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Abstract:
DEC performs the deconvolution of a cube of images (i.e. p images
corresponding to different orientations of the baseline). There are
four different methods for image deconvolution, according to the noise
model. For Poisson noise, the Richardson-Lucy (RL) and the Ordered-Subset
Expectation Maximization (OSEM) methods are available, while for Gaussian
noise both the Image Space Reconstruction Algorithm (ISRA) and the OS-ISRA
are implemented. (see [1] for details).
DEC also allows to reduce the boundary effects in the reconstructed
image (see [2] for details).
Accelerated versions of the algorithms are also available, following
the Biggs and Andrews method (see [3,4] for details).
When the object is complex, like a high dynamic object, a regularized
version of the algorithm can give better results. In this cases, five
different regularizations are available in DEC: Tikhonov, Laplacian, Entropy,
Edge Preserving, and High Dynamic Range (see [1] for details). Depending
on the regularization chosen, one or a couple of parameters control
the efficacy of the regularization.
The background evaluation performed by PRE module is used to restore
the object with a correct sky-value.
In this new version of DEC up to four different stopping rules are given.
Concerning both RL and OSEM algorithms, four stopping rules are implemented:
1) Set a total number of iterations and stop the algorithm when this number
is reached. This is valid for all available methods;
2) Stop the iteration when the discrepancy function crosses 1. This
criterion is called discrepancy principle for Poisson data (see [5])
and can be used when no regularization has been used.
3) Stop the iterations when the total functional is approximately constant,
according to a user-defined tolerance. This stopping rule can be
applied only when a regularization is chosen.
4) Stop the iterations when the relative r.m.s error reaches a minimum
value. This stopping rule can be used only in the case of numerical
simulations, when the true object is known.
The first and the last stopping rules are also available for ISRA and
OS-ISRA.
In DEC we also implemented an algorithm for super-resolving compact objects
such as a binary system with an angular separation smaller than the angular
resolution of the telescope. (see [6] for details). The method is based on
a simple modification of the RL/OSEM method and in general consist of 3
steps: the first one requires a large number of RL/OSEM iterations
(typically 10000), which are used to estimate the domain of the unresolved
object; the second one is a RL/OSEM restoration (typically 5000 iterations)
initialized with the mask of the domain, as estimated in step 1. These two
steps are used to estimate the positions of the two stars while their
magnitudes can be obtained in a possible 3rd step by solving a simple
least-squares problem. The first two steps are included in DEC.
In the second step it is possible to choose, in the GUI, the image and the
mask used to initialized the method. The mask is an image with values 0/1.
There are 3 kind of masks: the 1st is a mask based on percentage of the
image maximum, the 2nd one is a circular mask, and the 3rd is a
user-defined mask.
References:
[1] La Camera et al., 2012, "AIRY: a complete tool for the simulation
and the reconstruction of astronomical images", Proc. SPIE, toappear
[2] Anconelli et al., 2006, "Reduction of boundary effects in multiple
image deconvolution with an application to LBT LINC-NIRVANA",
A&A 448, 1217â€“1224.
[3] Biggs and Andrews, 1997, "Acceleration of iterative image
restoration algorithms", Applied Optics 36, 1766.
[4] B
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3/25/2007,
in category "Modules of the Software Package AIRY "
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