Corrupted Sensing: Novel Guarantees for Separating Structured Signals

Foygel, Rina; Mackey, Lester

doi:10.1109/tit.2013.2293654

Cited by 89 publications

(159 citation statements)

References 35 publications

(133 reference statements)

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“…The following theorem presents an upper bound for the reconstruction error of the proposed estimator in (31).…”

Section: Lorentzian-based Methodsmentioning

confidence: 99%

“…The LBP problem is hard to solve since it has a nonsmooth convex objective function and a nonconvex, noninear constraint. A sequential quadratic programming (SQP) method with a smooth approximation of the 1 norm is used in [41] to numerically solve the problem in (31). However, a less expensive approach is to solve a sequence of unconstrained problems of the form…”

Section: Theorem 3 ([41]) Letmentioning

confidence: 99%

“…Popilka et al, [21] were the first to analyze this model and proposed a reconstruction strategy that estimate first the sparse error pattern, and then estimate the true signal, in an iterative process. Related approaches are studied in [23][24][25][26][27][28][29][30][31][32]. These works assume a sparse error and estimate both signal and error at the same stage using a modified 1 minimization problem.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust compressive sensing of sparse signals: a review

Carrillo

Ramirez

Arce

et al. 2016

EURASIP J. Adv. Signal Process.

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Compressive sensing generally relies on the 2 norm for data fidelity, whereas in many applications, robust estimators are needed. Among the scenarios in which robust performance is required, applications where the sampling process is performed in the presence of impulsive noise, i.e., measurements are corrupted by outliers, are of particular importance. This article overviews robust nonlinear reconstruction strategies for sparse signals based on replacing the commonly used 2 norm by M-estimators as data fidelity functions. The derived methods outperform existing compressed sensing techniques in impulsive environments, while achieving good performance in light-tailed environments, thus offering a robust framework for CS.

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“…The following theorem presents an upper bound for the reconstruction error of the proposed estimator in (31).…”

Section: Lorentzian-based Methodsmentioning

confidence: 99%

Section: Theorem 3 ([41]) Letmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust compressive sensing of sparse signals: a review

Carrillo

Ramirez

Arce

et al. 2016

EURASIP J. Adv. Signal Process.

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“…In contrast, ideas from the contemporary signal processing literature frequently allow us to produce numerically sharp estimates for the Gaussian width of a cone. These techniques were developed in the papers [1,6,10,24,31]. We will outline one of the methods in Section 2.4.…”

Section: The Conic Gaussian Widthmentioning

confidence: 99%

Convex Recovery of a Structured Signal from Independent Random Linear Measurements

Tropp

2015

Applied and Numerical Harmonic Analysis

117

171

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This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar to recent results for standard Gaussian measurements, but the argument applies to a much wider class of measurement ensembles. To demonstrate the power of this approach, the chapter presents a short analysis of phase retrieval by tracenorm minimization. The key technical tool is a framework, due to Mendelson and coauthors, for bounding a nonnegative empirical process. MotivationSignal reconstruction from random measurements is a central preoccupation in contemporary signal processing. In this problem, we acquire linear measurements of an unknown, structured signal through a random sampling process. Given these random measurements, a standard method for recovering the unknown signal is to solve a convex optimization problem that enforces our prior knowledge about the structure. The basic question is how many measurements suffice to resolve a particular type of structure.Recent research has led to a comprehensive answer when the measurement operator follows the standard Gaussian distribution [1, 6, 10, 22, 24-26, 29, 31, 33]. The literature also contains satisfying answers for sub-Gaussian measurements [22] and subexponential measurements [18]. Other types of measurement systems are quite common, but we are not aware of a simple approach that allows us to analyze general measurements in a unified way.This chapter describes an approach that addresses a wide class of convex signal reconstruction problems involving random sampling. To understand these questions, the core challenge is to produce a lower bound on a nonnegative empirical process.

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“…In particular, the problem of extraction of block-sparse signals have been recently addressed in the community (e.g., [17]), while [18] provides guarantees for extraction of (non-block) sparse signals in presence of structured interference.…”

Section: Introductionmentioning

confidence: 99%

Attack-resilient state estimation in the presence of noise

Pajić

Tabuada

Lee

et al. 2015

2015 54th IEEE Conference on Decision and Control (CDC)

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Abstract-We consider the problem of attack-resilient state estimation in the presence of noise. We focus on the most general model for sensor attacks where any signal can be injected via the compromised sensors. An l0-based state estimator that can be formulated as a mixed-integer linear program and its convex relaxation based on the l1 norm are presented. For both l0 and l1-based state estimators, we derive rigorous analytic bounds on the state-estimation errors. We show that the worst-case error is linear with the size of the noise, meaning that the attacker cannot exploit noise and modeling errors to introduce unbounded state-estimation errors. Finally, we show how the presented attack-resilient state estimators can be used for sound attack detection and identification, and provide conditions on the size of attack vectors that will ensure correct identification of compromised sensors.

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Corrupted Sensing: Novel Guarantees for Separating Structured Signals

Cited by 89 publications

References 35 publications

Robust compressive sensing of sparse signals: a review

Robust compressive sensing of sparse signals: a review

Convex Recovery of a Structured Signal from Independent Random Linear Measurements

Attack-resilient state estimation in the presence of noise

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