The parametric Wiener filter is often used to deblur images that are relatively noise-free. If noise is more severe, the restored image may be obscured by a granular pattern that results when the noise is subjected to the deblurring filter. This effect may be reduced by using a larger noise parameter, but this leads to a restoration that is less sharp. We describe how the noise parameter may be varied from pixel to pixel, so that it is larger only where noise is greater. Pixels with low signal-to-noise ratios are identified by a thresholding process and by comparison with nearest neighbors. The effects of the estimated Wiener spectra on the restored image are discussed.