@article{CotroneiHolschneider2013,
  author    = {Cotronei, Mariantonia and Holschneider, Matthias},
  title     = {Partial parameterization of orthogonal wavelet matrix filters},
  series = {Journal of computational and applied mathematics},
  volume    = {243},
  journal   = {Journal of computational and applied mathematics},
  number    = {4},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0377-0427},
  doi       = {10.1016/j.cam.2012.11.016},
  pages     = {113 -- 125},
  year      = {2013},
  abstract  = {In this paper we propose a procedure which allows the construction of a large family of FIR d x d matrix wavelet filters by exploiting the one-to-one correspondence between QMF systems and orthogonal operators which commute with the shifts by two. A characterization of the class of filters of full rank type that can be obtained with such procedure is given. In particular, we restrict our attention to a special construction based on the representation of SO(2d) in terms of the elements of its Lie algebra. Explicit expressions for the filters in the case d = 2 are given, as a result of a local analysis of the parameterization obtained from perturbing the Haar system.},
  language  = {en}
}
@article{CotroneiDiSalvoHolschneideretal.2017,
  author    = {Cotronei, Mariantonia and Di Salvo, Rosa and Holschneider, Matthias and Puccio, Luigia},
  title     = {Interpolation in reproducing kernel Hilbert spaces based on random subdivision schemes},
  series = {Journal of computational and applied mathematics},
  volume    = {311},
  journal   = {Journal of computational and applied mathematics},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0377-0427},
  doi       = {10.1016/j.cam.2016.08.002},
  pages     = {342 -- 353},
  year      = {2017},
  abstract  = {In this paper we present a Bayesian framework for interpolating data in a reproducing kernel Hilbert space associated with a random subdivision scheme, where not only approximations of the values of a function at some missing points can be obtained, but also uncertainty estimates for such predicted values. This random scheme generalizes the usual subdivision by taking into account, at each level, some uncertainty given in terms of suitably scaled noise sequences of i.i.d. Gaussian random variables with zero mean and given variance, and generating, in the limit, a Gaussian process whose correlation structure is characterized and used for computing realizations of the conditional posterior distribution. The hierarchical nature of the procedure may be exploited to reduce the computational cost compared to standard techniques in the case where many prediction points need to be considered.},
  language  = {en}
}