FoCM 2014 conference
Workshop A2 - Computational Harmonic Analysis, Image and Signal Processing
No date set
Finitely generated shift invariant spaces with extra invariance nearest to observed data
Carolina Mosquera
Universidad de Buenos Aires, CONICET, Argentina - mosquera@dm.uba.ar
Let m,ℓ∈N, M be a closed subgroup of Rd containing Zd and F={f1,…,fm}⊂L2(Rd). We study the problem of finding the shift invariant space V of length less or equal to ℓ which is also M−invariant such that V is ``closest'' to the functions F in the sense that V=argminV′∈VℓMm∑j=1‖fj−PV′fj‖2,
where VℓM is the set of all shift invariant spaces V′ of length less or equal to ℓ which are also M−invariant, and PV′ is the orthogonal projection on V′.
Also we consider this problem for a particular set of translation invariant spaces.
Joint work with Carlos Cabrelli (Universidad de Buenos Aires, CONICET, Argentina).