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Asilomar Conference on Signals, Systems & Computers

作者： Louis L. Scharf Ali Pezeshki Departments of Electrical and Computer Engineering and Statistics Colorado State University Fort Collins CO USA Program Applied and Computational Mathematics Princeton University Princeton NJ USA

In this paper, we describe how an active radar/sonar imaging problem may be formulated as a virtual passive sensor array processing problem. We consider an active sensing problem where it is desired to form a range-Doppler image at a slow- time rate, even though the radar/sonar can transmit pulses at a fast time rate. By transmitting pulses at the fast time rate we can estimate the second-order statistics of an ambiguity vector, calculated at a coarse resolution. As we show this ambiguity vector plays the role of an array snapshot vector in passive sensor array processing. The noise free version of this ambiguity vector acts as a signature vector or steering vector, which can be steered around in delay and Doppler at a fine resolution to produce an image. We employ a MVDR-like principle to generate high resolution delay-Doppler images.

关键词： Array signal processing Sonar Sensor arrays Radar imaging Delay Image resolution Passive radar Image sensors Sensor phenomena and characterization Statistics

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Robust estimation of rotations from relative measurements by maximum likelihood

Robust estimation of rotations from relative measurements by...

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IEEE Annual Conference on Decision and Control

作者： Nicolas Boumal Amit Singer P.-A. Absil Department of Mathematical Engineering ICTEAM Institute Universite catholique de Louvain Belgium Program in Applied and Computational Mathematics Princeton University NJ USA

ISBN: (纸本)9781467357159

We estimate unknown rotation matrices R_i from a set of measurements of relative rotations R_iR_j~T. Measurements are strongly affected by noise such that a small fraction of them are well concentrated around the true relative rotations while the majority of measurements are outliers bearing little or no information. We propose a maximum likelihood estimator (MLE) that explicitly acknowledges this noise model, yielding a robust estimation algorithm. The MLE is computed via Riemannian trust-region optimization using the Manopt toolbox. Comparisons of the MLE with Cramer-Rao bounds suggest the estimator is asymptotically efficient.

关键词： Maximum likelihood estimation Noise Synchronization Rotation measurement Noise measurement Vectors Optimization

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Bayesian Perspective for Orientation Estimation in Cryo-EM and Cryo-ET

arXiv

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arXiv 2024年

作者： Xu, Sheng Balanov, Amnon Bendory, Tamir Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States School of Electrical Engineering Tel Aviv University Tel Aviv69978 Israel

Accurate orientation estimation is a crucial component of 3D molecular structure reconstruction, both in single-particle cryo-electron microscopy (cryo-EM) and in the increasingly popular field of cryo-electron tomography (cryo-ET). The dominant method, which involves searching for an orientation with maximum cross-correlation relative to given templates, falls short, particularly in low signal-to-noise environments. In this work, we propose a Bayesian framework to develop a more accurate and flexible orientation estimation approach, with the minimum mean square error (MMSE) estimator as a key example. This method effectively accommodates varying structural conformations and arbitrary rotational distributions. Through simulations, we demonstrate that our estimator consistently outperforms the cross-correlation-based method, especially in challenging conditions with low signal-to-noise ratios, and offer a theoretical framework to support these improvements. We further show that integrating our estimator into the iterative refinement in the 3D reconstruction pipeline markedly enhances overall accuracy, revealing substantial benefits across the algorithmic workflow. Finally, we show empirically that the proposed Bayesian approach enhances robustness against the "Einstein from Noise" phenomenon, reducing model bias and improving reconstruction reliability. These findings indicate that the proposed Bayesian framework could substantially advance cryo-EM and cryo-ET by enhancing the accuracy, robustness, and reliability of 3D molecular structure reconstruction, thereby facilitating deeper insights into complex biological systems. © 2024, CC BY.

关键词： Electron microscopy

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Recovering Signals from their FROG Trace

Recovering Signals from their FROG Trace

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IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Tamir Bendory Dan Edidin Yonina C. Eldar The Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Department of Mathematics University of Missouri Columbia Missouri USA The Andrew and Erna Viterbi Faculty of Electrical Engineering Technion - Israel Institute of Technology Haifa Israel

ISBN: (纸本)9781538646595

The problem of recovering a signal from its power spectrum is called phase retrieval. This problem appears in a variety of scientific applications, such as ultra-short laser pulse characterization and diffraction imaging. However, the problem for one-dimensional signals is ill-posed as there is no one-to-one mapping between a one-dimensional signal and its power spectrum. In the field of ultra-short laser pulse characterization, it is common to overcome this ill-posedness by using a technique called Frequency-Resolved Optical Gating (FROG). In FROG, the measured data, referred to as FROG trace, is the Fourier magnitude of the product of the underlying signal with several translated versions of itself. Therefore, in order to recover a signal from its FROG trace, one needs to invert a system of phaseless quartic equations. In this paper, we explore the symmetries and uniqueness of the FROG mapping. Our main result states that a signal bandlimited to B is determined uniquely, up to symmetries, by only 3B FROG measurements.

