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Quantum Hilbert Image Scrambling

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Abstract

Analogies between quantum image processing (QIP) and classical one indicate that quantum image scrambling (QIS), as important as quantum Fourier transform (QFT), quantum wavelet transform (QWT) and etc., should be proposed to promote QIP. Image scrambling technology is commonly used to transform a meaningful image into a disordered image by permutating the pixels into new positions. Although image scrambling on classical computers has been widely studied, we know much less about QIS. In this paper, the Hilbert image scrambling algorithm, which is commonly used in classical image processing, is carried out in quantum computer by giving the scrambling quantum circuits. First, a modified recursive generation algorithm of Hilbert scanning matrix is given. Then based on the flexible representation of quantum images, the Hilbert scrambling quantum circuits, which are recursive and progressively layered, is proposed. Theoretical analysis indicates that the network complexity scales squarely with the size of the circuit’s input n.

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Acknowledgments

This work is supported by the Beijing Municipal Education Commission Science and Technology Development Plan under Grants No. KM201310005021, KZ201210005007, the Fundamental Research Funds for the Central Universities under Grants No. 2012JBM041, and the Graduate Technology Fund of BJUT under Grants No. YKJ-2013-10282.

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Authors and Affiliations

  1. College of Computer, Beijing University of Technology, Beijing, 100124, China

    Nan Jiang, Luo Wang & Wen-Ya Wu

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  1. Nan Jiang
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  2. Luo Wang
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  3. Wen-Ya Wu
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Correspondence to Nan Jiang.

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Jiang, N., Wang, L. & Wu, WY. Quantum Hilbert Image Scrambling. Int J Theor Phys 53, 2463–2484 (2014). https://doi.org/10.1007/s10773-014-2046-4

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  • DOI: https://doi.org/10.1007/s10773-014-2046-4

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