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Relevant bibliographies by topics / Gradient Estimation

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Academic literature on the topic 'Gradient Estimation'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 February 2022

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Journal articles on the topic "Gradient Estimation"

1

Yamane, Ikko, Hiroaki Sasaki, and Masashi Sugiyama. "Regularized Multitask Learning for Multidimensional Log-Density Gradient Estimation." Neural Computation 28, no. 7 (2016): 1388–410. http://dx.doi.org/10.1162/neco_a_00844.

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Log-density gradient estimation is a fundamental statistical problem and possesses various practical applications such as clustering and measuring nongaussianity. A naive two-step approach of first estimating the density and then taking its log gradient is unreliable because an accurate density estimate does not necessarily lead to an accurate log-density gradient estimate. To cope with this problem, a method to directly estimate the log-density gradient without density estimation has been explored and demonstrated to work much better than the two-step method. The objective of this letter is to improve the performance of this direct method in multidimensional cases. Our idea is to regard the problem of log-density gradient estimation in each dimension as a task and apply regularized multitask learning to the direct log-density gradient estimator. We experimentally demonstrate the usefulness of the proposed multitask method in log-density gradient estimation and mode-seeking clustering.

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Alim, U., T. Möller, and L. Condat. "Gradient Estimation Revitalized." IEEE Transactions on Visualization and Computer Graphics 16, no. 6 (2010): 1495–504. http://dx.doi.org/10.1109/tvcg.2010.160.

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Prasad, Adarsh, Arun Sai Suggala, Sivaraman Balakrishnan, and Pradeep Ravikumar. "Robust estimation via robust gradient estimation." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 82, no. 3 (2020): 601–27. http://dx.doi.org/10.1111/rssb.12364.

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Vogt, J., E. Sorbalo, M. He, and A. Blagau. "Gradient estimation using configurations of two or three spacecraft." Annales Geophysicae 31, no. 11 (2013): 1913–27. http://dx.doi.org/10.5194/angeo-31-1913-2013.

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Abstract. The forthcoming three-satellite mission Swarm will allow us to investigate plasma processes and phenomena in the upper ionosphere from an in-situ multi-spacecraft perspective. Since with less than four points in space the spatiotemporal ambiguity cannot be resolved fully, analysis tools for estimating spatial gradients, wave vectors, or boundary parameters need to utilise additional information such as geometrical or dynamical constraints. This report deals with gradient estimation where the planar component is constructed using instantaneous three-point observations or, for quasi-static structures, by means of measurements along the orbits of two close spacecraft. A new least squares (LS) gradient estimator for the latter case is compared with existing finite difference (FD) schemes and also with a three-point LS technique. All available techniques are presented in a common framework to facilitate error analyses and consistency checks, and to show how arbitrary combinations of planar gradient estimators and constraints can be formed. The accuracy of LS and FD planar gradient estimators is assessed in terms of prescribed and adjustable discretization parameters to optimise their performance along the satellite orbits. Furthermore, we discuss the implications of imperfect constraint equations for error propagation, and address the effects of sub-scale structures. The two-spacecraft LS scheme is demonstrated using Cluster FGM measurements at a planar and essentially force-free plasma boundary in the solar wind where all three different types of constraints to construct out-of-plane derivatives can be applied.

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Baxter, J., P. L. Bartlett, and L. Weaver. "Experiments with Infinite-Horizon, Policy-Gradient Estimation." Journal of Artificial Intelligence Research 15 (November 1, 2001): 351–81. http://dx.doi.org/10.1613/jair.807.

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In this paper, we present algorithms that perform gradient ascent of the average reward in a partially observable Markov decision process (POMDP). These algorithms are based on GPOMDP, an algorithm introduced in a companion paper (Baxter & Bartlett, this volume), which computes biased estimates of the performance gradient in POMDPs. The algorithm's chief advantages are that it uses only one free parameter beta, which has a natural interpretation in terms of bias-variance trade-off, it requires no knowledge of the underlying state, and it can be applied to infinite state, control and observation spaces. We show how the gradient estimates produced by GPOMDP can be used to perform gradient ascent, both with a traditional stochastic-gradient algorithm, and with an algorithm based on conjugate-gradients that utilizes gradient information to bracket maxima in line searches. Experimental results are presented illustrating both the theoretical results of (Baxter & Bartlett, this volume) on a toy problem, and practical aspects of the algorithms on a number of more realistic problems.

