Introduction

The restoration of images obtained by the Hubble Space Telescope's first Wide Field and Planetary Camera (WF/PC-1), is still an unsolved problem. This is mainly due to the spatial variability of its point spread function (PSF), in conjunction with a variety of other factors. The purpose of this contribution is to investigate the algorithmic requirements for a comprehensive space-variant PSF (SV-PSF) restoration procedure, and to show that, based on the developments of the past three years, a full-frame WF/PC restoration has become feasible.

A comprehensive WF/PC restoration process (Fig. 1) has to address the following problems:

1. The point-spread function is spatially variable and relatively large. Restoration with a SV-PSF is known to be notoriously difficult, and generally demanding in terms of CPU-power. The PSF has to be computed from a parametric model, or somehow estimated from the data frame(s). An efficient algorithm must be used in view of the large data and PSF frame formats.
2. The data frames are undersampled. Observations must therefore be carefully designed in terms of splits, sub-pixel shifts and rotations. Often the registration parameters must be estimated post-facto, and different overlapping frames have to be combined.
3. Long exposures suffer from numerous cosmic ray (CR) hits. These have to be detected - a daunting task in the presence of undersampling - and the missing data have to be treated somehow.
4. There are other problems, such as detector contaminations dubbed ``measles'' and flat-field uncertainties.

In the following several algorithms addressing problems (1) to (3) above are presented. Firstly, the problem of restoring undersampled (multi-) frames is discussed. It is argued that the cosmic ray problem and the undersampling problem can be treated on the same footing. The proposed algorithm for irregular missing data with masks largely follows treatments by Adorf et al. (1993), White (1993), and recently by Freudling (1993), except for the up- and down-sampling aspects. Secondly, an algorithm for SV-PSF restoration is presented which combines the generalized ``co-addition'' algorithm of Lucy &Hook (Lucy 1991a; Lucy &Hook 1992, 1993) with the sectioned restoration method originally devised by Trussel &Hunt (1978a, 1978b). When designing these algorithms the following principles have been adhered to (in order of decreasing priority): preserve the integrity of the observational data; leave the Richardson-Lucy (RL) restoration method (Richardson 1972; Lucy 1974) intact as much as possible; strive for theoretically sound, yet efficient, algorithms rendering full-frame WF/PC restoration practical.