Resolution and robustness in image processing: a new regularization principle

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Abstract
As band-limited interpolation is possible to some extent, whereas band-limited extrapolation is strictly forbidden, it is natural to state the deconvolution problem in terms of weighted interpolation (in the frequency domain). The corresponding regularization principle, which is to be compared with that of Tikhonov, proves to be intimately related to the notion of resolution: the aperture to be synthesized explicitly appears in the definition of the stabilizing component of the objective function. The choice of this synthetic aperture of course depends on the error analysis. The study developed in this paper shows, in particular, how the amount and the nature of the interpolation to be performed play a central part in the error propagation. The corresponding analytic parameters are exhibited. This survey, which is illustrated with the aid of a simulated example, also indicates how to estimate the degree of confidence of any other deconvolution technique (clean, filtered singular-value decomposition, maximum-entropy, etc.).

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