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Hidden Cliques and the Certification of the Restricted Isometry Property [PDF]
IEEE Transactions on Information Theory, 2014 International audienceCompressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy this
Pascal Koiran, Anastasios Zouzias
exaly +6 more sources
Certifying the restricted isometry property is hard [PDF]
IEEE Transactions on Information Theory, 2012 This paper is concerned with an important matrix condition in compressed sensing known as the restricted isometry property (RIP). We demonstrate that testing whether a matrix satisfies RIP is NP-hard.
Bandeira, Afonso S. +3 more
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Restricted Isometry Property for General p-Norms [PDF]
IEEE Transactions on Information Theory, 2015 The Restricted Isometry Property (RIP) is a fundamental property of a matrix which enables sparse recovery. Informally, an $m \times n$ matrix satisfies RIP of order $k$ for the $\ell_p$ norm, if $\|Ax\|_p \approx \|x\|_p$ for every vector $x$ with at ...
Allen-Zhu, Zeyuan +2 more
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Computational Complexity of Certifying Restricted Isometry Property [PDF]
CoRR, 2014 Given a matrix $A$ with $n$ rows, a number ...
Natarajan, Abhiram, Wu, Yi
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The Restricted Isometry Property of Subsampled Fourier Matrices [PDF]
Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, 2015 A matrix $A \in \mathbb{C}^{q \times N}$ satisfies the restricted isometry property of order $k$ with constant $\varepsilon$ if it preserves the $\ell_2$ norm of all $k$-sparse vectors up to a factor of $1\pm \varepsilon$.
Haviv, Ishay, Regev, Oded
core +3 more sources
The road to deterministic matrices with the restricted isometry property [PDF]
Journal of Fourier Analysis and Applications, 2012 The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing.
A.S. Bandeira +39 more
core +6 more sources
Restricted Isometry Property of Random Subdictionaries [PDF]
IEEE Transactions on Information Theory, 2015 To appear in the IEEE Transactions on Information Theory, 2015.
Alexander Barg, Arya Mazumdar
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Orthogonal Matching Pursuit under the Restricted Isometry Property * [PDF]
Constructive Approximation, 2016 International audienceThis paper is concerned with the performance of Orthogonal Matching Pursuit (OMP) algorithms applied to a dictionary D in a Hilbert space H.
Cohen, Albert +2 more
core +8 more sources
Approximately Certifying the Restricted Isometry Property is Hard
IEEE Transactions on Information Theory, 2018 A matrix is said to possess the Restricted Isometry Property (RIP) if it acts as an approximate isometry when restricted to sparse vectors. Previous work has shown it to be NP-hard to determine whether a matrix possess this property, but only in a narrow range of parameters.
Jonathan Weed
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Fusion Frames and the Restricted Isometry Property [PDF]
Numerical Functional Analysis and Optimization, 2012 We will show that tight frames satisfying the restricted isometry property give rise to nearly tight fusion frames which are nearly orthogonal and hence are nearly equi-isoclinic. We will also show how to replace parts of the RIP frame with orthonormal sets while maintaining the RIP property.
Jameson Cahill, Peter G Casazza
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