A Survey on Quantum Image Processing
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摘要
Quantum image processing is the intersection of quantum computation and image processing. Due to it is a newly emerging thing, researchers are facing not only great opportunities but also many challenges to develop more efficient and practicable services. We provide a comprehensive survey on quantum image processing to gather the current mainstream and discuss the advances made in the area, including quantum image representations, processing algorithms, and image measurement. Moreover,some open challenges and future directions are pointed out to attract continued research efforts.
Quantum image processing is the intersection of quantum computation and image processing. Due to it is a newly emerging thing, researchers are facing not only great opportunities but also many challenges to develop more efficient and practicable services. We provide a comprehensive survey on quantum image processing to gather the current mainstream and discuss the advances made in the area, including quantum image representations, processing algorithms, and image measurement. Moreover,some open challenges and future directions are pointed out to attract continued research efforts.
Quantum image processing is the intersection of quantum computation and image processing. Due to it is a newly emerging thing, researchers are facing not only great opportunities but also many challenges to develop more efficient and practicable services. We provide a comprehensive survey on quantum image processing to gather the current mainstream and discuss the advances made in the area, including quantum image representations, processing algorithms, and image measurement. Moreover,some open challenges and future directions are pointed out to attract continued research efforts.
引文
[1]D.Castelvecchi,“Quantum computers ready to leap out of the lab in 2017”,Nature,Vol.541,pp.9-10,2017.
[2]S.E.Venegas-Andraca,“Introductory words:Special issue on quantum image processing published by quantum information processing”,Quantum Inf.Proc.,Vol.14,No.5,pp.1535-1537,2015.
[3]N.Jiang,Quantum Image Processing,Tsinghua University Press,Beijing,China,pp.1-137,2016.
[4]R.C.Gonzalez and R.E.Woods,Digital Image Processing(3rd Ed.),Prentice Hall,New Jersey,USA,pp.1-954,2007.
[5]W.K.Pratt,Digital Image Processing(4th Ed.),John Wiley&Sons,New York,USA,pp.1-812,2007.
[6]D.Murray,“Announcing Tensor Flow 0.8-Now with distributed computing support!”,available at https://research.googleblog.com/2016/04/announcing-tensorflow-08-now-with.html,2016-4-13.
[7]A.Y.Vlasov,“Quantum computations and image recognition”,ar Xiv:quant-ph/9703010,1997.
[8]G.Beach,C.Lomont and C.Cohen,“Quantum image processing”,Proc.of IEEE Workshop on Applied Imagery Pattern Recognition,Washington DC,USA,pp.39-44,2003.
[9]S.E.Venegas-Andraca and S.Bose,“Quantum computation and image processing:New trends in artificial intelligence”,Proc.of the International Conference on Artificial Intelligence,Las Vegas,Nevada,USA,pp.1563-1564,2003.
[10]S.E.Venegas-Andraca and S.Bose,“Storing,processing and retrieving an image using quantum mechanics”,Proc.of the SPIEConference Quantum Information and Computation,Orlando,Florida,USA,pp.137-147,2003.
[11]J.I.Latorre,“Image compression and entanglement”,ar Xiv:quant-ph/0510031,2005.
[12]R.P.Feynman,“Simulating physics with computers”,Int.J.Theor.Phys.,Vol.21,No.6/7,pp.467-488,1982.
[13]F.Yan,A.M.Iliyasu and S.E.Venegas-Andraca,“A survey of quantum image representations”,Quantum Inf.Proc.,Vol.15,No.1,pp.1-35,2016.
[14]P.Q.Le,F.Y.Dong and K.Hirota,“A flexible representation of quantum images for polynomial preparation,image compression,and processing operations”,Quantum Inf.Proc.,Vol.10,No.1,pp.63-84,2011.
[15]B.Sun,A.M.Iliyasu,F.Yan,et al.,“An RGB multi-channel representation for images on quantum computers”,Journal of Advanced Computational Intelligence and Intelligent Informatics,Vol.17,No.3,pp.404-417,2013.
[16]Y.Zhang,K.Lu,Y.H.Gao,et al.,“NEQR:A novel enhanced quantum representation of digital images”,Quantum Information Processing,Vol.12,No.12,pp.2833-2860,2013.
[17]N.Jiang and L.Wang,“Quantum image scaling using nearest neighbor interpolation”,Quantum Information Processing,Vol.14,No.5,pp.1559-1571,2015.
