We have applied a variant of the shift-and-add algorithm originally developed by Lynds, Worden, and Harvey [Astrophys. J. 207, 174 (1976)] to astronomical speckle interferometric data. A set of impulses corresponding in locations and magnitudes to the local maxima in each specklegram is generated and used to obtain an average speckle by means of a Wiener-type filter deconvolution procedure. This technique yields diffraction-limited images that appear to be self-calibrating for seeing effects. Realistic point spread functions have been obtained for a number of telescopes at different wavelengths, and results are also presented for the resolved red supergiant Alpha Orionis. The limiting signal-to-noise ratio of the technique as indicated by the results presented here suggests a dynamic range of =6 stellar magnitudes, with no evidence of residual seeing effects. A matched filter technique is demonstrated for use in locating the speckles of complicated objects or for objects dominated by photon noise.