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Jagabathula, Srikanth, Lakshminarayanan Subramanian, and Ashwin Venkataraman. "A Conditional Gradient Approach for Nonparametric Estimation of Mixing Distributions." Management Science 66, no. 8 (2020): 3635–56. http://dx.doi.org/10.1287/mnsc.2019.3373.

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Mixture models are versatile tools that are used extensively in many fields, including operations, marketing, and econometrics. The main challenge in estimating mixture models is that the mixing distribution is often unknown, and imposing a priori parametric assumptions can lead to model misspecification issues. In this paper, we propose a new methodology for nonparametric estimation of the mixing distribution of a mixture of logit models. We formulate the likelihood-based estimation problem as a constrained convex program and apply the conditional gradient (also known as Frank–Wolfe) algorithm to solve this convex program. We show that our method iteratively generates the support of the mixing distribution and the mixing proportions. Theoretically, we establish the sublinear convergence rate of our estimator and characterize the structure of the recovered mixing distribution. Empirically, we test our approach on real-world datasets. We show that it outperforms the standard expectation-maximization (EM) benchmark on speed (16 times faster), in-sample fit (up to 24% reduction in the log-likelihood loss), and predictive (average 28% reduction in standard error metrics) and decision accuracies (extracts around 23% more revenue). On synthetic data, we show that our estimator is robust to different ground-truth mixing distributions and can also account for endogeneity. This paper was accepted by Serguei Netessine, operations management.

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Baxter, J., and P. L. Bartlett. "Infinite-Horizon Policy-Gradient Estimation." Journal of Artificial Intelligence Research 15 (November 1, 2001): 319–50. http://dx.doi.org/10.1613/jair.806.

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Gradient-based approaches to direct policy search in reinforcement learning have received much recent attention as a means to solve problems of partial observability and to avoid some of the problems associated with policy degradation in value-function methods. In this paper we introduce GPOMDP, a simulation-based algorithm for generating a biased estimate of the gradient of the average reward in Partially Observable Markov Decision Processes POMDPs controlled by parameterized stochastic policies. A similar algorithm was proposed by (Kimura et al. 1995). The algorithm's chief advantages are that it requires storage of only twice the number of policy parameters, uses one free beta (which has a natural interpretation in terms of bias-variance trade-off), and requires no knowledge of the underlying state. We prove convergence of GPOMDP, and show how the correct choice of the parameter beta is related to the mixing time of the controlled POMDP. We briefly describe extensions of GPOMDP to controlled Markov chains, continuous state, observation and control spaces, multiple-agents, higher-order derivatives, and a version for training stochastic policies with internal states. In a companion paper (Baxter et al., this volume) we show how the gradient estimates generated by GPOMDP can be used in both a traditional stochastic gradient algorithm and a conjugate-gradient procedure to find local optima of the average reward.

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Hua, Binh-Son, Adrien Gruson, Derek Nowrouzezahrai, and Toshiya Hachisuka. "Gradient-Domain Photon Density Estimation." Computer Graphics Forum 36, no. 2 (2017): 31–38. http://dx.doi.org/10.1111/cgf.13104.

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Acquaviva, Roberto, Stefano Mangione, and Giovanni Garbo. "Image-based MRI gradient estimation." Magnetic Resonance Imaging 49 (June 2018): 138–44. http://dx.doi.org/10.1016/j.mri.2017.12.028.

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Mehdi Fateh, Mohammad, Siamak Azargoshasb, and Saeed Khorashadizadeh. "Model-free discrete control for robot manipulators using a fuzzy estimator." COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 33, no. 3 (2014): 1051–67. http://dx.doi.org/10.1108/compel-05-2013-0185.

