The Hubble Space Telescope (HST) observations, before the COSTAR correction, were strongly blurred by the spherical aberration of the primary mirror. In that case, conventional procedures in image restoration such as inverse filtering, matched filtering, etc., turned out to be unsuited to this problem.
The ``new HST'' now provides improved dynamic ranges, sensitivity to faint sources and increased resolution. However, the algorithms that were used on the old set of HST images are still relevant to the new instrument, since they are designed to perform better when applied to higher quality data.
In Sect. 2, we remind the reader the general principles of the reconstruction algorithm IDEA (Interactive Deconvolution with Error Analysis) (Lannes et al. 1987a-c). The deconvolution problem is stated in terms of weighted spectral interpolation and partial extrapolation. This operation is quantitatively related to the choice of a synthetic aperture which defines a limit in resolution. We propose variations on the general scheme by examining the contribution of Multiresolution Analysis (Mallat 1989). In Sect. 3, we compare our deterministic viewpoint with two probabilistic approaches: the Richardson-Lucy Method (RLM; Lucy 1974) and the Maximum Entropy Method (MEM; Narayan & Nityananda 1986) applied to images of SN 1987A, M 87 and 3C 66B. Sect. 4 is devoted to an interpretation of the results and to an astrophysical discussion.