The replica-symmetric prediction for compressed sensing with Gaussian matrices is exact

@article{Reeves2016TheRP,
  title={The replica-symmetric prediction for compressed sensing with Gaussian matrices is exact},
  author={Galen Reeves and Henry D. Pfister},
  journal={2016 IEEE International Symposium on Information Theory (ISIT)},
  year={2016},
  pages={665-669}
}
  • Galen Reeves, Henry D. Pfister
  • Published in
    IEEE International Symposium…
    2016
  • Computer Science, Mathematics
  • This paper considers the fundamental limit of compressed sensing for i.i.d. signal distributions and i.i.d. Gaussian measurement matrices. Its main contribution is a rigorous characterization of the asymptotic mutual information (MI) and minimum mean-square error (MMSE) in this setting. Under mild technical conditions, our results show that the limiting MI and MMSE are equal to the values predicted by the replica method from statistical physics. This resolves a well-known problem that has… CONTINUE READING

    Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

    Figures, Tables, and Topics from this paper.

    Explore Further: Topics Discussed in This Paper

    Citations

    Publications citing this paper.
    SHOWING 1-10 OF 62 CITATIONS

    I-MMSE relations in random linear estimation and a sub-extensive interpolation method

    • Jean Barbier, Nicolas Macris
    • Mathematics, Computer Science, Physics
    • 2017 IEEE International Symposium on Information Theory (ISIT)
    • 2017
    VIEW 16 EXCERPTS
    CITES BACKGROUND, RESULTS & METHODS
    HIGHLY INFLUENCED

    Understanding Phase Transitions via Mutual Information and MMSE

    VIEW 3 EXCERPTS
    CITES BACKGROUND

    Compressed sensing under optimal quantization

    VIEW 6 EXCERPTS
    CITES METHODS, BACKGROUND & RESULTS

    The stochastic interpolation method: A simple scheme to prove replica formulas in Bayesian inference

    VIEW 4 EXCERPTS
    CITES METHODS & BACKGROUND
    HIGHLY INFLUENCED

    Conditional central limit theorems for Gaussian projections

    • Galen Reeves
    • Mathematics, Computer Science
    • 2017 IEEE International Symposium on Information Theory (ISIT)
    • 2016
    VIEW 3 EXCERPTS
    CITES BACKGROUND

    Bayes-Optimal Convolutional AMP

    VIEW 1 EXCERPT
    CITES BACKGROUND

    Rigorous Dynamics of Expectation-Propagation-Based Signal Recovery from Unitarily Invariant Measurements

    • Keigo Takeuchi
    • Computer Science
    • IEEE Transactions on Information Theory
    • 2020
    VIEW 1 EXCERPT
    CITES METHODS

    FILTER CITATIONS BY YEAR

    2016
    2020

    CITATION STATISTICS

    • 3 Highly Influenced Citations

    • Averaged 18 Citations per year from 2017 through 2019

    • 27% Increase in citations per year in 2019 over 2018

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 50 REFERENCES

    Randomly spread CDMA: asymptotics via statistical physics

    VIEW 5 EXCERPTS
    HIGHLY INFLUENTIAL

    Asymptotic MMSE analysis under sparse representation modeling

    VIEW 1 EXCERPT

    Conditional central limit theorems for Gaussian projections

    • Galen Reeves
    • Mathematics, Computer Science
    • 2017 IEEE International Symposium on Information Theory (ISIT)
    • 2016
    VIEW 2 EXCERPTS

    The replica-symmetric prediction for compressed sensing with Gaussian matrices is exact

    VIEW 1 EXCERPT

    Compressed sensing phase transitions: Rigorous bounds versus replica predictions

    Functional Properties of Minimum Mean-Square Error and Mutual Information

    VIEW 1 EXCERPT