Accelerated projected steepest descent method for nonlinear inverse problems with sparsity constraints

@article{Teschke2010AcceleratedPS,
  title={Accelerated projected steepest descent method for nonlinear inverse problems with sparsity constraints},
  author={G. Teschke and C. Borries},
  journal={Inverse Problems},
  year={2010},
  volume={26},
  pages={025007}
}
  • G. Teschke, C. Borries
  • Published 2010
  • Mathematics
  • Inverse Problems
    • This paper is concerned with the construction of an iterative algorithm to solve nonlinear inverse problems with an l1 constraint on x. One extensively studied method to obtain a solution of such an l1 penalized problem is iterative soft-thresholding. Regrettably, such iteration schemes are computationally very intensive. A subtle alternative to iterative soft-thresholding is the projected gradient method that was quite recently proposed by Daubechies et al (2008 J. Fourier Anal. Appl. 14 764… CONTINUE READING
    View PDF
    97 Citations
    Highly Influential Citations
    7
    Background Citations
    19
    Methods Citations
    14

    Figures from this paper

    Figures

    97 Citations
    Citation Type

    Citation Type

    An efficient projection method for nonlinear inverse problems with sparsity constraints
    • 1
    Multilevel preconditioning for sparse optimization of functionals with nonconvex fidelity terms
    • 7
    • PDF
    A proximal iteratively regularized Gauss–Newton method for nonlinear inverse problems
    • 6
    Multilevel Preconditioning for Adaptive Sparse Optimization
    • 55
    • PDF
    Sparse Recovery in Inverse Problems
    • 10
    • PDF
    Projected gradient iteration for nonlinear operator equation
    • Highly Influenced
    An analysis of a multi-level projected steepest descent iteration for nonlinear inverse problems in Banach spaces subject to stability constraints
    • 23
    • PDF
    A convergence analysis of a multi-level projected steepest descent iteration for nonlinear inverse problems in Banach spaces subject to stability constraints
    • 15
    • PDF
    On the convergence analysis of Rothe ’ s method
    • 33
    • PDF
    Preconditioning Stochastic Galerkin Saddle Point Problems
    • 56
    • PDF

    References

    SHOWING 1-10 OF 32 REFERENCES
    Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints
    • 270
    • Highly Influential
    • PDF
    Domain decomposition methods for linear inverse problems with sparsity constraints
    • 59
    • PDF
    Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems
    • 2,991
    • PDF
    A Tikhonov-based projection iteration for nonlinear Ill-posed problems with sparsity constraints
    • 116
    • PDF
    An Iterative Thresholding Algorithm for Linear Inverse Problems with a Sparsity Constraint
    • 3,927
    • PDF
    A compressive Landweber iteration for solving ill-posed inverse problems
    • 91
    • PDF
    Iteratively solving linear inverse problems under general convex constraints
    • 129
    • PDF
    Tikhonov replacement functionals for iteratively solving nonlinear operator equations
    • 65
    • PDF
    Greedy solution of ill-posed problems: error bounds and exact inversion
    • 103
    • PDF
    On Some Iterative Concepts for Image Restoration
    • 15
    • PDF