Sonneberg Observatory, Sternwartestr. 32, D-96515 Sonneberg

Technical University of Ilmenau, Faculty of Computer Science and Automation, Computer Graphics Program, POB 100565, D-98684 Ilmenau, Email: rico.nestler@tu-ilmenau.de

We report applications of the Pixon Restoration Method to digitized plates of
the Sonneberg Plate Archive - the world's 2nd largest. Results so far
obtained show that the severe astigmatism/coma distortion present in the
outer parts of the wide field images can be almost completely removed.
Object definition (FHWM) of point sources and S/N also improve by
factors of 2 to 7,
depending on the object strength and location, background etc. We briefly
address implications for the inclusion of digitized archives
in the virtual observatory context.

Many different telescopes, cameras and photographic emulsions have been used over the years to collect these data, each of them with its own peculiarities and shortcomings. In particular, we are dealing with wide angle astrophotography for which there is no comparison in the era of CCDs. The field size is about 4.3$^$ for the Schmidt plates, 11$^$ for astrograph plates, and 27$^$ for the Sky Patrol plates. The latter, on which we shall concentrate here, suffer from severe astigmatism affecting more than 75% of the plate area. It is therefore obvious that the processing of the digitized data should include steps beyond the basic reduction of dark current subtraction and flat-fielding.

We report here on our attempts to roll back part of the image degradation that occurs between infalling starlight and the digitized plate, using the Pixon image deconvolution method, first described by Pina & Puetter (1993) and then further developed by others (e.g., Eke 2001).

We are convinced that the data currently buried in our and the other existing archives deserve to be excavated and treated using modern methods of mass image processing. Since each plate of the Sky Patrol contains information on some 100,000 stars, such an effort would extend current surveys back by about 50 years down to the plate limits of . Not only are many more variable stars likely to be detected by an automated search, but topical questions such as the existence of sun-like cycles in stars, or simply the long term behaviour of ``normal" stars, could also be attacked on a broad basis (Kroll 1999). To do this, we have to push the detection threshold and photometry to the limits.

The idea of regularization is to take all a-priori-information into account to select and weight the solutions in the set. This prior information is combined with the data and defines a best solution by trying to achieve smoothness and yet remain faithful to the data. The pixon method is an efficient way to regularize inverse problems. ``Pixons" instead of image pixels are used to obtain the ``simplest" solution that explains the data through the imaging model. Details of the theoretical basis and some practical implementations can be found in Pina & Puetter (1993), Puetter (1994) and Puetter (1996).

We use a fuzzy pixon basis to represent our solution . In this
``correlation" approach adjacent pixons share some of each other's signal
instead of having hard boundaries. The unblurred image is described as the
local convolution of a so called ``pseudo-image"
containing the signal with a scale-dependent symmetric 2d-Gaussian
pixon-kernel. The distribution of the local pixon sizes represents the
model-part, , of the image description. The goal of the restoration
process is to determine a combined image-model-* pair*, in a
nonlinear iterative manner. That task can be interpreted in terms of a
Bayesian estimation scheme in which the solution sought maximizes the joint
probability
:

The image-model-pair is calculated in a modified version of the scheme introduced in Pina & Puetter (1993). Instead of calculating a pixon width distribution approximately, our procedure estimates a Bayesian model. Therefore a regularization is needed to weight the influences of the likelihood and prior terms on the solution. In addition, some ideas from other researchers in the field of pixon restoration are used, adapted and refined, such as a specific weight of the signal distribution with respect to the current distribution of pixon sizes (Eke 2001). The calculation of the cost functions and their derivatives is done mainly by FFT-convolutions, thus preserving the scaling of the algorithm.

* Statistical Results:* The automatic identifications of stars
was based on the ``find" procedure in the IDL
Astronomy Library.
On the M31 field ``find" found 38 (36) stars on the restored (original) image,
for which the median FWHM is 1.8 (5.4) pixels and the median S/N-ratio is
15.9 (6.1). The corresponding figures for the Cas field are 747 (606)
stars, 1.8 (3.4) pixel and 10.5 (3.0) for S/N respectively.

* Individual Stars:* Close doubles are well separated in the restored image.
A limiting case is the pair marked ``15". Here the original profile of the pair can hardly be
distinguished from that of a single luminous star, whereas the restored profile shows a shoulder and
has the maximum displaced by 1 pixel, indicating the distinction between the
star PPM43223 and its
NE companion.

The non-stellarity of M32 appears more pronounced in the restored image than in the original data. If the excess of the FWHM of M32 over the median of the sample stars is expressed in units of the mean absolute deviation from the median, this excess is 1.5 times larger in the restored image than in the original data although the M32-FWHM itself is a factor of 3.5 smaller. The galaxy shape of M110 also comes out much more clearly in the restored image. Finally, there are a number of stars which can only be evaluated photometrically in the restored image, e.g., the ``boxed'' group on the NE ridge of M31, and it shows some real stars (e.g., ``a", ``b"), which one would not have guessed the existence of from the original.

We consider it essential to make digitized plate archives--the work of generations of observers--accessible in the virtual observatories to come. From our results we conclude that somewhere in the query chain a web-based (pixon) deconvolution tool should be available.

Eke, V. 2001, MNRAS, 324, 108

Kroll, P. 1999, in Treasure Hunting in Astronomical Plate Archives, eds. Kroll P., la Dous C., Bräuer H.-J. (Frankfurt am Main: Deutsch), 97

Puetter, R. 1996, in Digital Image Recovery and Synthesis III, SPIE., 2827, 12

Puetter, R. 1994, in Digital Image Recovery and Synthesis III, SPIE., 2302, 112

Pina, R., & Puetter, R. 1993, PASP, 105, 630

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