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Purpose – Discrete control of robot manipulators with uncertain model is the purpose of this paper. Design/methodology/approach – The proposed control design is model-free by employing an adaptive fuzzy estimator in the controller for the estimation of uncertainty as unknown function. An adaptive mechanism is proposed in order to overcome uncertainties. Parameters of the fuzzy estimator are adapted to minimize the estimation error using a gradient descent algorithm. Findings – The proposed model-free discrete control is robust against all uncertainties associated with the model of robotic system including the robot manipulator and actuators, and external disturbances. Stability analysis verifies the proposed control approach. Simulation results show its efficiency in the tracking control. Originality/value – A novel model-free discrete control approach for electrically driven robot manipulators is proposed. An adaptive fuzzy estimator is used in the controller to overcome uncertainties. The parameters of the estimator are regulated by a gradient descent algorithm. The most gradient descent algorithms have used a known cost function based on the tracking error for adaptation whereas the proposed gradient descent algorithm uses a cost function based on the uncertainty estimation error. Then, the uncertainty estimation error is calculated from the joint position error and its derivative using the closed-loop system.

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Dissertations / Theses on the topic "Gradient Estimation"

1

Swapp, David. "Estimation of visual textural gradient using Gabor functions." Thesis, University of Strathclyde, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.320238.

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Lee, Choon. "Interframe image coding with three-dimensional gradient motion estimation." Diss., This resource online, 1990. http://scholar.lib.vt.edu/theses/available/etd-08252008-162144/.

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Zotov, Alexander. "Models of disparity gradient estimation in the visual cortex." Birmingham, Ala. : University of Alabama at Birmingham, 2007. https://www.mhsl.uab.edu/dt/2008r/zotov.pdf.

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Mehrparvar, Arash. "ATTITUDE ESTIMATION FOR A GRAVITY GRADIENT MOMENTUM BIASED NANOSATELLITE." DigitalCommons@CalPoly, 2013. https://digitalcommons.calpoly.edu/theses/1097.

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Attitude determination and estimation algorithms are developed and implemented in simulation for the Exocube satellite currently under development by PolySat at Cal Poly. A mission requirement of ±5˚ of attitude knowledge has been flowed down from the NASA Goddard developed payload, and this requirement is to be met with a basic sensor suite and the appropriate algorithms. The algorithms selected in this work are TRIAD and an Extended Kalman Filter, both of which are placed in a simulation structure along with models for orbit propagation, spacecraft kinematics and dynamics, and sensor and reference vector models. Errors inherent from sensors, orbit position knowledge, and reference vector generation are modeled as well. Simulations are then run for anticipated dynamic states of Exocube while varying parameters for the spacecraft, attitude algorithms, and level of error. The nominal case shows steady state convergence to within 1˚ of attitude knowledge, with sensor errors set to 3.5˚ and reference vector errors set to 2˚. The algorithms employed have their functionality confirmed with the use of STK, and the simulations have been structured to be used as tools to help evaluate attitude knowledge capabilities for the Exocube mission and future PolySat missions.

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Miyoshi, Naoto. "Studies on Gradient Estimation for Stationary Single-Server Queues." Kyoto University, 1997. http://hdl.handle.net/2433/202289.

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Kyoto University (京都大学)<br>0048<br>新制・課程博士<br>博士(工学)<br>甲第6839号<br>工博第1590号<br>新制||工||1063(附属図書館)<br>15926<br>UT51-97-H223<br>京都大学大学院工学研究科応用システム科学専攻<br>(主査)教授長谷川利治, 教授沖野教郎, 教授茨木俊秀<br>学位規則第4条第1項該当

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Shahnaz, Sabina. "Gas flux estimation from surface gas concentrations." Thesis, Georgia Institute of Technology, 2016. http://hdl.handle.net/1853/55073.

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A gradient-independent model of gas fluxes was formulated and tested. The model is built on the relationship between gas flux and the time history of surface gas concentration, known as half-order derivative (HOD), when the transport of the gas in the boundary layer is described by a diffusion equation. The eddy-diffusivity of gas is parameterized based on the similarity theory of boundary layer turbulence combined with the MEP model of surface heat fluxes. Test of the new model using in-situ data of CO2 concentration and fluxes at several locations with diverse vegetation cover, geographic and climatic conditions confirms its usefulness and potential for monitoring and modeling greenhouse gases. The proposed model may also be used for estimating other GHGS fluxes such as methane (CH4) and Water vapor flux. This proof-of-concept study justifies the proposed model as a practical solution for monitoring and modeling global GHGS budget over remote areas and oceans where ground observations of GHGS fluxes are limited or non-existent. One focus of the on-going research is to investigate its application to producing regional and global distributions of carbon fluxes for identifying sinks and sources of carbon and re-evaluating the regional and global carbon budget at monthly and annual time scales.

