SVD-tail: a new linear-sampling method for inverse scattering problems

                 M. Fares, S. Gratton and Ph. L. Toint
     
                      Report 09/09  March 2009

A new numerical procedure (SVD-tail) is proposed for the reconstruction of the
shape and  volume of unknown objects  from measurements of  their radiation in
the far field.  This efficient procedure is a variant  and the linear sampling
method  and  has  a  very  acceptable computational  load.  At  variance  with
previously  published  techniques  where  the  solution is  constructed  as  a
regularized  solution  of the  far-field  equations  using  a variant  of  the
Tikhonov-Morozov type,  the new method  uses a new eigenspace  recovery method
which  exploits  the  combined  presence  of  error in  the  operator  and  of
eigenvalue  clusters. The performance  of the  new technique  on a  battery of
examples and its comparison with existing methods is shown to be promising.