Optimal convergence rates for sparsity promoting wavelet-regularization in Besov spaces

@article{Hohage2018OptimalCR,
  title={Optimal convergence rates for sparsity promoting wavelet-regularization in Besov spaces},
  author={Thorsten Hohage and Philip Miller},
  journal={Inverse Problems},
  year={2018},
  volume={35},
  pages={065005}
}
  • Thorsten Hohage, Philip Miller
  • Published 2018
  • Mathematics
  • Inverse Problems
  • This paper deals with Tikhonov regularization for linear and nonlinear ill-posed operator equations with wavelet Besov norm penalties. We focus on $B^0_{p,1}$ penalty terms which yield estimators that are sparse with respect to a wavelet frame. Our framework includes among others, the Radon transform and some nonlinear inverse problems in differential equations with distributed measurements. Using variational source conditions it is shown that such estimators achieve minimax-optimal rates of… CONTINUE READING

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