Phase diversity is applied in the sensing of sparse-aperture systems. The accuracy of the wavefront phase estimation and the iteration time are researched by the image noise. The noise reduction is processing for the noise degradation images by the second order butterworth low-pass filter. Meanwhile the image spectrum by filtering and the optical transfer function are being as constraint with apodization to obtain the low frequency area of high signalto-noise ratio, and take the corresponding optical transfer function. The improvement of the object function for the phase diversity is derived after filtering by apodization. Digital simulation indicates that under the condition of different noise intensities, the proposed method can reduce the noise effectively and improve the phase estimation precision, the algorithm iteration time can be reduced simultaneously.