Compressive Sensing Using Low Density Frames
Abstract
We consider the compressive sensing of a sparse or compressible signal ${\bf x} \in {\mathbb R}^M$. We explicitly construct a class of measurement matrices, referred to as the low density frames, and develop decoding algorithms that produce an accurate estimate $\hat{\bf x}$ even in the presence of additive noise. Low density frames are sparse matrices and have small storage requirements. Our decoding algorithms for these frames have $O(M)$ complexity. Simulation results are provided, demonstrating that our approach significantly outperforms state-of-the-art recovery algorithms for numerous cases of interest. In particular, for Gaussian sparse signals and Gaussian noise, we are within 2 dB range of the theoretical lower bound in most cases.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2009
- DOI:
- 10.48550/arXiv.0903.0650
- arXiv:
- arXiv:0903.0650
- Bibcode:
- 2009arXiv0903.0650A
- Keywords:
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- Computer Science - Information Theory;
- Statistics - Computation
- E-Print:
- 11 pages, 6 figures, Submitted to IEEE Transactions on Signal Processing