Estimates of the Restricted Isometry Constant in Super Greedy Algorithms

Wei, Xiujie; Ye, Peixin

doi:10.14257/ijfgcn.2015.8.5.14

Cited by 2 publications

(1 citation statement)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper, we consider the orthogonal super greedy algorithm (OSGA), which is more efficient than OGA from the viewpoint of computational complexity. The performances of (OSGA) in greedy approximation and signal recovering were analyzed in [8][9][10][11][12]. We will make further study on the efficiency of the OSGA from two aspects.…”

Section: Introductionmentioning

confidence: 99%

Efficiency of orthogonal super greedy algorithm under the restricted isometry property

Wei

2019

J Inequal Appl

Self Cite

View full text Add to dashboard Cite

We investigate the efficiency of orthogonal super greedy algorithm (OSGA) for sparse recovery and approximation under the restricted isometry property (RIP). We first show that under the RIP conditions of the measurement matrix Φ and the minimum magnitude of the nonzero coordinates of the signal, for l 2 bounded or l ∞ bounded noise vector e, with explicit stopping rules, OSGA can recover the support of an arbitrary K-sparse signal x from y = Φx + e in at most K steps. Then, we investigate the error performance of OSGA in m term approximation with regards to dictionaries satisfying the RIP in a separable Hilbert space. We establish a Lebesgue-type inequality for OSGA. Based on this inequality, we obtain the optimal rate of convergence for the sparse class induced by such dictionaries.

show abstract

Section: Introductionmentioning

confidence: 99%

Efficiency of orthogonal super greedy algorithm under the restricted isometry property

Wei

2019

J Inequal Appl

Self Cite

View full text Add to dashboard Cite

show abstract

Almost optimality of orthogonal super greedy algorithms for incoherent dictionaries

Shao

2017

Int. J. Wavelets Multiresolut Inf. Process.

View full text Add to dashboard Cite

We investigate the efficiency of weak orthogonal super greedy algorithm (WOSGA) for [Formula: see text]-term approximation with respect to dictionaries which are [Formula: see text]-unconditional in arbitrary Hilbert space [Formula: see text] For an element [Formula: see text], let [Formula: see text] be the output of WOSGA after [Formula: see text] steps for some constant [Formula: see text]. We show that the residual [Formula: see text] can be bounded by a constant multiplying the error of best [Formula: see text]-term approximation to [Formula: see text] Moreover, we get an element [Formula: see text], through a simple postprocessing of [Formula: see text] by retaining its [Formula: see text] largest components in absolute value, which realizes near best [Formula: see text]-term approximation for [Formula: see text] Our results are obtained for dictionaries in [Formula: see text] which satisfies the weaker assumption than the RIP condition.

show abstract

Estimates of the Restricted Isometry Constant in Super Greedy Algorithms

Abstract: Abstract

Cited by 2 publications

References 3 publications

Efficiency of orthogonal super greedy algorithm under the restricted isometry property

Efficiency of orthogonal super greedy algorithm under the restricted isometry property

Almost optimality of orthogonal super greedy algorithms for incoherent dictionaries

Contact Info

Product

Resources

About