TY  - JOUR
A1  - Cotronei, Mariantonia
A1  - Holschneider, Matthias
T1  - Partial parameterization of orthogonal wavelet matrix filters
JF  - Journal of computational and applied mathematics
N2  - 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.
KW  - Full rank matrix filters
KW  - Multichannel wavelets
KW  - Quadrature mirror filters
KW  - Vector subdivision schemes
Y1  - 2013
U6  - https://doi.org/10.1016/j.cam.2012.11.016
SN  - 0377-0427
VL  - 243
IS  - 4
SP  - 113
EP  - 125
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Cotronei, Mariantonia
A1  - Di Salvo, Rosa
A1  - Holschneider, Matthias
A1  - Puccio, Luigia
T1  - Interpolation in reproducing kernel Hilbert spaces based on random subdivision schemes
JF  - Journal of computational and applied mathematics
N2  - 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.
KW  - Subdivision schemes
KW  - Interpolation
KW  - Simulation of Gaussian processes
KW  - Bayesian inversion
Y1  - 2016
U6  - https://doi.org/10.1016/j.cam.2016.08.002
SN  - 0377-0427
SN  - 1879-1778
VL  - 311
SP  - 342
EP  - 353
PB  - Elsevier
CY  - Amsterdam
ER  -