iterative regularization

On regularized structure exploiting Quasi-Newton methods for inverse problems

  • Raphael Kuess
  • Andrea Walther
    • Categories Infinite Dimensional Optimization, Nonlinear Systems and Least-Squares Tags , , , ,

    This paper introduces a regularized, structure-exploiting Powell-Symmetric-Broyden (RSE-PSB) method under modified secant conditions for solving ill-posed inverse problems in both infinite dimensional and finite dimensional settings. The approximation of the symmetric, yet potentially indefinite, second-order term, which is neglected by standard Levenberg-Marquardt (LM) approaches, integrates regularization and structure exploitation directly within the Quasi-Newton (QN) framework, … Read more

    On the regularizing behavior of recent gradient methods in the solution of linear ill-posed problems

  • Roberta De Asmundis
  • Daniela di Serafino
  • Germana Landi
    • Categories Nonlinear Optimization Tags , , ,

    We analyze the regularization properties of two recently proposed gradient methods applied to discrete linear inverse problems. By studying their filter factors, we show that the tendency of these methods to eliminate first the eigencomponents of the gradient corresponding to large singular values allows to reconstruct the most significant part of the solution, thus yielding … Read more