Methodology

This study focussed on pure stellar images, since they are probably the kind of object most often imaged by HST. Also, they present the most difficult challenge to any restoration algorithm, since the intensity gradient and dynamic range in such an image are very large when compared to usual ``terrestrial'' scenes, to which restoration algorithms are usually designed.

The main data set used in this study is a simulated WFPC I observation of a ``star cluster'', similar to the ones available in STEIS. The simulated image was built on a 8 8 oversampled data grid, later block-averaged to the actual instrument resolution. The PSF was computed by TinyTIM (Krist 1991) at Å, at center of CCD #1. Finally, the appropriate noise model for WF CCDs, including Poisson and readout (Gaussian) components, was added to the image.

Algorithms studied include current STSDAS implementations of the Richardson-Lucy iteration (Richardson 1972, Lucy 1974), Maximum Entropy (Wu 1993), the Wiener filter (Andrews &Hunt 1977), -CLEAN (Keel 1991) and a standard Iterative Least Squares algorithm (e.g. Katsaggelos 1991). Also, an independent implementation of the Iterative/Recursive least squares algorithm (Coggins et al. 1993, Fullton et al. 1993) was tested.

Criteria to evaluate restoration quality include both generic and astronomical-specific ones. An often used goodness-of-fit criterion in image restoration work is a measure of the ``distance'' between the restored image and the ``truth'' image (the one without any degradation) where is the observation at pixel . The measure is expressed in dB, and increases as long as the restored image becomes ``closer'' to the truth image. We also used an absolute-value distance which correlates better than with visual quality evaluation. Both and are independent of image content.

Astronomical criteria include photometric linearity, precision, and sky background statistics. Photometric evaluation was performed on star images using standard aperture techniques.

Algorithm sensitivity to PSF errors was evaluated by restoring the test image using both the original PSF, as well as another TinyTIM PSF, computed for a bluer star and situated pixels away from the the CCD center.