Signal Recovery by Proximal Forward-Backward Splitting

@article{Combettes2005SignalRB,
  title={Signal Recovery by Proximal Forward-Backward Splitting},
  author={P. L. Combettes and Val{\'e}rie R. Wajs},
  journal={Multiscale Model. Simul.},
  year={2005},
  volume={4},
  pages={1168-1200}
}
  • P. L. Combettes, Valérie R. Wajs
  • Published 2005
  • Mathematics, Computer Science
  • Multiscale Model. Simul.
  • We show that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties. This formulation makes it possible to derive existence, uniqueness, characterization, and stability results in a unified and standardized fashion for a large class of apparently disparate problems. Recent results on monotone operator splitting methods are applied to establish the convergence of a forward-backward… CONTINUE READING
    2,217 Citations
    A constrained forward-backward algorithm for image recovery problems
    • 7
    • PDF
    Monotone operator splitting for optimization problems in sparse recovery
    • 25
    • PDF
    Dualization of Signal Recovery Problems
    • 93
    • PDF
    Local Linear Convergence of Forward-Backward under Partial Smoothness
    • 67
    • PDF
    A Novel Forward-Backward Algorithm for Solving Convex Minimization Problem in Hilbert Spaces
    • 1
    • Highly Influenced
    • PDF
    Proximal Splitting Methods in Signal Processing
    • P. L. Combettes, J. Pesquet
    • Computer Science, Mathematics
    • Fixed-Point Algorithms for Inverse Problems in Science and Engineering
    • 2011
    • 2,052
    • PDF
    Strong convergence of the forward–backward splitting method with multiple parameters in Hilbert spaces
    • 9
    • Highly Influenced

    References

    SHOWING 1-10 OF 88 REFERENCES
    Image recovery via total variation minimization and related problems
    • 1,488
    • PDF
    A Variational Method in Image Recovery
    • 355
    • PDF
    A fast quadratic programming algorithm for positive signal restoration
    • 22
    A multiprojection algorithm using Bregman projections in a product space
    • 797
    The Convex Feasibility Problem in Image Recovery
    • 383
    • PDF
    Wavelet-Constrained Image Restoration
    • 26
    • PDF
    Image Restoration by the Method of Convex Projections: Part 1ߞTheory
    • D. Youla, H. Webb
    • Mathematics, Medicine
    • IEEE Transactions on Medical Imaging
    • 1982
    • 1,091
    • PDF
    Image Decomposition and Restoration Using Total Variation Minimization and the H1
    • 496