[18]N.Jiang,J.Wang and Y.Mu,“Quantum image scaling up based on nearest-neighbor interpolation with integer scaling ratio”,Quantum Inf.Proc.,Vol.14,No.11,pp.4001-4026,2015.
[19]N.Jiang,W.Y.Wu,L.Wang,et al.,“Quantum image pseudo color coding based on the density-stratified method”,Quantum Inf.Proc.,Vol.14,No.5,pp.1735-1755,2015.
[20]S.Caraiman and V.Manta,“Image processing using quantum computing”,Proc.of the 16th International Conference on System Theory,Control and Computing,Sinaia,Romania,pp.1-6,2012.
[21]Y.Zhang,K.Lu,Y.H.Gao,et al.,“A novel quantum representation for log-polar images”,Quantum Information Processing,Vol.12,No.9,pp.3103-3126,2013.
[22]S.Yuan,X.Mao,Y.Xue,et al.,“SQR:A simple quantum representation of infrared images”,Quantum Inf.Proc.,Vol.13,No.6,pp.1353-1379,2014.
[23]H.Li,Q.Zhu,S.Lan,et al.,“Image storage,retrieval,compression and segmentation in a quantum system”,Quantum Inf.Proc.,Vol.12,No.6,pp.2269-2290,2013.
[24]H.Li,Q.Zhu,R.Zhou,et al.,“Multi-dimensional color image storage and retrieval for a normal arbitrary quantum superposition state”,Quantum Information Processing,Vol.13,No.4,pp.991-1011,2014.
[25]P.Le,A.Iliyasu,F.Dong,et al.,“Fast geometric transformations on quantum images”,IAENG International Journal of Applied Mathematics,Vol.40,No.3,pp.113-123,2010.
[26]N.Jiang,X.W.Lu,H.Hu,et al.,“A novel quantum image compression method based on JPEG”,Int.J.Theor.Phys.,Vol.57,No.3,pp.611-636,2018.
[27]J.Wang,N.Jiang and L.Wang,“Quantum image translation”,Quantum Inf.Proc.,Vol.14,No.5,pp.1589-1604,2015.
[28]N.Jiang,L.Wang and W.Y.Wu,“Quantum Hilbert image scrambling”,Int.J.Theor.Phys.,Vol.53,No.7,pp.2463-2484,2014.
[29]N.Jiang,W.Y.Wu and L.Wang,“The quantum realization of Arnold and Fibonacci image scrambling”,Quantum Information Processing,Vol.13,No.5,pp.1223-1236,2014.
[30]N.Jiang and L.Wang,“Analysis and improvement of the quantum Arnold image scrambling”,Quantum Information Processing,Vol.13,No.7,pp.1545-1551,2014.
[31]R.Zhou,Y.Sun and P.Fan,“Quantum image gray-code and bit-plane scrambling”,Quantum Inf.Proc.,Vol.14,No.5,pp.1717-1734,2015.
[32]S.E.Venegas-Andraca and J.L.Ball,“Processing images in entangled quantum system”,Quantum Inf.Proc.,Vol.9,No.1,pp.1-11,2010.
[33]S.Caraiman and V.Manta,“Histogram-based segmentation of quantum images”,Theoretical Computer Science,Vol.529,No.6,pp.46-60,2014.
[34]S.Caraiman and V.Manta,“Image segmentation on a quantum computer”,Quantum Inf.Proc.,Vol.14,No.5,pp.1693-1715,2015.
[35]Y.Zhang,K.Lu and Y.Gao,“Qsobel:A novel quantum image edge extraction algorithm”,Science China Information Sciences,Vol.58,No.1,pp.1-13,2015.
[36]Y.Zhang,K.Lu,K.Xu,et al.,“Local feature point extraction for quantum images”,Quantum Information Processing,Vol.14,No.5,pp.1573-1588,2015.
[37]N.R.Zhou,T.X.Hua,L.H.Gong,et al.,“Quantum image encryption based on generalized Arnold transform and double random-phase encoding”,Quantum Information Processing,Vol.14,No.4,pp.1193-1213,2015.
[38]T.X.Hua,J.M.Chen and D.J.Pei,“Quantum image encryption algorithm based on image correlation decomposition”,Int.J.Theor.Phys.,Vol.54,No.2,pp.526-537,2015.
[39]S.Wang,X.H.Song and X.M.Niu,“A novel encryption algorithm for quantum images based on quantum wavelet transform and diffusion”,Intelligent Data Analysis and Its Applications,Vol.II,No.298,pp.243-250,2014.
