When the spatial frequencies of the object are insufficiently sampled, the reconstruction of ghost imaging will suffer from repetitive visual artifacts, which cannot be effectively tackled by existing ghost imaging reconstruction techniques. In this Letter, extensions of the CLEAN algorithm applied in ghost imaging are explored to eliminate those artifacts. Combined with the point spread function estimation using the second-order coherence measurement in ghost imaging, our modified CLEAN algorithm is demonstrated to have a fast and noteworthy improvement against the spatial-frequency insufficiency, even for the extreme sparse sampling cases. A brief explanation of the algorithm and performance analysis are given.