According to the model of images restoration for sparse aperture optical systems, the adapted conditions to the algorithms of image restoration for the Wiener filtering and the least squares filtering are analyzed. Considering sparse aperture optical systems with noises, the theoretically calculation of Wiener filtering could be optimized. By contrasting with the experiments, it is known that the restoration result of the least squares filtering is better than that of the Wiener filtering in the case of having not known the noise power spectrum.