Corpus ID: 215769089

# Sampling Rates for $\ell^1$-Synthesis

@inproceedings{Marz2020SamplingRF,
title={Sampling Rates for \$\ell^1\$-Synthesis},
author={Maximilian Marz and C. Boyer and J. Kahn and P. Weiss},
year={2020}
}
This work investigates the problem of signal recovery from undersampled noisy sub-Gaussian measurements under the assumption of a synthesis-based sparsity model. Solving the `1-synthesis basis pursuit allows for a simultaneous estimation of a coefficient representation as well as the sought-for signal. However, due to linear dependencies within redundant dictionary atoms it might be impossible to identify a specific representation vector, although the actual signal is still successfully… Expand

#### References

SHOWING 1-10 OF 74 REFERENCES
Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization
• Computer Science, Medicine
• Proceedings of the National Academy of Sciences of the United States of America
• 2003
Signal Space CoSaMP for Sparse Recovery With Redundant Dictionaries
• Computer Science, Mathematics
• IEEE Transactions on Information Theory
• 2013
Recovery of exact sparse representations in the presence of bounded noise
• J. Fuchs
• Computer Science, Mathematics
• IEEE Transactions on Information Theory
• 2005
The Convex Geometry of Linear Inverse Problems
• Mathematics, Computer Science
• Found. Comput. Math.
• 2012
Just relax: convex programming methods for identifying sparse signals in noise
• J. Tropp
• Mathematics, Computer Science
• IEEE Transactions on Information Theory
• 2006
Analysis versus synthesis in signal priors
• Mathematics, Computer Science
• 2006 14th European Signal Processing Conference
• 2006
Performance analysis of ℓ1-synthesis with coherent frames
• Computer Science, Mathematics
• 2012 IEEE International Symposium on Information Theory Proceedings
• 2012