Reconstruction of Sparse Signals From &lt;formula formulatype="inline"&gt; &lt;tex Notation="TeX"&gt;$\ell_1$&lt;/tex&gt;&lt;/formula&gt; Dimensionality-Reduced Cauchy Random Projections

Ramirez, Ana B.; Arce, Gonzalo R.; Otero, Daniel; Paredes, José Luís; Sadler, Brian M.

doi:10.1109/tsp.2012.2208954

Cited by 17 publications

(12 citation statements)

References 42 publications

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“…A modified version, that accelerates the reconstruction of sparse signals by determining which coordinates are allowed to be estimated at each iteration, was proposed in [83].…”

Section: Lorentzian-based Coordinate Descent Algorithmmentioning

confidence: 99%

“…Carrillo et al propose reconstruction approaches based on the Lorentzian norm as the data fidelity term [41,42]. In addition, Ramirez et al develop an iterative algorithm to solve a Lorentzian 0 -regularized cost function using iterative weighted myriad filters [43]. A similar approach is used in [44] by solving an 0 -regularized least absolute deviation (LAD) regression problem yielding an iterative weighted median algorithm.…”

Section: Introductionmentioning

confidence: 99%

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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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“…A modified version, that accelerates the reconstruction of sparse signals by determining which coordinates are allowed to be estimated at each iteration, was proposed in [83].…”

Section: Lorentzian-based Coordinate Descent Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust compressive sensing of sparse signals: a review

Carrillo

Ramirez

Arce

et al. 2016

EURASIP J. Adv. Signal Process.

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“…However, Ramirez et al, proposed in [14] a distancepreserving condition between the geometric mean of the projections in the dimensionality reduced space, and the 1 norm of the original high-dimensional space satisfied by Cauchy random matrices. More precisely, the definition of the distance preservation condition for Cauchy random matrices is as follows.…”

Section: Robust Sampling Using Cauchy Random Projectionsmentioning

confidence: 99%

“…The · 0 -norm encourages sparsity in the solution and the Lorentzian norm is chosen in robust linear regression problems because it has optimality properties for Cauchy distributed samples [3,4]. The algorithm used to solve the problem in (4) is based on a coordinate-descent method, where at each iteration all the entries of the sparse vector are held constant except one, which is allowed to vary, and is estimated by a weighted myriad operator [14].…”

Section: Lorentzian Based Coordinate-descent Algorithmmentioning

confidence: 99%

“…Carrillo et al, propose reconstruction approaches based on the Lorentzian norm as data fidelity term [12,13]. In addition, Ramirez et al, develop an iterative algorithm to solve a Lorentzian 0 -regularized cost function using iterative weighted myriad filters [14]. A similar approach is used in [15] by solving an 0 -regularized least absolute deviation regression problem yielding an iterative weighted median algorithm.…”

Section: Introductionmentioning

confidence: 99%

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An overview of robust compressive sensing of sparse signals in impulsive noise

Ramirez

Carrillo

Arce

et al. 2015

2015 23rd European Signal Processing Conference (EUSIPCO)

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While compressive sensing (CS) has traditionally relied on 2 as an error norm, a broad spectrum of applications has emerged where robust estimators are required. Among those, applications where the sampling process is performed in the presence of impulsive noise, or where the sampling of the high-dimensional sparse signals requires the preservation of a distance different than 2 . This article overviews robust sampling and nonlinear reconstruction strategies for sparse signals based on the Cauchy distribution and the Lorentzian norm for the data fidelity. The derived methods outperform existing compressed sensing techniques in impulsive environments, thus offering a robust framework for CS.

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