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The experimental data
are blurred values
of
on a finite list of frequencies in the
Fourier domain:
![$\displaystyle \mathcal{L}_e = \{ \mathbf{u}_e(1), \mathbf{u}_e(2), \dots, \mathbf{u}_e(N_e)\}.$](img1654.png) |
(16.6) |
As the object function of interest
is a
real-valued function, it is natural to define
as the complex conjugate of
.
The experimental frequency list
is defined
consequently:
if
, then
(except for the null frequency
: in the convention
adopted here, either it does not lie in
, or there
exists only one occurrence of this point).
The experimental frequency coverage generated by
is therefore centrosymmetric (see Fig. 16.3).
Figure 16.3:
An example of an experimental frequency coverage
provided by the IRAM interferometer. Here, the number of
points
in the experimental frequency
list
is equal to
.
![\resizebox{8.0cm}{!}{\includegraphics{eafig3r.eps}}](img1660.png) |
The experimental data vector
lies in the
experimental data space
, the real Euclidian space
underlying the space of complex-valued functions
on
,
such that
.
The dimension of this space is equal to
: the number of points
in the experimental frequency list
.
Next: 16.4 Image reconstruction process
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Anne Dutrey