The simplest strategy of the iterative search was introduced by
(). It works as follows
- Localization of the strongest intensity pixel in the current residual map:
\(\mathrm{max}(\vert{I_\mathrm{res}}\vert)\)
.
- Add
\(\gamma.\mathrm{max}(\vert I_\mathrm{res}\vert)\)
and its spatial position to
the clean component list.
- Convolution of
\(\gamma.\mathrm{max}(\vert{I_\mathrm{res}}\vert)\)
by the dirty
beam.
- Subtract the resulting convolution from the residual map in order to
clean out the side lobes associated to the localized clean component.
\(\gamma\)
is the loop gain. It controls the convergence of the method. In
theory,
\( 0 < \gamma < 2\)
.
\( \gamma =1\)
would in principle give
faster convergence, since the remaining flux at one position is
\( \propto (1-\gamma)^n\)
,
where
\(n\)
is the number of
clean components found at this position. But, in practice, one should use
\(\gamma \simeq 0.1 - 0.2\)
, depending on sidelobe levels, source structure
and dynamic range. Indeed, deviations (such as thermal noise, phase noise
or calibration errors) from an ideal convolution equation force to use low
gain values in order to avoid non linear amplifications of errors.
An important property of
HOGBOM algorithm is that only the inner
quarter of the dirty image can be properly cleaned when dirty beam and
images are computed on the same spatial grid. Indeed, the subtraction of
the dirty sidelobes associated to any clean component is possible only in
the spatial extent of the dirty beam image. When the user defines a support
(a priori knowledge), the cleaned region becomes even smaller than
the inner quarter of the dirty map.
