# On Asymptotic Incoherence and Its Implications for Compressed Sensing of Inverse Problems

@article{Jones2016OnAI, title={On Asymptotic Incoherence and Its Implications for Compressed Sensing of Inverse Problems}, author={A. Jones and B. Adcock and A. Hansen}, journal={IEEE Transactions on Information Theory}, year={2016}, volume={62}, pages={1020-1037} }

Recently, it has been shown that incoherence is an unrealistic assumption for compressed sensing when applied to many inverse problems. Instead, the key property that permits efficient recovery in such problems is the so-called local incoherence. Similarly, the standard notion of sparsity is also inadequate for many real-world problems. In particular, in many applications, the optimal sampling strategy depends on asymptotic incoherence and the signal sparsity structure. The purpose of this… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 66 REFERENCES

Breaking the coherence barrier: A new theory for compressed sensing

- Computer Science, Mathematics
- 2013

185

Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing

- Computer Science
- 2013

60

Generalized Sampling and Infinite-Dimensional Compressed Sensing

- Mathematics, Computer Science
- 2016

117

Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies

- Computer Science, Mathematics
- 2015

132

Sparse MRI: The application of compressed sensing for rapid MR imaging.

- Medicine, Mathematics
- 2007

4761

Generalized sampling: stable reconstructions, inverse problems and compressed sensing over the continuum

- Mathematics, Computer Science
- 2013

32