Turbulence-degraded images can be restored by using the Knox–Thompson algorithm. This algorithm is briefly described, and its photon-noise limitations are discussed. Peculiar difficulties related to the phase dislocations in the Fourier space are pointed out, and a solution to this problem is proposed. This algorithm does not require more photons than the speckle-interferometry technique and could provide much more information on complex astronomical objects. To illustrate these phase dislocations and signal-to-noise ratio problems, different restorations are presented that result from degraded images obtained with a turbulence-simulation facility and from astronomical data.