关键词： phase retrieval phaseless quartic system of equations ultra-short laser pulse characterization FROG signals Ultrashort laser pulses power spectra frogs Amphibians RECOVERING Trace One dimensional quartic equations

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Exploring 3D Reconstruction with Drone Images: Advances and Challenges in Urban Environments 50

Exploring 3D Reconstruction with Drone Images: Advances and ...

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50th Annual Conference of the IEEE Industrial Electronics Society, IECON 2024

作者： Miranda Baldivieso, Thiago João da Silva Batista, Taise Grazielle Chagas, Fabio Suim Rodrigues Velho, Luiz Carlos Pacheco Ferreira Rosa, Paulo Fernando Defense Engineering Graduate Program Military Institute of Engineering Rio de Janeiro Brazil State Institute of the Environment Inea RJ Rio de Janeiro Brazil Department of Science and Industry systems University of South-Eastern Norway Kongsberg Norway Department of Computer Graphics Institute for Pure and Applied Mathematics Rio de Janeiro Brazil Electrical Engineering Graduate Program Military Institute of Engineering Rio de Janeiro Brazil

ISBN: (纸本)9781665464543

This working-in-progress paper aims to present a three-dimensional reconstruction using aerial images in different environments. The experiments were conducted with aircraft in both external and internal settings, starting with image acquisition, followed by the application of specific photogrammetry software-both commercial and open-source-and concluding with a qualitative evaluation of the results. © 2024 IEEE.

关键词： Aerial photography

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On Phase Reduction and Time Period of Noisy Oscillators

On Phase Reduction and Time Period of Noisy Oscillators

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IEEE Annual Conference on Decision and Control

作者： Zahra Aminzare Philip Holmes Vaibhav Srivastava Department of Mathematics University of Iowa IA USA Program in Applied and Computational Mathematics Princeton Neuroscience Institute Princeton University Princeton NJ USA Electrical and Computer Engineering Michigan State University East Lansing MI USA

ISBN: (数字)9781728113982

ISBN: (纸本)9781728113999

We study phase reduction for noisy oscillator models by deriving a reduced order stochastic differential equation describing the phase evolution using the first and second order Phase Response Curves (PRCs). We discuss direct methods and ordinary differential equations for computing these PRCs, and derive approximate first and second moments of the time period of the oscillator models in terms of functions of the PRCs. We illustrate the theoretical results on a noisy Hopf bifurcation normal form, on a noisy Van der Pol oscillator, and on a noisy bursting neuron model.

关键词： Oscillators Limit-cycles Noise measurement Biological system modeling Perturbation methods Bifurcation Stochastic processes

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A new algorithm for linearization up to multi-output and multi-input injection for a class of systems with implicitly defined outputs

A new algorithm for linearization up to multi-output and mul...

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European Control Conference (ECC)

作者： Sérgio S. Rodrigues A. Pedro Aguiar Öaw Institute for Computational and Applied Mathematics (RICAM) Linz Austria Department of Electrical and Computer Engineering Laboratory of Robotics and Systems in Engineering and Science (LARSyS) Lisbon Portugal

ISBN: (纸本)9781479901890

Given a class of nonlinear systems with implicitly defined outputs, we provide a new algorithm to find appropriate local coordinates, in which the resulting system takes a desired target form that is state-affine, up to output and input injection. Once in the target form, it is possible to construct a state-space observer with linear, possibly time-varying, error dynamics.

