Abstract
Efficient recovery of smooth functions which are s-sparse with respect
to the basis of so-called prolate spheroidal wave functions from a small number of
random sampling points is considered. The main ingredient in the design of both the
algorithms we propose here consists in establishing a uniform L? bound on the measurement
ensembles which constitute the columns of the sensingmatrix. Such a bound
provides us with the restricted isometry property for this rectangular random matrix,
which leads to either the exact recovery property or the "best s-term approximation"
of the original signal by means of the 1 minimization program. The first algorithm
considers only a restricted number of columns for which the L? holds as a consequence
of the fact that eigenvalues of the Bergman's restriction operator are close to
1 whereas the second one allows for a wider system of PSWF by taking advantage
of a preconditioning technique. Numerical examples are spread throughout the text to
illustrate the results.
Anno
2013
Autori IAC
Tipo pubblicazione
Altri Autori
Laurent Gosse
Editore
Azzoguidi
Rivista
Annali dell'Università di Ferrara. Sezione 7: Scienze matematiche