Using Multilayer Perceptrons to Align High Range Resolution Radar Signals

Gil-Pita, Roberto; Rosa-Zurera, Manuel; Jarabo-Amores, P.; López-Ferreras, F.

doi:10.1007/11550907_144

Cited by 14 publications

(12 citation statements)

References 6 publications

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“…Multireference alignment (MRA) seeks to estimate a signal from numerous noisy and cyclically shifted copies of itself. This problem serves as a model for scientific problems in structural biology [1,2,3,4], radar [5,6] and image processing [7,8,9]. Algorithmic and statistical properties of MRA have been analyzed in [10,11,12,13,14].…”

Section: Introductionmentioning

confidence: 99%

Heterogeneous multireference alignment: A single pass approach

Boumal

Bendory

Lederman

et al. 2018

2018 52nd Annual Conference on Information Sciences and Systems (CISS)

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Multireference alignment (MRA) is the problem of estimating a signal from many noisy and cyclically shifted copies of itself. In this paper, we consider an extension called heterogeneous MRA, where K signals must be estimated, and each observation comes from one of those signals, unknown to us. This is a simplified model for the heterogeneity problem notably arising in cryo-electron microscopy. We propose an algorithm which estimates the K signals without estimating either the shifts or the classes of the observations. It requires only one pass over the data and is based on low-order moments that are invariant under cyclic shifts. Given sufficiently many measurements, one can estimate these invariant features averaged over the K signals. We then design a smooth, non-convex optimization problem to compute a set of signals which are consistent with the estimated averaged features. We find that, in many cases, the proposed approach estimates the set of signals accurately despite non-convexity, and conjecture the number of signals K that can be resolved as a function of the signal length L is on the order of √ L.

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Section: Introductionmentioning

confidence: 99%

Heterogeneous multireference alignment: A single pass approach

Boumal

Bendory

Lederman

et al. 2018

2018 52nd Annual Conference on Information Sciences and Systems (CISS)

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“…The signal is thus subjected to both random translation and additive noise. The MRA problem arises in numerous applications, including structural biology [1][2][3][4][5][6], single cell genomic sequencing [7], radar [8,9], crystalline simulations [10], image registration [11][12][13], and signal processing [8]. It is a simplified model relevant for Cryo-Electron Microscopy (Cryo-EM), an imaging technique for molecules which achives near atomic resolution [14][15][16].…”

Section: Model 1 (Classic Mra)mentioning

confidence: 99%

“…where b Φ ( f , M ) is a bias term depending on the choice of Φ, f , and the signal corruption model M . If (9) holds and if we can compute a b such that E bΦ (y (8) to reduce the bias:…”

Section: Motivation and Related Workmentioning

confidence: 99%

Wavelet invariants for statistically robust multi-reference alignment

Hirn¹,

Little²

2019

Preprint

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We propose a nonlinear, wavelet based signal representation that is translation invariant and robust to both additive noise and random dilations. Motivated by the multi-reference alignment problem and generalizations thereof, we analyze the statistical properties of this representation given a large number of independent corruptions of a target signal. We prove the nonlinear wavelet based representation uniquely defines the power spectrum but allows for an unbiasing procedure that cannot be directly applied to the power spectrum. After unbiasing the representation to remove the effects of the additive noise and random dilations, we recover an approximation of the power spectrum by solving a convex optimization problem, and thus obtain the target signal up to an unknown phase. Extensive numerical experiments demonstrate the statistical robustness of this approximation procedure. Multi-reference alignment, method of invariants, wavelets, signal processing, wavelet scattering transform

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“…The Multi Reference Alignment (MRA) problem is a simple model that captures fundamental characteristics of various statistical models with latent group actions. It arises in various questions across science and engineering such as structural biology [Sad89, Dia92, SVN + 05, PMMC11, TS12, PC14], image recognition [Bro92, DM98, FZB02, RFM07], robotics [RCBL19] and signal processing [ZvdHGG03,GPRZJALF05]. This problem also serves as a simplification for more complex ones that feature repeated observations of a signal subject to latent group actions and additive measurement noise.…”

Section: Introduction 1the Mra Problemmentioning

confidence: 99%

Sparse Multi-Reference Alignment : Phase Retrieval, Uniform Uncertainty Principles and the Beltway Problem

Ghosh¹,

Rigollet²

2021

Preprint

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Motivated by cutting-edge applications like cryo-electron microscopy (cryo-EM), the Multi-Reference Alignment (MRA) model entails the learning of an unknown signal from repeated measurements of its images under the latent action of a group of isometries and additive noise of magnitude σ. Despite significant interest, a clear picture for understanding rates of estimation in this model has emerged only recently, particularly in the high-noise regime σ ≫ 1 that is highly relevant in applications. Recent investigations have revealed a remarkable asymptotic sample complexity of order σ 6 for certain signals whose Fourier transforms have full support, in stark contrast to the traditional σ 2 that arise in regular models. Often prohibitively large in practice, these results have prompted the investigation of variations around the MRA model where better sample complexity may be achieved. In this paper, we show that sparse signals exhibit an intermediate σ 4 sample complexity even in the classical MRA model. Our results explore and exploit connections of the MRA estimation problem with two classical topics in applied mathematics: the beltway problem from combinatorial optimization, and uniform uncertainty principles from harmonic analysis.

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Using Multilayer Perceptrons to Align High Range Resolution Radar Signals

Cited by 14 publications

References 6 publications

Heterogeneous multireference alignment: A single pass approach

Heterogeneous multireference alignment: A single pass approach

Wavelet invariants for statistically robust multi-reference alignment

Sparse Multi-Reference Alignment : Phase Retrieval, Uniform Uncertainty Principles and the Beltway Problem

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