Abstract: Computational ghost imaging is a hot topic in the field of optical imaging due to its characteristics of

single pixel and low imaging cost. Distinguished from conventionally computational ghost imaging，in this paper，a

computational ghost imaging based on Hadamard matrix under the condition of under-sampling is investigated. The

theory and experimental setup are presented，and then the imaging results for four under sampling cases are analyzed.

The experimental results show that，under different sampling conditions，imaging duplication and edge distortion

emerge，however，what’s intriguing is that positive and negative images could be found. These phenomena arise

from the regular modulated distribution of Hadamard masks. The results achieved herein are not only helpful in

deepening the understanding of computational ghost imaging，but also are valuable for the analysis of the imaging

edge distortion in the long-distance imaging.

Key words: computational ghost imaging, Hadamard matrix, under-sampling