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Yang, Junjun. "Seafloor Topography Estimation from Gravity Gradients." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1512048462472145.

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Siow, Bernard, Ivana Drobnjak, Andrada Ianus, Isabel N. Christie, Mark F. Lythgoe, and Daniel C. Alexander. "Axon radius estimation with Oscillating Gradient Spin Echo (OGSE) diffusion MRI." Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-184163.

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The estimation of axon radius provides insights into brain function [1] and could provide progression and classification biomarkers for a number of white matter diseases [2-4]. A recent in silico study [5] has shown that optimised gradient waveforms (GEN) and oscillating gradient waveform spin echo (OGSE) have increased sensitivity to small axon radius compared to pulsed gradient spin echo (PGSE) diffusion MR sequences. In a follow-up study [6], experiments with glass capillaries show the practical feasibility of GEN sequences and verify improved pore-size estimates. Here, we compare PGSE with sine, sine with arbitrary phase, and square wave OGSE (SNOGSE, SPOGSE, SWOGSE, respectively) for axon radius mapping in the corpus callosum of a rat, ex-vivo. Our results suggest improvements in pore size estimates from OGSE over PGSE, with greatest improvement from SWOGSE, supporting theoretical results from [5] and other studies [7-9].

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Siow, Bernard, Ivana Drobnjak, Andrada Ianus, Isabel N. Christie, Mark F. Lythgoe, and Daniel C. Alexander. "Axon radius estimation with Oscillating Gradient Spin Echo (OGSE) diffusion MRI." Diffusion fundamentals 18 (2013) 1, S. 1-6, 2013. https://ul.qucosa.de/id/qucosa%3A13707.

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The estimation of axon radius provides insights into brain function [1] and could provide progression and classification biomarkers for a number of white matter diseases [2-4]. A recent in silico study [5] has shown that optimised gradient waveforms (GEN) and oscillating gradient waveform spin echo (OGSE) have increased sensitivity to small axon radius compared to pulsed gradient spin echo (PGSE) diffusion MR sequences. In a follow-up study [6], experiments with glass capillaries show the practical feasibility of GEN sequences and verify improved pore-size estimates. Here, we compare PGSE with sine, sine with arbitrary phase, and square wave OGSE (SNOGSE, SPOGSE, SWOGSE, respectively) for axon radius mapping in the corpus callosum of a rat, ex-vivo. Our results suggest improvements in pore size estimates from OGSE over PGSE, with greatest improvement from SWOGSE, supporting theoretical results from [5] and other studies [7-9].

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Valstad, Bård Arve. "Parameter Estimation and Control of a Dual Gradient Managed Pressure Drilling System." Thesis, Norwegian University of Science and Technology, Department of Engineering Cybernetics, 2009. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9025.

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<p>The increasing demand for oil and gas in the world, and the fact that most of the easily accessible reservoirs are in production or already abandoned, result in a need to develop new resources. These may be new reservoirs that have previously been considered uneconomical or impossible to develop, or extended operation of existing fields. Developing smaller reservoirs, means that more wells have to be drilled per barrel, which gives both more and eventually greater challenges as more and more wells are drilled because the wells has to be drilled further and into more difficult formations. Mature fields are drained, which leads to lowering of reservoir pressure and therefore tighter pressure margins for drilling. Because of the challenges with deep water drilling and depleted reservoirs, there is a need to precisely control the pressure profile in the well during drilling in such formations. Some of the parameters that are needed to control the well precisely are not easily obtained during drilling, and an estimation of these will therefore be crucial to be able to use a model to control the well. The transmission of measurements from a well is also often either delayed or absent during periods of drilling, which will cause problems for the control of the well. It is therefore required that an estimation scheme is able to estimate the pressure in the well for the time interval between the updates of the measurements from the well. The conventional method for transmitting measurements from the bottom of the well is by mud pulse telemetry which is pressure waves transmitted through the drilling mud. These measurements will be delayed, so accurate real-time measurements will never be available. To estimate the bottom hole pressure, a extended kalman filter was evaluated. This filter is based on a simple mathematical model derived for the drilling process. The states in the filter is height of mud in the riser, mud weight and different friction factors for the well. The filter is tested when the measurements are continuous available, with delayed update of the bottom hole measurement, and for cases where one of the measurements are absent. A simple controller to control the bottom hole pressure is implemented to control the pressure for reference tracking and during a simulated pipe connection. During simulations, it was not possible to achieve convergence for the friction factor for normal flows, and this led to errors in the other states. The friction factor would only converge to its true value during very high flows during the nominal testing, which led to the other states also achieving their correct values. The problem in estimating the friction factor applied to all different forms for friction parameters. The kalman filter was tested against an artificial well simulated in WeMod, and gave decent estimates of the bottom hole pressure except for at low flows.</p>