关键词： Vectors Equations Observers Gold Geometry Nonlinear dynamical systems

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Elastic and Thermodynamic Properties of Complex Mg-Al Intermetallic Compounds via Orbital-Free Density Functional Theory

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Physical Review applied 2016年第6期5卷 064021-064021页

作者： Houlong Zhuang Mohan Chen Emily A. Carter Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics and Andlinger Center for Energy and the Environment Princeton University Princeton New Jersey 08544 USA

Magnesium-aluminum (Mg-Al) alloys are important metal alloys with a wide range of engineering applications. We investigate the elastic and thermodynamic properties of Mg, Al, and four stoichiometric Mg-Al compounds including Mg17Al12, Mg13Al14, and Mg23Al30, and MgAl2 with orbital-free density-functional theory (OFDFT). We first calculate the lattice constants, zero-temperature formation energy, and independent elastic constants of these six materials and compare the results to those computed via Kohn-Sham DFT (KSDFT) benchmarks. We obtain excellent agreement between these two methods. Our calculated elastic constants of hexagonal close-packed Mg and face-centered-cubic Al are also consistent with available experimental data. We next compute their phonon spectra using the force constants extracted from the very fast OFDFT calculations, because such calculations are computationally challenging using KSDFT. This is especially the case for the Mg23Al30 compound, whose 3×3×3 supercell consists of 1431 atoms. We finally employ the quasiharmonic approximation to investigate temperature-dependent thermodynamic properties, including formation energies, heat capacities, and thermal expansion of the four Mg-Al intermetallic compounds. The calculated heat capacity and thermal expansion of both Mg and Al agree well with experimental data. We additionally find that Mg13Al14 and MgAl2 are both unstable, consistent with their absence from the equilibrium Mg-Al phase diagram. Our work demonstrates that OFDFT is an efficient and accurate quantum-mechanical computational tool for predicting elastic and thermodynamic properties of complicated Mg-Al alloys and also should be applicable to many other engineering alloys.

关键词： Elastic deformation Elastic modulus First-principles calculations Specific heat Thermal expansion Alloys

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Downlink Coverage Analysis in a Heterogeneous Cellular Network

Downlink Coverage Analysis in a Heterogeneous Cellular Netwo...

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IEEE Global Communications Conference

作者： Prasanna Madhusudhanan Juan G. Restrepo Youjian (Eugene) Liu Timothy X. Brown Department of Electrical Computer and Energy Engineering University of Colorado Department of Applied Mathematics Interdisciplinary University of Colorado Telecommunications Program University of Colorado

ISBN: (纸本)9781467309202

In this paper, we consider the downlink signal-to-interference-plus-noise ratio (SINR) analysis in a heterogeneous cellular network with K tiers. Each tier is characterized by a base-station (BS) arrangement according to a homogeneous Poisson point process with certain BS density, transmission power, random shadow fading factors with arbitrary distribution, arbitrary path-loss exponent and a certain bias towards admitting the mobile-station (MS). The MS associates with the BS that has the maximum instantaneous biased received power under the open access cell association scheme. For such a general setting, we provide an analytical characterization of the coverage probability at the MS.

关键词： Multi-tier networks Cellular Radio Co-channel Interference Fading channels Poisson point process Cochannel interference Fading channels point operation cellular radio Bahamas Downlink received power Mass spectroscopy Multiple Sclerosis Coverage Cells

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T-Cal: an optimal test for the calibration of predictive models

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2023年第1期24卷 15959-16030页

作者： Donghwan Lee Xinmeng Huang Hamed Hassani Edgar Dobriban Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia PA Department of Electrical and Systems Engineering University of Pennsylvania Philadelphia PA Department of Statistics and Data Science University of Pennsylvania Philadelphia PA

The prediction accuracy of machine learning methods is steadily increasing, but the calibration of their uncertainty predictions poses a significant challenge. Numerous works focus on obtaining well-calibrated predictive models, but less is known about reliably assessing model calibration. This limits our ability to know when algorithms for improving calibration have a real effect, and when their improvements are merely artifacts due to random noise in finite datasets. In this work, we consider detecting mis-calibration of predictive models using a finite validation dataset as a hypothesis testing problem. The null hypothesis is that the predictive model is calibrated, while the alternative hypothesis is that the deviation from calibration is sufficiently *** find that detecting mis-calibration is only possible when the conditional probabilities of the classes are sufficiently smooth functions of the predictions. When the conditional class probabilities are Hölder continuous, we propose T-Cal, a minimax optimal test for calibration based on a debiased plug-in estimator of the ℓ2-Expected Calibration Error (ECE). We further propose adaptive T-Cal, a version that is adaptive to unknown smoothness. We verify our theoretical findings with a broad range of experiments, including with several popular deep neural net architectures and several standard post-hoc calibration methods. T-Cal is a practical general-purpose tool, which--combined with classical tests for discrete-valued predictors--can be used to test the calibration of virtually any probabilistic classification method. T-Cal is available at https://***/dh7401/T-Cal.

关键词： uncertainty quantification calibration nonparametric statistics hypothesis testing minimax optimality

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