NEQR: a novel enhanced quantum representation of digital images
Quantum computation is becoming an important and effective tool to overcome the high real-time computational requirements of classical digital image processing. In this paper, based on analysis of existing quantum image representations, a novel enhanced quantum representation (NEQR) for digital images is proposed, which improves the latest flexible representation of quantum images (FRQI). The newly proposed quantum image representation uses the basis state of a qubit sequence to store the gray-scale value of each pixel in the image for the first time, instead of the probability amplitude of a qubit, as in FRQI. Because different basis states of qubit sequence are orthogonal, different gray scales in the NEQR quantum image can be distinguished. Performance comparisons with FRQI reveal that NEQR can achieve a quadratic speedup in quantum image preparation, increase the compression ratio of quantum images by approximately 1.5X, and retrieve digital images from quantum images accurately. Meanwhile, more quantum image operations related to gray-scale information in the image can be performed conveniently based on NEQR, for example partial color operations and statistical color operations. Therefore, the proposed NEQR quantum image model is more flexible and better suited for quantum image representation than other models in the literature.
KeywordsQuantum computation Image representation Image compression Image retrieving Color operation
The authors appreciate the kind comments and professional criticisms of the anonymous reviewer. This has greatly enhanced the overall quality of the manuscript and opened numerous perspectives geared toward improving the work. This work is supported in part by the National High-tech R&D Program of China (863 Program) under Grants 2012AA01A301 and 2012AA010901. And it is partially supported by National Science Foundation (NSF) China 61103082 and 61170261. Moreover, it is a part of Innovation Fund Sponsor Project of Excellent Postgraduate Student (B120601 and CX2012A002).
- 3.Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. Proceeding of 35th Annual Symposium Foundations of Computer Science, IEEE Computer Soc. Press, Los Almitos, CA, pp. 124–134 (1994)Google Scholar
- 4.Grover, L.: A fast quantum mechanical algorithm for database search. Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, pp. 212–219 (1996)Google Scholar
- 5.Gonzalez, Rafael C., Woods, Richard E., Eddins, Steven L.: Digital Image Processing. Publishing House of Electronics Industry, Beijing (2002)Google Scholar
- 6.Venegas-Andraca, S.E., Bose, S.: Storing, processing and retrieving an image using quantum mechanics. Proceeding of the SPIE Conference Quantum Information and Computation, pp. 137–147 (2003)Google Scholar
- 8.Latorre, J.I.: Image compression and entanglement. arXiv:quant-ph/0510031 (2005)Google Scholar
- 10.Tseng, C.-C., Hwang, T.-M.: Quantum digital image processing algorithms. 16th IPPR Conference on Computer Vision, Graphics and Image Processing, pp. 827–834 (2003)Google Scholar
- 11.Xiaowei Fu, Ding, Mingyue: A new quantum edge detection algorithm for medical images. Proceeding of Medical Imaging, Parallel Processing of Images and Optimization Techniques, SPIE vol. 7497 (2009)Google Scholar
- 13.Le, P.Q., Iliyasu, A.M., Dong, F., Hirota, K.: Efficient color transformations on quantum images. J. Adv. Comput. Intell. Intell. Inform. 15(6), (2011)Google Scholar
- 14.Sun, B., Le, P.Q., Iliyasu, A.M.: A multi-channel representation for images on quantum computers using the RGB\(\alpha \) color Space. Proceedings of the IEEE 7th International Symposium on Intelligent, Signal Processing, pp. 160–165 (2011)Google Scholar
- 16.Zhang, W., Gao, F., Liu, B., Wen, Q., Chen, H.: A watermark strategy for quantum images based on quantum fourier transform. Quantum Inform. Process. doi: 10.1007/s11128-012-0423-6 (2012)
- 20.Pang, C., Zhou, Z., Guo, G.: A hybrid quantum encoding algorithm of vector quantization for image compression. Chin. Phys. arXiv:cs/0605002 (2006)Google Scholar
- 21.Durr, C., Hoyer, P.: A quantum algorithm for finding the minimum. arXiv:quant-ph/9607014 (1996)Google Scholar