@misc{Rastogi2019,
  author    = {Rastogi, Abhishake},
  title     = {Tikhonov regularization with oversmoothing penalty for linear statistical inverse learning problems},
  series = {AIP Conference Proceedings : third international Conference of mathematical sciences (ICMS 2019)},
  volume    = {2183},
  journal   = {AIP Conference Proceedings : third international Conference of mathematical sciences (ICMS 2019)},
  publisher = {American Institute of Physics},
  address   = {Melville},
  isbn      = {978-0-7354-1930-8},
  issn      = {0094-243X},
  doi       = {10.1063/1.5136221},
  pages     = {4},
  year      = {2019},
  abstract  = {In this paper, we consider the linear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is considered in the reproducing kernel Hilbert space framework to reconstruct the estimator from the random noisy data. We discuss the rates of convergence for the regularized solution under the prior assumptions and link condition. For regression functions with smoothness given in terms of source conditions the error bound can explicitly be established.},
  language  = {en}
}
@article{Rastogi2020,
  author    = {Rastogi, Abhishake},
  title     = {Tikhonov regularization with oversmoothing penalty for nonlinear statistical inverse problems},
  series = {Communications on Pure and Applied Analysis},
  volume    = {19},
  journal   = {Communications on Pure and Applied Analysis},
  number    = {8},
  publisher = {American Institute of Mathematical Sciences},
  address   = {Springfield},
  issn      = {1534-0392},
  doi       = {10.3934/cpaa.2020183},
  pages     = {4111 -- 4126},
  year      = {2020},
  abstract  = {In this paper, we consider the nonlinear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is considered to reconstruct the estimator from the random noisy data. In this statistical learning setting, we derive the rates of convergence for the regularized solution under certain assumptions on the nonlinear forward operator and the prior assumptions. We discuss estimates of the reconstruction error using the approach of reproducing kernel Hilbert spaces.},
  language  = {en}
}