[40]X.H.Song,S.Wang,A.Ahmed,et al.,“Quantum image encryption based on restricted geometric and color transformations”,Quantum Inf.Proc.,Vol.13,No.8,pp.1765-1787,2014.
[41]R.G.Zhou,Q.Wu and M.Q.Zhang,“A Quantum image encryption algorithm based on quantum image geometric transformations”,Proc.of the Chinese Conference on Pattern Recognition,Beijing,China,pp.480-487,2012.
[42]R.G.Zhou,Q.Wu and M.Q.Zhang,“Quantum image encryption and decryption algorithms based on quantum image geometric transformations”,International Journal of Theoretical Physics,Vol.52,No.6,pp.1802-1817,2013.
[43]A.Akhshani,A.Akhavan,S.C.Lim,et al.,“An image encryption scheme based on quantum logistic map”,Communications in Nonlinear Science and Numerical Simulation,Vol.17,No.12,pp.4653-4661,2012.
[44]Y.G.Yang,J.Xia,X.Jia,et al.,“Novel image encryption/decryption based on quantum Fourier transform and double phase encoding”,Quantum Inf.Proc.,Vol.12,No.11,pp.3477-3493,2013.
[45]Y.G.Yang,J.Tian,H.Lei,et al.,“Novel quantum image encryption using one-dimensional quantum cellular automata”,Information Sciences,Vol.345,pp.257-270,2016.
[46]A.M.Iliyasu,P.Q.Le,F.Dong,et al.,“Watermarking and authentication of quantum images based on restricted geometric transformations”,Information Sciences,Vol.186,pp.126-149,2012.
[47]F.Yan,A.M.Iliyasu,B.Sun,et al.,“A duple watermarking strategy for multi-channel quantum images”,Quantum Information Processing,Vol.14,No.5,pp.1675-1692,2015.
[48]W.W.Zhang,F.Gao and B.Liu,“A watermark strategy for quantum images based on quantum Fourier transform”,Quantum Information Processing,Vol.12,No.4,pp.793-803,2013.
[49]W.W.Zhang,F.Gao and B.Liu,“A quantum watermark protocol”,Int.J.Theor.Phys.,Vol.52,No.2,pp.504-513,2013.
[50]X.H.Song,S.Wang,S.Liu,et al.,“A dynamic watermarking scheme for quantum images using quantum wavelet transform”,Quantum Inf.Proc.,Vol.12,No.12,pp.3689-3706,2013.
[51]X.H.Song,S.Wang,S.Liu,et al.,“Dynamic watermarking scheme for quantum images based on Hadamard transform”,Multimedia Systems,Vol.20,No.4,pp.379-388,2014.
[52]S.Wang,X.H.Song and X.M.Niu,“Quantum Cosine transform based watermarking scheme for quantum images”,Chinese Journal of Electronics,Vol.24,No.2,pp.321-325,2015.
[53]N.Jiang and L.Wang,“A novel strategy for quantum image steganography based on Moir′e pattern”,International Journal of Theoretical Physics,Vol.54,No.3,pp.1021-1032,2015.
[54]N.Jiang,N.Zhao and L.Wang,“LSB based quantum image steganography algorithm”,International Journal of Theoretical Physics,Vol.55,No.1,pp.107-123,2016.
[55]S.Heidari and M.Naseri,“A novel LSB based quantum watermarking”,Int.J.Theor.Phys.,Vol.55,No.10,pp.4205-4218,2016.
[56]S.Miyake and K.Nakamae,“A quantum watermarking scheme using simple and small-scale quantum circuits”,Quantum Information Processing,Vol.15,No.5,pp.1849-1864,2016.
[57]Z.H.Wei,X.B.Chen,S.J.Xu,et al.,“A spatial domain quantum watermarking scheme”,Communications in Theoretical Physics,Vol.66,No.1,pp.66-76,2016.
[58]S.Yuan,X.Mao,T.Li,et al.,“Quantum morphology operations based on quantum representation model”,Quantum Inf.Proc.,Vol.14,No.5,pp.1625-1645,2015.
[59]R.Zhou,Z.Chang,P.Fan,et al.,“Quantum image morphology processing based on quantum set operation”,Int.J.Theor.Phys.,Vol.54,No.6,pp.1974-1986,2015.
[60]S.Caraiman and V.Manta,“Quantum image filtering in the frequency domain”,Advances in Electrical and Computer Engineering,Vol.13,No.3,pp.77-84,2013.
