The method requires 3 steps:
from 
.
find a sequence 
of
points 
with 
,
, 
and determine 
as the solution of the
exterior Helmholtz problem (3).
from and 
from
t. Do an inverse Fourier transform to obtain q.
, hence
(4) reads
For 
the unit ball, 
, this equation can
be solved by spherical harmonics: Let
Since
the solution is
Unfortunately, 
if 
. This means that
is poorly determined for . Thus,
can be determined stably only on the subspace 
of 
. This does not come as a
surprise since we expect the resolution in an inverse scattering
experiment with wave number k to be of the order k.
On the other hand, in step (ii), we have to apply to the
high frequency function 
( 
is large!). Thus the
information on we get from step (i) is not sufficient for
step (ii). All we can expect is an 
- approximation
to q. But this can be achieved much easier by other methods. Besides,
the computational cost of step (ii) is probably prohibitive, unless one
finds expedient asymptotic methods for solving (3) for large.