Robust compressive sensing of sparse signals: a review

  title={Robust compressive sensing of sparse signals: a review},
  author={Rafael E. Carrillo and Ana B. Ramirez and Gonzalo R. Arce and Kenneth E. Barner and Brian M. Sadler},
  journal={EURASIP Journal on Advances in Signal Processing},
Compressive sensing generally relies on the ℓ2 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 ℓ2 norm by M… 

A Comprehensive Review on Compressive Sensing

This study aims to present an overview of existing Compressive Sensing approaches so that researchers can better understand existing limitations and seek to improve accuracy and precision.

Compressive Sensing Using Symmetric Alpha-Stable Distributions – Part I : Robust Nonlinear Sampling

An effcient compressive sampling method that suppresses the effects of impulsive observation noise by designing a robust nonlinear sampling operator based on a generalized alpha-stable matched flter is introduced.

Robust Sparse Recovery via Weakly Convex Regularization

Theoretical results prove that the sparse signal can be precisely reconstructed by RPGG from compressive measurements with sparse noise or robustly recovered from those with impulsive noise, and simulations demonstrate that RPGG with tuned parameters outperforms other robust sparse recovery algorithms.

Weakly Convex Regularized Robust Sparse Recovery Methods With Theoretical Guarantees

Theoretical results prove that the sparse signal can be precisely reconstructed by RPGG from compressive measurements with sparse noise or robustly recovered from those with impulsive noise, and simulations demonstrate that RPGG with tuned parameters outperforms other robust sparse recovery algorithms.

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Comparison with existing robust CS reconstruction algorithms is conducted via simulations, showing that the proposed $l_0$-MCC and MB-$l-0$ -MCC can achieve significantly better performance than other algorithms.

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ADMM-based approach for compressive sensing with negative weights

: In general, weighted compressive sensing recovery needs to solve optimisation problems with the objective function being the sum of a weighted ℓ 1 -norm and a regularised differentiable convex



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Numerical simulations demonstrated that the proposed robust formulation for sparse recovery using the generalized ℓp-norm with 0 <; p <; 2 as the metric for the residual error under ™1-norm regularization can achieve state-of-the-art robust performance in highly impulsive noise.

Robust iterative hard thresholding for compressed sensing

A robust IHT method based on ideas from M-estimation that estimates the sparse signal and the scale of the error distribution simultaneously simultaneously is proposed that has a negligible performance loss compared to IHT under Gaussian noise, but superior performance under heavy-tailed non-Gaussian noise conditions.

Robust greedy algorithms for compressed sensing

The problem of sparse signal reconstruction in the presence of possibly impulsive noise is studied and a robust M-estimation based ridge regression is considered and shown to possess high potential when utilized in CS algorithms.

Exact signal recovery from sparsely corrupted measurements through the Pursuit of Justice

It is demonstrated that a simple algorithm, which is dubbed Justice Pursuit (JP), can achieve exact recovery from measurements corrupted with sparse noise.

Robust Sampling and Reconstruction Methods for Sparse Signals in the Presence of Impulsive Noise

This paper proposes a robust nonlinear measurement operator based on the weighed myriad estimator employing a Lorentzian norm constraint on the residual error to recover sparse signals from noisy measurements and demonstrates that the proposed methods significantly outperform commonly employed compressed sensing sampling and reconstruction techniques in impulsive environments.

Reconstruction of sparse signals from highly corrupted measurements by nonconvex minimization

  • Marko Filipovic
  • Computer Science
    2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
  • 2014
A theoretical justification of the proposed approach based on ℓ<sub>p</sub> minimization for 0 <; p ≤ 1 is provided, based on analogous reasoning as in the case when measurements are not corrupted by large errors.

Lorentzian Iterative Hard Thresholding: Robust Compressed Sensing With Prior Information

Simulation results demonstrate that the Lorentzian-based IHT algorithm significantly outperform commonly employed sparse reconstruction techniques in impulsive environments, while providing comparable performance in less demanding, light-tailed environments.

Improved Image Recovery From Compressed Data Contaminated With Impulsive Noise

An iterative algorithm is proposed for solving the robust CS problem that exploits the power of existing CS solvers and the upper bound on the recovery error in the case of non-Gaussian noise is reduced.

Bayesian compressed sensing using generalized Cauchy priors

This paper forms the sparse recovery problem in a Bayesian framework using algebraic-tailed priors from the generalized Cauchy distribution (GCD) family for the signal coefficients and develops an iterative reconstruction algorithm from this Bayesian formulation.

Recovery of Sparsely Corrupted Signals

Deterministic recovery guarantees based on a novel uncertainty relation for pairs of general dictionaries are presented and corresponding practicable recovery algorithms are provided.