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Astronomical Data Analysis Software and Systems VII
ASP Conference Series, Vol. 145, 1998
R. Albrecht, R. N. Hook and H. A. Bushouse, e
Ö Copyright 1998 Astronomical Society of the Pacific. All rights reserved.
ds.
Recognition of Anomalous Events
S. Monai 1,2 and F.Pasian 2
1 Osservatorio Astronomico di Brera Merate, Italy
2 Osservatorio Astronomico di Trieste, Italy
Abstract. We present an original algorithm for the recognition of
anomalous events in a CCD frame (i.e., cosmic hits, bad pixels etc.). The
algorithm is able to distinguish between these events and real features by
comparing the standard deviation and the kurtosis of a synthetic PSF,
whose width is given by the user, and the corresponding values in a run­
ning window, whose size is chosen by the user, in the actual frame. The
anomalous pixels are therefore filtered with a neighbourhood average.
Raw images, as read from a CCD, are often a#ected by some events which
are revealed by anomalous pixel values, i.e., single saturated pixels or pixels at
zero intensity (also named hot or bad pixels). Often cosmic rays cross the CCD
during the exposure and are revealed as strange features normally a#ecting a
few contiguous pixels. It is not always simple to disentangle automatically these
features. Among the approaches to this recognition problem we have: ­ IRAF
tasks cosmicrays; ­ MIDAS task filter/cosmic; ­ a locally adaptive modified
Haar transform approach due to Richter (1991) and Richter et al. (1991); ­
a median filter approach due to Meurs et al. (1991) and van Moorsel (1991);
­ a method using filters based on ordered statistics (Pasian 1991); ­ an image
restoration, followed by flagging badly restored ``objects'' as bad pixels, and re­
restoring (Weir 1991), this last allows the addition of a point spread function
(PSF) fitting, coupled with the flagging of poorly restored ``objects''; ­ a three
step procedure is used by Yee et al. (1996).
In this work we make only one reasonable assumption about this kind of events:
The anomalous events are smaller than the actual PSF of the instru­
ment. This is not always true, but if this is the case we think there are no
classic criteria, a#ordable by a classical algorithm, to distinguish these events
(di#erent approaches are those of Priebe et al. (1993) and Murtagh (1994), both
use object recognition techniques).
When the previous assumption is true (by far the great majority of cases) we
have the possibility to establish some precise criteria to identify, and filter, the
anomalous events, without a#ecting the real features (which are normally de­
graded by a normal filtering technique). First of all we must know the PSF width
in pixel units, and this is not very di#cult both for imaging and spectroscopical
observations. A Gaussian fit across a star or an emission line is su#cient to
determine the actual PSF width (the seeing normally prevents us to see the true
di#raction pattern). With this datum we are able to compute two important
parameters: the standard deviation and the kurtosis in a window centered on
a synthetic PSF (the window width is chosen by the user). The first parame­
75

76 Monai and Pasian
ter allows recognition of events having an anomalous intensity variation across
the specified window, while the second recognizes the event's shape which must
have a profile narrower than the PSF (i.e., a greater kurtosis). The standard
deviation of the real image derives from the signal variations across the feature
plus the image noise; the deviation factor from the corresponding synthetic PSF
must be chosen appropriately. This parameter must therefore be tuned: after
several experiments on di#erent images and spectra taken with di#erent instru­
ments, we suggest a deviation factor of at least 5. With these criteria we are
confident not to identify as anomalous a real feature. When in a window the
standard deviation is more than 5 times greater and the kurtosis is larger than
the corresponding values of the PSF, the central pixel is identified as anomalous,
its coordinates are stored and we can substitute taking twice the average value
of its neighbours.
We want to stress that only the contemporaneous satisfaction of both require­
ments allows us to identify an anomalous event; in fact a large kurtosis alone
doesn't mean a narrower profile since the condition is necessary but not suf­
ficient. The double averaging step is necessary because some events could be
spread over more than one pixel and a simple filtering could not remove the
anomalies, with a second iteration we are averaging the already filtered pixels
and we are quite sure to eliminate completely the anomaly. If the anomalous
event is spread along more than the window's width (but only in one direction)
the algorithm still recognizes it but the neighbour average could not remove it
completely. In this case the entire procedure should be repeated once more.
Acknowledgments. We are grateful to Dr. M. Nonino for having o#ered
the image of the Seyfert galaxy. This work has been carried out thanks to a grant
of the ``Oss. Astron. di Brera Merate'' for the realisation of the Data Reduction
Software for the DOLORES instrument, in the framework of the TNG project.
References
Meurs E.J.A., Bonifacio V.H., & Lima N.M. 1991, in 3rd ESO/ST­ECF Data
Analysis Workshop, 45
Pasian F. 1991, in 3rd ESO/ST­ECF Data Analysis Workshop, 57
Priebe A., Liebscher E., Lorenz H., & Richter G.M. 1993, in ASP Conf. Ser.,
Vol. 52, Astronomical Data Analysis Software and Systems II, ed. R. J. Hanisch,
R. J. V. Brissenden & Jeannette Barnes (San Francisco: ASP), 442
Richter G.M. 1991, in 3rd ESO/ST­ECF Data Analysis Workshop, 37
Richter G.M., Boehm P., Lorenz A., & Capaccioli M. 1991, Astron. Nach.
312,345
van Moorsel G. 1991, ST­ECF Tech. Rep
Weir N. 1991, in 3rd ESO/ST­ECF Data Analysis Workshop, 115
Yee H.K.C., Ellingson E., & Carlberg R.G. 1996, Ap. J. Supp. Ser. 102,269

Recognition of Anomalous Events 77
Figure 1. Assonometric projection of a raw image
Figure 2. Assonometric projection of the cleaned image
Figure 3. Assonometric projection of the residuals
Figure 4. The cross­cut of a cosmic hit filtering steps