A method is presented for restoring a fixed screen, which is imaged through a random time-varying medium, from a number of observation frames contaminated by additive detection noise. The method is based on frame-pixel separability. First, frames are deblurred individually (ignoring additive noise). Then a pixel is treated individually by finding an estimate of its value based on its values in all deblurred frames. In some conditions the final estimate turns out to depend on only two statistics: the frame-averaged image and the frame-averaged spatial correlation function. The latter is the basis of speckle interferometry.