2015 International Conference on Sampling Theory and Applications (SampTA) 2015
DOI: 10.1109/sampta.2015.7148900
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On random and deterministic compressed sensing and the Restricted Isometry Property in levels

Abstract: Compressed sensing (CS) is one of the great successes of computational mathematics in the past decade. There are a collection of tools which aim to mathematically describe compressed sensing when the sampling pattern is taken in a random or deterministic way. Unfortunately, there are many practical applications where the well studied concepts of uniform recovery and the Restricted Isometry Property (RIP) can be shown to be insufficient explanations for the success of compressed sensing. This occurs both when t… Show more

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Cited by 8 publications
(11 citation statements)
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“…with weights w j > 0. We show that for w opt,i = 1/ √ K i , the admissible RIP constant δ Σ ( f w opt ) does not depend on the ratios K i /K j contrary to the result for w i = 1 and simple sparsity from [11].…”
Section: Extension To Block Structured Sparsitycontrasting
confidence: 71%
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“…with weights w j > 0. We show that for w opt,i = 1/ √ K i , the admissible RIP constant δ Σ ( f w opt ) does not depend on the ratios K i /K j contrary to the result for w i = 1 and simple sparsity from [11].…”
Section: Extension To Block Structured Sparsitycontrasting
confidence: 71%
“…Even with adjusted weights, our lower bound δ Σ ( f w opt ) depends on J. In light of Bastounis et al [11],…”
Section: Extension To Block Structured Sparsitymentioning
confidence: 69%
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“…In [1], a model of sparsity in levels was introduced: it is in fact a structured sparsity in levels model with classical sparsity (each group is reduced to a single coordinate) in each level. In [6], Bastounis et al showed that when the model Σ is sparsity in levels and f (·) = j · Aj = · 1 (i.e., with weights w j = 1, in this case, κ 2 w = κ 2 1 is the maximum ratio of sparsity between levels), the RIP with constant δ = 1/ J(κ 1 + 0.25) 2 + 1) on Σ − Σ guarantees recovery. This constant is improved to the constant δ Σ (f w ) ≥ 1/ √ 2 + J when weighting the norm of each level with w j = 1/ k j .…”
Section: Example: the Case Of Sparsity In Levelsmentioning
confidence: 99%