Results 131 to 140 of about 794 (157)

Covering radius and the Restricted Isometry Property

2011 IEEE Information Theory Workshop, 2011
The Restricted Isometry Property or RIP introduced by Candes and Tao requires an n × p dictionary to act as a near isometry on all k-sparse signals. This paper provides a very simple condition under which a dictionary Φ(C) obtained by exponentiating codewords from a binary linear code C satisfies the RIP with high probability.
A. Robert Calderbank, Sina Jafarpour, Maria Nastasescu   +2 more
openaire   +1 more source

The restricted isometry property for random block diagonal matrices

Applied and Computational Harmonic Analysis, 2015
In Compressive Sensing, the Restricted Isometry Property (RIP) ensures that robust recovery of sparse vectors is possible from noisy, undersampled measurements via computationally tractable algorithms. It is by now well-known that Gaussian (or, more generally, sub-Gaussian) random matrices satisfy the RIP under certain conditions on the number of ...
Han Lun Yap, Christopher J Rozell, Michael B Wakin   +2 more
exaly   +5 more sources

Compressed Sensing: How Sharp Is the Restricted Isometry Property? [PDF]

SIAM Review, 2011
Compressed Sensing (CS) seeks to recover an unknown vector with $N$ entries by making far fewer than $N$ measurements; it posits that the number of compressed sensing measurements should be comparable to the information content of the vector, not simply $N$. CS combines the important task of compression directly with the measurement task.
Jeffrey D Blanchard, Jared Tanner
exaly   +7 more sources

Analysis of Orthogonal Matching Pursuit Using the Restricted Isometry Property [PDF]

IEEE Transactions on Information Theory, 2010
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 $δ< \frac{1}{3\sqrt{K}}$) is sufficient for OMP to ...
Mark A Davenport, Michael B Wakin
exaly   +3 more sources

The Restricted Isometry Property for block diagonal matrices

2011 45th Annual Conference on Information Sciences and Systems, 2011
In compressive sensing (CS), the Restricted Isometry Property (RIP) is a powerful condition on measurement operators which ensures robust recovery of sparse vectors is possible from noisy, undersampled measurements via computationally tractable algorithms.
Han Lun Yap, Armin Eftekhari, Michael B. Wakin, Christopher J. Rozell   +3 more
openaire   +1 more source

Restricted Isometry Property

2013
This chapter introduces the concept of restricted isometry constants. This is a more powerful tool than the less involved notion of coherence to assess the quality of a measurement matrix for sparse recovery. Some basic properties of the restricted isometry constants and of the related restricted orthogonality constants are presented first as well as ...
Simon Foucart, Holger Rauhut
openaire   +1 more source

The Statistical Restricted Isometry Property For Gabor Systems

2018 IEEE Statistical Signal Processing Workshop (SSP), 2018
Gabor matrices are important in many different areas of timefrequency analysis like radar or communications. For applications with sparse data, the question arises whether these matrices satisfy some recovery guarantees for compressive sampling, and which generating windows yield a matrix with restricted isometric property.
Alihan Kaplan, Volker Pohl, Dae Gwan Lee
openaire   +1 more source

Analysis of the Restricted Isometry Property for Gaussian Random Matrices

2015 IEEE Global Communications Conference (GLOBECOM), 2014
In the context of compressed sensing, we provide a new approach to the analysis of the symmetric and asymmetric restricted isometry property for Gaussian measurement matrices. The proposed method relies on the exact distribution of the extreme eigenvalues for Wishart matrices, or on its approximation based on the Tracy-Widom law, which in turn can be ...
Chiani, Marco, Elzanaty, Ahmed, Giorgetti, Andrea, IEEE   +3 more
openaire   +3 more sources

Deterministic matrices with the restricted isometry property

SPIE Proceedings, 2011
The state of the art in compressed sensing uses sensing matrices which satisfy the restricted isometry property (RIP). Unfortunately, the known deterministic RIP constructions fall short of the random constructions, which are only valid with high probability.
Matthew Fickus, Dustin G. Mixon
openaire   +1 more source

Restricted $p$-Isometry Properties of Nonconvex Matrix Recovery

IEEE Transactions on Information Theory, 2013
Recently, a nonconvex relaxation of low-rank matrix recovery (LMR), called the Schatten- p quasi-norm minimization (0
Min Zhang 0062, Zheng-Hai Huang, Ying Zhang   +2 more
openaire   +1 more source