Deconvolution Wiener filtering

The Wiener filter therefore avoids noise amplification and provides the best solution according to some quality criterion. We will see that these features are common to all other methods which correctly solve the deconvolution inverse problem. The result of applying Wiener inverse-filter to the simulated image is shown in Fig. 3b. 

How can this approach be adapted to deconvolution The problem is similar, but now we ask that y(x) also incorporate the inverse of s(x). Both Bracewell (1958) and Helstrom (1967) have derived this variant of the Wiener filter. Accordingly, we may minimize... 

For a basic deconvolution problem involving band-limited data, the trial solution d(0) may be the inverse- or Wiener-filtered estimate y(x) (x) i(x). Application of a typical constraint may involve chopping off the nonphysical parts. Transforming then reveals frequency components beyond the cutoff, which are retained. The new values within the bandpass are discarded and replaced by the previously obtained filtered estimate. The resulting function, comprising the filtered estimate and the new superresolving frequencies, is then inverse transformed, and so forth. 

Fig. 1. Wiener filter deconvolution of HD 161796 at 12.S /on. Contours cae at intervals of 0.1 times the peak. The FWHM of a deconvolved pmnt source is 0.4".

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