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

@article{Li2016CompressedSW, title={Compressed sensing with local structure: uniform recovery guarantees for the sparsity in levels class}, author={Chen Li and B. Adcock}, journal={ArXiv}, year={2016}, volume={abs/1601.01988} }

In compressed sensing, it is often desirable to consider signals possessing additional structure beyond sparsity. One such structured signal model - which forms the focus of this paper - is the local sparsity in levels class. This class has recently found applications in problems such as compressive imaging, multi-sensor acquisition systems and sparse regularization in inverse problems. In this paper we present uniform recovery guarantees for this class when the measurement matrix corresponds… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 42 REFERENCES

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

- Mathematics, Computer Science
- 2016

20

Sparsity and parallel acquisition: Optimal uniform and nonuniform recovery guarantees

- Computer Science, Mathematics
- 2016

4

Structure dependent sampling in compressed sensing: theoretical guarantees for tight frames

- Mathematics, Computer Science
- 2015

15

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

- Computer Science, Mathematics
- 2015

25

Compressed sensing with structured sparsity and structured acquisition

- Mathematics, Computer Science
- 2015

40

Compressed Sensing and Matrix Completion with Constant Proportion of Corruptions

- Computer Science, Mathematics
- 2011

131