# Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling

@article{Adcock2019UniformRI, title={Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling}, author={B. Adcock and Vegard Antun and A. Hansen}, journal={ArXiv}, year={2019}, volume={abs/1905.00126} }

Infinite-dimensional compressed sensing deals with the recovery of analog signals (functions) from linear measurements, often in the form of integral transforms such as the Fourier transform. This framework is well-suited to many real-world inverse problems, which are typically modelled in infinite-dimensional spaces, and where the application of finite-dimensional approaches can lead to noticeable artefacts. Another typical feature of such problems is that the signals are not only sparse in… CONTINUE READING

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#### References

SHOWING 1-10 OF 33 REFERENCES

On oracle-type local recovery guarantees in compressed sensing

- Computer Science, Mathematics
- ArXiv
- 2018

9- PDF

Compressed sensing with local structure: uniform recovery guarantees for the sparsity in levels class

- Mathematics, Computer Science
- ArXiv
- 2016

23- PDF

A Note on Compressed Sensing of Structured Sparse Wavelet Coefficients From Subsampled Fourier Measurements

- Mathematics, Computer Science
- IEEE Signal Processing Letters
- 2016

21- PDF

Generalized Sampling and Infinite-Dimensional Compressed Sensing

- Mathematics, Computer Science
- Found. Comput. Math.
- 2016

127- PDF

Robustness to Unknown Error in Sparse Regularization

- Mathematics, Computer Science
- IEEE Transactions on Information Theory
- 2018

22- PDF

Stable recovery of low-dimensional cones in Hilbert spaces: One RIP to rule them all

- Computer Science, Mathematics
- ArXiv
- 2015

28- PDF

On the Absence of Uniform Recovery in Many Real-World Applications of Compressed Sensing and the Restricted Isometry Property and Nullspace Property in Levels

- Computer Science, Mathematics
- SIAM J. Imaging Sci.
- 2017

9- PDF