Corpus ID: 821322

Local stability and robustness of sparse dictionary learning in the presence of noise

@article{Jenatton2012LocalSA,
  title={Local stability and robustness of sparse dictionary learning in the presence of noise},
  author={Rodolphe Jenatton and R{\'e}mi Gribonval and Francis R. Bach},
  journal={ArXiv},
  year={2012},
  volume={abs/1210.0685}
}
  • Rodolphe Jenatton, Rémi Gribonval, Francis R. Bach
  • Published in ArXiv 2012
  • Computer Science, Mathematics
  • A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical successes in various fields ranging from image to audio processing, there have only been a few theoretical arguments supporting these evidences. In particular, sparse coding, or sparse dictionary learning, relies on a non-convex procedure whose local minima have… CONTINUE READING

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

    Citations

    Publications citing this paper.
    SHOWING 1-10 OF 33 CITATIONS

    On the Identifiability of Overcomplete Dictionaries via the Minimisation Principle Underlying K-SVD

    VIEW 6 EXCERPTS
    CITES BACKGROUND, RESULTS & METHODS
    HIGHLY INFLUENCED

    NOODL: Provable Online Dictionary Learning and Sparse Coding

    VIEW 3 EXCERPTS
    CITES BACKGROUND

    A Clustering Approach to Learning Sparsely Used Overcomplete Dictionaries

    VIEW 1 EXCERPT
    CITES BACKGROUND

    On the Reconstruction Risk of Convolutional Sparse Dictionary Learning

    VIEW 1 EXCERPT
    CITES BACKGROUND

    Learning Sparsely Used Overcomplete Dictionaries via Alternating Minimization

    VIEW 2 EXCERPTS
    CITES BACKGROUND

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 37 REFERENCES

    On the local correctness of ℓ1-minimization for dictionary learning

    VIEW 11 EXCERPTS
    HIGHLY INFLUENTIAL

    Linear algebra in action

    VIEW 3 EXCERPTS
    HIGHLY INFLUENTIAL

    Recovery of exact sparse representations in the presence of bounded noise

    • Jean-Jacques Fuchs
    • Computer Science, Mathematics
    • IEEE Transactions on Information Theory
    • 2005
    VIEW 5 EXCERPTS
    HIGHLY INFLUENTIAL

    Compressible Distributions for High-Dimensional Statistics

    VIEW 1 EXCERPT

    Optimization with Sparsity-Inducing Penalties