Volume 30, pp. 54-74, 2008.

Regularization properties of Tikhonov regularization with sparsity constraints

Ronny Ramlau

Abstract

In this paper, we investigate the regularization properties of Tikhonov regularization with a sparsity (or Besov) penalty for the inversion of nonlinear operator equations. We propose an a posteriori parameter choice rule that ensures convergence in the used norm as the data error goes to zero. We show that the method of surrogate functionals will at least reconstruct a critical point of the Tikhonov functional. Finally, we present some numerical results for a nonlinear Hammerstein equation.

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Key words

inverse problems, sparsity

AMS subject classifications

65J15, 65J20, 65J22

ETNA articles which cite this article

Vol. 37 (2010), pp. 87-104 Ronny Ramlau and Elena Resmerita: Convergence rates for regularization with sparsity constraints

Vol. 39 (2012), pp. 476-507 Ronny Ramlau and Clemens A. Zarzer: On the minimization of a Tikhonov functional with a non-convex sparsity constraint

Vol. 59 (2023), pp. 116-144 Simon Hubmer, Ekaterina Sherina, and Ronny Ramlau: Characterizations of adjoint Sobolev embedding operators with applications in inverse problems

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