Methods for Sparse Signal Recovery Using Kalman Filtering With Embedded Pseudo-Measurement Norms and Quasi-Norms

@article{Carmi2010MethodsFS,
  title={Methods for Sparse Signal Recovery Using Kalman Filtering With Embedded Pseudo-Measurement Norms and Quasi-Norms},
  author={Avishy Carmi and P. Gurfil and D. Kanevsky},
  journal={IEEE Transactions on Signal Processing},
  year={2010},
  volume={58},
  pages={2405-2409}
}
  • Avishy Carmi, P. Gurfil, D. Kanevsky
  • Published 2010
  • Computer Science, Mathematics
  • IEEE Transactions on Signal Processing
  • We present two simple methods for recovering sparse signals from a series of noisy observations. The theory of compressed sensing (CS) requires solving a convex constrained minimization problem. We propose solving this optimization problem by two algorithms that rely on a Kalman filter (KF) endowed with a pseudo-measurement (PM) equation. Compared to a recently-introduced KF-CS method, which involves the implementation of an auxiliary CS optimization algorithm (e.g., the Dantzig selector), our… CONTINUE READING
    An Iterative Kalman-Like Algorithm Ignoring Noise and Initial Conditions
    • 135
    Kalman filtering for compressed sensing
    • 26
    • PDF
    Sparse Recovery of Streaming Signals Using $\ell_1$-Homotopy
    • 120
    • PDF
    Tracking dynamic sparse signals using Hierarchical Bayesian Kalman filters
    • 39
    • PDF
    Sparsity penalties in dynamical system estimation
    • 93
    • PDF
    Convex feasibility modeling and projection methods for sparse signal recovery
    • 12
    • PDF
    Dynamic filtering of sparse signals using reweighted ℓ1
    • 27
    • PDF

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 17 REFERENCES
    Kalman filtered Compressed Sensing
    • 290
    • Highly Influential
    • PDF
    Sparse MRI: The application of compressed sensing for rapid MR imaging
    • 4,854
    • PDF
    Exact Reconstruction of Sparse Signals via Nonconvex Minimization
    • 1,077
    Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
    • 13,393
    • Highly Influential
    • PDF
    Atomic Decomposition by Basis Pursuit
    • 9,288
    • PDF
    Compressive sampling
    • Emamnuel J. Candès
    • 2006
    • 2,302
    • Highly Influential
    • PDF
    On Kalman Filtering With Nonlinear Equality Constraints
    • 266
    • PDF
    Regression Shrinkage and Selection via the Lasso
    • 29,282
    • PDF
    Compressed sensing in dynamic MRI
    • 501
    Least angle regression
    • 7,811
    • PDF