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
  • D. Donoho, Michael Elad
  • 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
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
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
Analysis ℓ1-recovery with Frames and Gaussian Measurements
Compressed Sensing with 1D Total Variation: Breaking Sample Complexity Barriers via Non-Uniform Recovery
Performance analysis of ℓ1-synthesis with coherent frames
...
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3
4
5
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