which users transmitted is mathematically equivalent to a certain sparsity detection problem considered in compressed sensing. Using recent sparsity results, we derive upper and lower bounds on the capacities of these channels. We show that common sparsity detection algorithms, such as lasso and orthogonal matching pursuit (OMP), can be used as tractable multiuser detection schemes and have significantly better performance than single-user detection. These methods do achieve some near-far resistance but--at high signal-to-noise ratios (SNRs)--may achieve capacities far below optimal maximum likelihood detection. We then present a new algorithm, called sequential OMP, that illustrates that iterative detection combined with power ordering or power shaping can significantly improve the high SNR performance. Sequential OMP is analogous to successive interference cancellation in the classic multiple access channel. Our results thereby provide insight into the roles of power control and multiuser detection on random-access signalling.
2009-01-01T00:00:00ZDifferential effects of anesthetics on resting state functional connectivity in the mouse
https://hdl.handle.net/2144/42499
Differential effects of anesthetics on resting state functional connectivity in the mouse
Xie, Hongyu; Chung, David Y; Kura, Sreekanth; Sugimoto, Kazutaka; Aykan, Sanem A; Wu, Yi; Sakadžić, Sava; Yaseen, Mohammad A; Boas, David A; Ayata, Cenk
Blood oxygen level-dependent (BOLD) functional MRI (fMRI) is a standard approach to examine resting state functional connectivity (RSFC), but fMRI in animal models is challenging. Recently, functional optical intrinsic signal imaging-which relies on the same hemodynamic signal underlying BOLD fMRI-has been developed as a complementary approach to assess RSFC in mice. Since it is difficult to ensure that an animal is in a truly resting state while awake, RSFC measurements under anesthesia remain an important approach. Therefore, we systematically examined measures of RSFC using non-invasive, widefield optical intrinsic signal imaging under five different anesthetics in male C57BL/6J mice. We find excellent seed-based, global, and interhemispheric connectivity using tribromoethanol (Avertin) and ketamine-xylazine, comparable to results in the literature including awake animals. Urethane anesthesia yielded intermediate results, while chloral hydrate and isoflurane were both associated with poor RSFC. Furthermore, we found a correspondence between the strength of RSFC and the power of low-frequency hemodynamic fluctuations. In conclusion, Avertin and ketamine-xylazine provide robust and reproducible measures of RSFC in mice, whereas chloral hydrate and isoflurane do not.
2020-04-01T00:00:00ZNonlinear digital post-processing to mitigate jitter in sampling
https://hdl.handle.net/2144/42497
Nonlinear digital post-processing to mitigate jitter in sampling
Weller, Daniel S.; Goyal, Vivek K.
This paper describes several new algorithms for estimating the parameters of a periodic bandlimited signal from samples corrupted by jitter (timing noise) and additive noise. Both classical (non-random) and Bayesian formulations are considered: an Expectation-Maximization (EM) algorithm is developed to compute the maximum likelihood (ML) estimator for the classical estimation framework, and two Gibbs samplers are proposed to approximate the Bayes least squares (BLS) estimate for parameters independently distributed according to a uniform prior. Simulations are performed to demonstrate the significant performance improvement achievable using these algorithms as compared to linear estimators. The ML estimator is also compared to the Cramer-Rao lower bound to determine the range of jitter for which the estimator is approximately efficient. These simulations provide evidence that the nonlinear algorithms derived here can tolerate 1.4-2 times more jitter than linear estimators, reducing on-chip ADC power consumption by 50-75 percent.
2018-01-01T00:00:00Z