iterative regularization

On regularized structure exploiting Quasi-Newton methods for ill-posed problems

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

    Inverse problems are inherently ill-posed, leading standard optimization techniques to fail and necessitating the use of regularization. This paper introduces a regularized, structure-exploiting Powell-Symmetric-Broyden method under modified secant conditions for solving ill-posed inverse problems in both infinite dimensional and finite dimensional settings. Our approach integrates regularization and structure exploitation directly within the Quasi-Newton framework, leveraging … 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