# Sparse signal recovery in Hilbert spaces

@article{Pope2012SparseSR, title={Sparse signal recovery in Hilbert spaces}, author={Graeme Pope and Helmut B{\"o}lcskei}, journal={2012 IEEE International Symposium on Information Theory Proceedings}, year={2012}, pages={1463-1467} }

This paper reports an effort to consolidate numerous coherence-based sparse signal recovery results available in the literature. We present a single theory that applies to general Hilbert spaces with the sparsity of a signal defined as the number of (possibly infinite-dimensional) subspaces participating in the signal's representation. Our general results recover uncertainty relations and coherence-based recovery thresholds for sparse signals, block-sparse signals, multi-band signals, signals…

## 3 Citations

### Sampling and reconstruction in sparse atomic spaces

- Mathematics2013 IEEE International Conference on Acoustics, Speech and Signal Processing
- 2013

This paper provides a quantitative notion of the sparsity for infinite dimensional atomic spaces, and shows that the so defined sparsity can be expressed in terms of the support of the spectral density of the sequence which generates the atomic space.

### Structured sparce signal recovery in general Hilbert spaces

- Computer Science
- 2013

This thesis presents a general framework for a wide class of sparse signal recovery results, and shows how to make use of additional structure in the data, such as the clustering of the non-zero entries, or that the Non-Zero entries form a low-rank matrix, to solve underdetermined linear systems.

### Performance of Sparse Recovery Algorithms for the Reconstruction of Radar Images From Incomplete RCS Data

- Environmental Science, MathematicsIEEE Geoscience and Remote Sensing Letters
- 2015

In this letter, we compare the performances of sparse recovery algorithms (SRAs) for the reconstruction of a 2-D inverse synthetic aperture radar (ISAR) image from incomplete radar-cross-section…

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