[61]M.Mastriani,“Quantum boolean image denoising”,Quantum Inf.Proc.,Vol.14,No.5,pp.1647-1673,2015.
[62]F.Yan,A.Iliyasu,P.Le,et al.,“A parallel comparison of multiple pairs of images on quantum computers”,International Journal of Innovative Computing and Applications,Vol.5,No.4,pp.199-212,2013.
[63]R.Zhou and Y.Sun,“Quantum multidimensional color images similarity comparison”,Quantum Information Processing,Vol.14,No.5,pp.1605-1624,2015.
[64]F.Yan,A.Iliyasu,C.Fatichah,et al.,“Quantum image searching based on probability distributions”,Journal of Quantum Information Science,Vol.2,No.3,pp.55-60,2012.
[65]N.Jiang,Y.J.Dang and J.Wang,“Quantum image matching”,Quantum Inf.Proc.,Vol.15,No.9,pp.3543-3572,2016.
[66]N.Jiang,Y.J.Dang and N.Zhao,“Quantum image location”,Int.J.Theor.Phys.,Vol.55,No.10,pp.4501-4512,2016.
[67]Y.Zhao,X.Chen,Z.Shi,et al.,“Implementation of one-way quantum computing with a hybrid solid-state quantum system”,Chinese Journal of Electronics,Vol.26,No.1,pp.27-34,2017.
[68]H.Xiong,“Multi-level Bell-type inequality from information causality and noisy computations”,Chinese Journal of Electronics,Vol.24,No.2,pp.408-413,2015.
[69]A.Iliyasu,“Towards realising secure and efficient image and video processing applications on quantum computers”,Entropy,Vol.15,No.8,pp.2874-2974,2013.
[2]S.E.Venegas-Andraca,“Introductory words:Special issue on quantum image processing published by quantum information processing”,Quantum Inf.Proc.,Vol.14,No.5,pp.1535-1537,2015.
[3]N.Jiang,Quantum Image Processing,Tsinghua University Press,Beijing,China,pp.1-137,2016.
[4]R.C.Gonzalez and R.E.Woods,Digital Image Processing(3rd Ed.),Prentice Hall,New Jersey,USA,pp.1-954,2007.
[5]W.K.Pratt,Digital Image Processing(4th Ed.),John Wiley&Sons,New York,USA,pp.1-812,2007.
[6]D.Murray,“Announcing Tensor Flow 0.8-Now with distributed computing support!”,available at https://research.googleblog.com/2016/04/announcing-tensorflow-08-now-with.html,2016-4-13.
[7]A.Y.Vlasov,“Quantum computations and image recognition”,ar Xiv:quant-ph/9703010,1997.
[8]G.Beach,C.Lomont and C.Cohen,“Quantum image processing”,Proc.of IEEE Workshop on Applied Imagery Pattern Recognition,Washington DC,USA,pp.39-44,2003.
[9]S.E.Venegas-Andraca and S.Bose,“Quantum computation and image processing:New trends in artificial intelligence”,Proc.of the International Conference on Artificial Intelligence,Las Vegas,Nevada,USA,pp.1563-1564,2003.
[10]S.E.Venegas-Andraca and S.Bose,“Storing,processing and retrieving an image using quantum mechanics”,Proc.of the SPIEConference Quantum Information and Computation,Orlando,Florida,USA,pp.137-147,2003.
[11]J.I.Latorre,“Image compression and entanglement”,ar Xiv:quant-ph/0510031,2005.
[12]R.P.Feynman,“Simulating physics with computers”,Int.J.Theor.Phys.,Vol.21,No.6/7,pp.467-488,1982.
[13]F.Yan,A.M.Iliyasu and S.E.Venegas-Andraca,“A survey of quantum image representations”,Quantum Inf.Proc.,Vol.15,No.1,pp.1-35,2016.
[14]P.Q.Le,F.Y.Dong and K.Hirota,“A flexible representation of quantum images for polynomial preparation,image compression,and processing operations”,Quantum Inf.Proc.,Vol.10,No.1,pp.63-84,2011.
[15]B.Sun,A.M.Iliyasu,F.Yan,et al.,“An RGB multi-channel representation for images on quantum computers”,Journal of Advanced Computational Intelligence and Intelligent Informatics,Vol.17,No.3,pp.404-417,2013.
[16]Y.Zhang,K.Lu,Y.H.Gao,et al.,“NEQR:A novel enhanced quantum representation of digital images”,Quantum Information Processing,Vol.12,No.12,pp.2833-2860,2013.
