Methods for mitigating sidelobes and aliases, providing levels of suppression in excess of 20 dB. The methods may include 1) a version of the CLEAN algorithm developed in radio astronomy, modified to work on sub-aperture images; 2) weighting functions based on the phase and amplitude statistics of the sub-aperture image pixels to select points in the CLEAN algorithm; and 3) weighting functions based on the phase and amplitude statistics of the sub-aperture image pixels to mitigate sidelobes and aliases, in conjunction with CLEAN or separately. The methods may be used with all synthetic aperture techniques and are not limited to SAR.