The effect of the optical system aberrations on the restoration imagery is investigated when the speckle imaging technique is used to process the images of the astronomic telescope. Under the basis of analyzing the method and the theory on the restoration of the modulus and the phase, a speckle imaging model which includes the Labeyrie's speckle interferometry and the Knox-Thompson imaging technique is presented. The effects of telescope aberrations on the involving the modulus and the phase of object Fourier transform due to the random wave front phase distribution of system trarfer function and the restoration of the object phase are discussed. The deterministic optical aberrations are submerged in the random phase of the transfer function introduced by the atmospheric turbulence. The restoration image shows that the speckle imaging technique can remove the effects of the deterministic aberrations and atmospheric turbulence on the estimated images, and the high resolution image is obtained. A method of compensating optical system aberrations is proposed.