We have shown in this paper that deconvolution can bring a wealth of additional information even in a difficult case like the spherical aberration of HST and even when applied to low signal-to-noise ratio images. In many cases RLM yields over-resolution and MEM totally fails for signal-to-noise ratios lower than 10. Even if we apply more sophisticated version of MEM, like the Method of Maximum Entropy on the Mean (MMEM) (see Le Besnerais et al. 1995) the results are not drastically improved. IDEA has proven to be extremely powerful in two respects: control over error propagation and efficiency at low signal-to-noise ratios. Both points are essential to astronomers. Moreover, the approach of IDEA allows us an interactive choice for the compromise between gain in resolution and stability of the solution. As to CPU time, the three codes are comparable. IDEA usually converges in a lower number of iterates but each one lasts longer (involving an iterate of the conjugate gradients method).
The main astrophysical result of this study is that for all images (the ring of SN 1987A or the jets of M 87 and 3C 66B) IDEA preserves the filamentary aspects of the objects and does not generate artificial ``blobs''.
We would like to emphasize that IDEA has been developed independently from the spherical aberration of the HST, so that it can be used on any kind of images. Indeed, even the COSTAR-corrected HST could still benefit from deconvolution. In addition improvements of the method are in progress. For instance, using orthogonal bases of compactly supported wavelets, Roques et al. (1996) have incorporated, in the wavelet domain, the Donoho & Johnstone denoising method (Donoho 1992), which consists in a non-linear shrinkage of the wavelet coefficients. This allows us to recover the denoised image, whose Fourier transform, compared to raw Fourier data, yields the pointwise spectral signal-to-noise ratio which explicitly occurs in the formulation of the regularization function g . The advantages of this procedure are that the noise is almost entirely suppressed, and features sharp in the original remain sharp in the denoised image.