The problem of imaging through turbulent media has been studied frequently in connection with astronomical imaging and airborne radars. Therefore most image restoration methods encountered in the literature assume a stationary object, e.g., a star or a piece of land. In this paper the problem of interferometric measurements of slowly moving or deforming objects in the presence of air disturbances and vibrations is discussed. Measurement noise is reduced by postprocessing the data with a digital noise suppression filter that uses a reference noise signal measured on a small stationary plate inserted in the field of view. The method has proven successful in reducing noise in the vicinity of the reference point where the size of the usable area depends on the degree of spatial correlation in the noise, which in turn depends on the spatial scales present in the air turbulence. Vibrations among the optical components in the setup tend to produce noise that is highly correlated across the field of view and is thus efficiently reduced by the filter.