The mathematical problem arising from HST image restoration provides an example of an inverse problem which can be fruitfully treated by regularization techniques. Among these methods, LWPOS seems to provide the best compromise between accuracy and computational effort. On the other hand it is not evident, from the numerical experiments performed in this work, which is the best choice between LWPOS and the well-known R-L method: a larger set of test problems, covering a wide range of astronomical objects, has to be taken into account.
The forthcoming correction of the imaging disorders with the installation of COSTAR and WFPC II should restore near perfect imaging to the HST. However, the possibility of reconstructing even diffraction limited images is attractive since some super-resolution will be possible (Bertero et al. 1989). For this reason, restoration techniques able to provide good results coupled with a tolerable computational cost will be greatly appreciated even after the first servicing mission of December 1993. Non-isoplanatic corrections will be highly desirable.
In this context we cannot forget that the R-L method, the most popular algorithm used for the restoration up to now, is efficient at the further expenses of a computational overload since there are four FFT operations per iteration, that makes it easily the most expensive in computer time of all the methods apart from the Maximum Entropy method.
Acknowledgments
The work of F. Maggio has been supported by Sardinian Regional Authorities. The work at King's College has been supported by US Army grant DAAL03-92-G-0142.