Restricted isometry properties and nonconvex compressive sensing

Станева, Валентина

doi:10.2172/1454956

Cited by 176 publications

(360 citation statements)

References 0 publications

Supporting

Mentioning

353

Contrasting

Order By: Relevance

“…When it is satisfied, the RIP for a matrix Φ provides a sufficient condition to guarantee successful sparse recovery using a wide variety of algorithms [8,[11][12][13][14][15][16][17][18][19]. As an example, the RIP of order 2K (with isometry constant δ < √ 2 − 1) is a sufficient condition to permit ℓ 1 -minimization (the canonical convex optimization problem for sparse approximation) to exactly recover any K-sparse signal and to approximately recover those that are nearly sparse [11].…”

Section: The Restricted Isometry Propertymentioning

confidence: 99%

Analysis of Orthogonal Matching Pursuit using the Restricted Isometry Property

2009

View full text Add to dashboard Cite

Orthogonal Matching Pursuit (OMP) is the canonical greedy algorithm for sparse approximation. In this paper we demonstrate that the restricted isometry property (RIP) can be used for a very straightforward analysis of OMP. Our main conclusion is that the RIP of order K + 1 (with isometry constant δ <) is sufficient for OMP to exactly recover any K-sparse signal. Our analysis relies on simple and intuitive observations about OMP and matrices which satisfy the RIP. For restricted classes of K-sparse signals (those that are highly compressible), a relaxed bound on the isometry constant is also established. A deeper understanding of OMP may benefit the analysis of greedy algorithms in general. To demonstrate this, we also briefly revisit the analysis of the Regularized OMP (ROMP) algorithm.

show abstract

Section: The Restricted Isometry Propertymentioning

confidence: 99%

Analysis of Orthogonal Matching Pursuit using the Restricted Isometry Property

2009

View full text Add to dashboard Cite

show abstract

“…Remark. The Reweighted l 1 and the Reweighted LS both need a value of ǫ (or even a sequence of such values as in [5]) which is hard to optimize ahead of time, whereas the value u in the Alternating l 1 is a Lagrange multiplier, i.e. a dual variable.…”

Section: Monte Carlo Experimentsmentioning

confidence: 99%

An Alternating $l_1$ Approach to the Compressed Sensing Problem

Chretien¹

2010

IEEE Signal Process. Lett.

View full text Add to dashboard Cite

Compressed sensing is a new methodology for constructing sensors which allow sparse signals to be efficiently recovered using only a small number of observations. The recovery problem can often be stated as the one of finding the solution of an underdetermined system of linear equations with the smallest possible support. The most studied relaxation of this hard combinatorial problem is the l1-relaxation consisting of searching for solutions with smallest l1-norm. In this short note, based on the ideas of Lagrangian duality, we introduce an alternating l1 relaxation for the recovery problem enjoying higher recovery rates in practice than the plain l1 relaxation and the recent reweighted l1 method of Candès, Wakin and Boyd.

show abstract

“…The L p,∞ penalty is a convex relaxation of a pseudo-norm which counts the number of non-zero rows in W . Another consideration in L pq norm is the choice of p. Some works such as [28] have investigated the L p norm with 0 < p < 1. It is worth noting that for 0 < p < 1, Eq.…”

Section: Compact Representation Of the Featuresmentioning

confidence: 99%

Feature encoding in band-limited distributed surveillance systems

Rahimpour

Taalimi

2017

2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

View full text Add to dashboard Cite

Distributed surveillance systems have become popular in recent years due to security concerns. However, transmitting high dimensional data in bandwidth-limited distributed systems becomes a major challenge. In this paper, we address this issue by proposing a novel probabilistic algorithm based on the divergence between the probability distributions of the visual features in order to reduce their dimensionality and thus save the network bandwidth in distributed wireless smart camera networks. We demonstrate the effectiveness of the proposed approach through extensive experiments on two surveillance recognition tasks.

show abstract

Restricted isometry properties and nonconvex compressive sensing

Cited by 176 publications

References 0 publications

Analysis of Orthogonal Matching Pursuit using the Restricted Isometry Property

Analysis of Orthogonal Matching Pursuit using the Restricted Isometry Property

An Alternating $l_1$ Approach to the Compressed Sensing Problem

Feature encoding in band-limited distributed surveillance systems

Contact Info

Product

Resources

About