A Quantum Algorithm of Constructing Image Histogram

Authors: Yi Zhang, Kai Lu, Ying-hui Gao, Mo Wang

Abstract:

Histogram plays an important statistical role in digital image processing. However, the existing quantum image models are deficient to do this kind of image statistical processing because different gray scales are not distinguishable. In this paper, a novel quantum image representation model is proposed firstly in which the pixels with different gray scales can be distinguished and operated simultaneously. Based on the new model, a fast quantum algorithm of constructing histogram for quantum image is designed. Performance comparison reveals that the new quantum algorithm could achieve an approximately quadratic speedup than the classical counterpart. The proposed quantum model and algorithm have significant meanings for the future researches of quantum image processing.

Keywords: Quantum Image Representation, Quantum Algorithm, Image Histogram.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1332446

References:

[1] Venegas-Andraca, S. E., Ball, J. L.: Storing images in engtangled quantum systems. arXiv:quant-ph/0402085 (2003).
[2] Venegas-Andraca S.E., Ball J.L., K. Burnett, and S. Bose. Processing images in entangled quantum systems. Quantum Information Processing 9:1-11 (2010).
[3] Latorre, J. I.: Image compression and entanglement. arXiv:quant-ph/ 0510031 (2005)
[4] P.Q. Le, F. Dong, K. Hirota, A flexible representation of quantum images for polynomial preparation, image compression, and processing operations, Quantum Information Processing 10(1), 63-84 (2011).
[5] P.Q. Le, A.M. Iliyasu, F. Dong, K. Hirota, Strategies for designing geometric transformations on quantum images, Theoretical Computer Science 412, 1406-1418 (2011).
[6] P.Q. Le, A.M. Iliyasu, F. Dong, K. Hirota, Efficient Color Transformations on Quantum Images, Journal of Advanced Computational Intelligence and Intelligent Informatics, 15(6), (2011).
[7] A. M. Iliyasu, P. Q. Le, F. Dong, K. Hirota. Watermarking and authentication of quantum images based on restricted geometric transformations, Information Sciences 186, 126-149 (2012).
[8] W. Zhang, F. Gao, B. Liu, Q. Wen, H. Chen, A watermark strategy for quantum images based on quantum fourier transform. Quantum Information Processing. DOI 10.1007/s11128-012-0423-6 (2012).
[9] F. Lu and D. C. Marinescu. An RCmax Quantum Scheduling Algorithm. Quantum Information Processing, 6(3), 159-178 (2007).
[10] Grover, L., A fast quantum mechanical algorithm for database search, Proc. of the 28th Ann. ACM Symp. on the Theory of Computing, pp. 212-219 (1996).
[11] M. W. Coffey, Z. Prezkuta. A Quantum Algorithm for Finding the Modal Value. Quantum Information Processing, 7(1), 51-54 (2008).G. O. Young, "Synthetic structure of industrial plastics (Book style with paper title and editor)," in Plastics, 2nd ed. vol. 3, J. Peters, Ed. New York: McGraw-Hill, 1964, pp. 15-64.