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Books on the topic "Gradient Estimation"

1

Gradient estimation via perturbation analysis. Kluwer Academic Publishers, 1991.

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Glasserman, Paul. Gradient estimation via perturbation analysis. Kluwer Academic, 1991.

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Fu, Michael. Conditional Monte Carlo: Gradient estimation and optimization applications. Kluwer Academic Publishers, 1997.

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Fu, Michael. Conditional Monte Carlo: Gradient Estimation and Optimization Applications. Springer US, 1997.

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Skifstad, Kurt D. High-speed range estimation based on intensity gradient analysis. Springer-Verlag, 1991.

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Skifstad, Kurt D. High-Speed Range Estimation Based on Intensity Gradient Analysis. Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4612-3112-7.

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Skifstad, Kurt D. High-speed range estimation based on intensity gradient analysis. Springer-Verlag, 1991.

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High-speed range estimation based on intensity gradient analysis. Springer-Verlag, 1991.

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An introduction to cut-off grade estimation. Society for Mining, Metallurgy, and Exploration, 2008.

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Atherton, Gary L. Grading and paving construction: A practical approach to management and estimating. Sandcastles, 1986.

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Book chapters on the topic "Gradient Estimation"

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Fu, Michael C. "Stochastic Gradient Estimation." In Handbook of Simulation Optimization. Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-1384-8_5.

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Fu, Michael, and Jian-Qiang Hu. "Conditional Monte Carlo Gradient Estimation." In Conditional Monte Carlo. Springer US, 1997. http://dx.doi.org/10.1007/978-1-4615-6293-1_3.

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Zhang, Bin, Yubo Tao, and Hai Lin. "Robust Color Gradient Estimation for Photographic Volumes." In E-Learning and Games. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-40259-8_34.

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Zhang, He, François Petitjean, and Wray Buntine. "Hierarchical Gradient Smoothing for Probability Estimation Trees." In Advances in Knowledge Discovery and Data Mining. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-47426-3_18.

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Romashin, Sergey N., Victoria Yu Presnetsova, Larisa Yu Frolenkova, Vladimir S. Shorkin, and Svetlana I. Yakushina. "Theoretical Estimation of the Strength of Thin-film Coatings." In Higher Gradient Materials and Related Generalized Continua. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-30406-5_11.

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Guzman, Yuneisy E. Garcia, Michael Lunglmayr, and Mario Huemer. "A Gradient Ascent Approach for Multiple Frequency Estimation." In Computer Aided Systems Theory – EUROCAST 2019. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45096-0_3.

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Calzolari, Giorgio, and Lorenzo Panattoni. "Gradient Methods in Fiml Estimation of Econometric Models." In Developments of Control Theory for Economic Analysis. Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-009-3495-5_10.

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Frühwirth, Rudolf, and Are Strandlie. "Statistics and Numerical Methods." In Pattern Recognition, Tracking and Vertex Reconstruction in Particle Detectors. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-65771-0_3.

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AbstractThe chapter gives an outline of some statistical and numerical methods that will be applied in later chapters. The first section deals with the minimization of functions. Several gradient-based methods and a popular non-gradient method are discussed. The following section discusses statistical models and the estimation of model parameters. The basics of linear and nonlinear regression models and state space models are presented, including least-squares estimation and the (extended) Kalman filter. The final section gives a brief overview of clustering and different types of clustering algorithms.

