In the general framework of
regularization of inverse problems,
we define the main contours of the reconstruction algorithm
IDEA (*Interactive Deconvolution with Error Analysis*) that is
developed in our group, giving only some methodological principles.
The deconvolution problem is stated in terms of weighted spectral
interpolation: the amount and the nature of the interpolation
to be performed is related --- in a quantitative manner --- to the choice of a
synthetic coverage linked to the target resolution.
We illustrate this deterministic viewpoint on the SN1987A image of HST
and compare the result with two
Bayesian approaches: the Richardson-Lucy Method (RLM)
and the Maximum Entropy Method (MEM) in terms of gain in resolution,
error propagation, speed of convergence, and some relevant
astrophysical criteria.

Pages 64-71

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