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Huang, Junchu, Zhiheng Zhou, Bingyuan Xu, and Yu Huang. "Accelerating Stochastic Variance Reduced Gradient Using Mini-Batch Samples on Estimation of Average Gradient." In Advances in Neural Networks - ISNN 2017. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59072-1_41.

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Tashlinskii, Alexandr. "Computational Expenditure Reduction in Pseudo-Gradient Image Parameter Estimation." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/3-540-44862-4_48.

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Conference papers on the topic "Gradient Estimation"

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Merron, J., and M. Brady. "Isotropic gradient estimation." In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition. IEEE, 1996. http://dx.doi.org/10.1109/cvpr.1996.517142.

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Sarkar, T. K., and R. D. Brown. "Real time deconvolution using the conjugate gradient algorithm." In Fifth ASSP Workshop on Spectrum Estimation and Modeling. IEEE, 1990. http://dx.doi.org/10.1109/spect.1990.205594.

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Glynn, Peter W. "Likelilood ratio gradient estimation." In the 19th conference. ACM Press, 1987. http://dx.doi.org/10.1145/318371.318612.

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Glasserman, Paul, and Peter W. Glynn. "Gradient estimation for regenerative processes." In the 24th conference. ACM Press, 1992. http://dx.doi.org/10.1145/167293.167350.

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Djemel Ziou and Shengrui Wang. "Isotropic processing for gradient estimation." In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition. IEEE, 1996. http://dx.doi.org/10.1109/cvpr.1996.517143.

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Gu, Li-dan, Chuan-sheng Yang, and Chao Wang. "Atmospheric Light Estimation Using Gradient Information." In the 2nd International Conference. ACM Press, 2019. http://dx.doi.org/10.1145/3339363.3339392.

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Shi, Wenqiang, Shuang Zhang, Jianchang Zhao, Shudong Chen, and Xin Guo. "Gradient Tolerance Estimation of Overhauser Magnetometer." In 2019 IEEE 4th Advanced Information Technology, Electronic and Automation Control Conference (IAEAC). IEEE, 2019. http://dx.doi.org/10.1109/iaeac47372.2019.8997914.

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Hazen, Megan, and Maya R. Gupta. "Gradient estimation in global optimization algorithms." In 2009 IEEE Congress on Evolutionary Computation (CEC). IEEE, 2009. http://dx.doi.org/10.1109/cec.2009.4983165.

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Seybold, Tamara, Florian Kuhn, Julian Habigt, Mark Hartenstein, and Walter Stechele. "Automatic denoising parameter estimation using gradient histograms." In 2014 Visual Communications and Image Processing (VCIP). IEEE, 2014. http://dx.doi.org/10.1109/vcip.2014.7051580.

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Rueda-Escobedo, Juan G., and Jaime A. Moreno. "Non-linear gradient algorithm for parameter estimation." In 2015 54th IEEE Conference on Decision and Control (CDC). IEEE, 2015. http://dx.doi.org/10.1109/cdc.2015.7402855.

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Reports on the topic "Gradient Estimation"

1

Glynn, Peter W., Pierre L'Ecuyer, and Michel Ades. Gradient Estimation for Ratios. Defense Technical Information Center, 1991. http://dx.doi.org/10.21236/ada248453.

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Glasserman, Paul, and Peter W. Glynn. Gradient Estimation for Regenerative Processes. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada263766.

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Glynn, Peter W. Likelihood Ratio Gradient Estimation: An Overview. Defense Technical Information Center, 1987. http://dx.doi.org/10.21236/ada197085.

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Turner, Daniel Z. An overview of the gradient-based local DIC formulation for motion estimation in DICe. Office of Scientific and Technical Information (OSTI), 2016. http://dx.doi.org/10.2172/1561808.

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Montalvo-Bartolomei, Axel, Bryant Robbins, and John Murphy. Experimental Evaluation of Kovács’ Equations for Estimating Critical Gradients. Geotechnical and Structures Laboratory (U.S.), 2018. http://dx.doi.org/10.21079/11681/28066.

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Eichel, P. H. The phase gradient autofocus algorithm: An optimal estimator of the phase derivative. Office of Scientific and Technical Information (OSTI), 1989. http://dx.doi.org/10.2172/5609345.

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