[17]N.Jiang and L.Wang,“Quantum image scaling using nearest neighbor interpolation”,Quantum Information Processing,Vol.14,No.5,pp.1559-1571,2015.
[18]N.Jiang,J.Wang and Y.Mu,“Quantum image scaling up based on nearest-neighbor interpolation with integer scaling ratio”,Quantum Inf.Proc.,Vol.14,No.11,pp.4001-4026,2015.
[19]N.Jiang,W.Y.Wu,L.Wang,et al.,“Quantum image pseudo color coding based on the density-stratified method”,Quantum Inf.Proc.,Vol.14,No.5,pp.1735-1755,2015.
[20]S.Caraiman and V.Manta,“Image processing using quantum computing”,Proc.of the 16th International Conference on System Theory,Control and Computing,Sinaia,Romania,pp.1-6,2012.
[21]Y.Zhang,K.Lu,Y.H.Gao,et al.,“A novel quantum representation for log-polar images”,Quantum Information Processing,Vol.12,No.9,pp.3103-3126,2013.
[22]S.Yuan,X.Mao,Y.Xue,et al.,“SQR:A simple quantum representation of infrared images”,Quantum Inf.Proc.,Vol.13,No.6,pp.1353-1379,2014.
[23]H.Li,Q.Zhu,S.Lan,et al.,“Image storage,retrieval,compression and segmentation in a quantum system”,Quantum Inf.Proc.,Vol.12,No.6,pp.2269-2290,2013.
[24]H.Li,Q.Zhu,R.Zhou,et al.,“Multi-dimensional color image storage and retrieval for a normal arbitrary quantum superposition state”,Quantum Information Processing,Vol.13,No.4,pp.991-1011,2014.
[25]P.Le,A.Iliyasu,F.Dong,et al.,“Fast geometric transformations on quantum images”,IAENG International Journal of Applied Mathematics,Vol.40,No.3,pp.113-123,2010.
[26]N.Jiang,X.W.Lu,H.Hu,et al.,“A novel quantum image compression method based on JPEG”,Int.J.Theor.Phys.,Vol.57,No.3,pp.611-636,2018.
[27]J.Wang,N.Jiang and L.Wang,“Quantum image translation”,Quantum Inf.Proc.,Vol.14,No.5,pp.1589-1604,2015.
[28]N.Jiang,L.Wang and W.Y.Wu,“Quantum Hilbert image scrambling”,Int.J.Theor.Phys.,Vol.53,No.7,pp.2463-2484,2014.
[29]N.Jiang,W.Y.Wu and L.Wang,“The quantum realization of Arnold and Fibonacci image scrambling”,Quantum Information Processing,Vol.13,No.5,pp.1223-1236,2014.
[30]N.Jiang and L.Wang,“Analysis and improvement of the quantum Arnold image scrambling”,Quantum Information Processing,Vol.13,No.7,pp.1545-1551,2014.
[31]R.Zhou,Y.Sun and P.Fan,“Quantum image gray-code and bit-plane scrambling”,Quantum Inf.Proc.,Vol.14,No.5,pp.1717-1734,2015.
[32]S.E.Venegas-Andraca and J.L.Ball,“Processing images in entangled quantum system”,Quantum Inf.Proc.,Vol.9,No.1,pp.1-11,2010.
[33]S.Caraiman and V.Manta,“Histogram-based segmentation of quantum images”,Theoretical Computer Science,Vol.529,No.6,pp.46-60,2014.
[34]S.Caraiman and V.Manta,“Image segmentation on a quantum computer”,Quantum Inf.Proc.,Vol.14,No.5,pp.1693-1715,2015.
[35]Y.Zhang,K.Lu and Y.Gao,“Qsobel:A novel quantum image edge extraction algorithm”,Science China Information Sciences,Vol.58,No.1,pp.1-13,2015.
[36]Y.Zhang,K.Lu,K.Xu,et al.,“Local feature point extraction for quantum images”,Quantum Information Processing,Vol.14,No.5,pp.1573-1588,2015.
[37]N.R.Zhou,T.X.Hua,L.H.Gong,et al.,“Quantum image encryption based on generalized Arnold transform and double random-phase encoding”,Quantum Information Processing,Vol.14,No.4,pp.1193-1213,2015.
[38]T.X.Hua,J.M.Chen and D.J.Pei,“Quantum image encryption algorithm based on image correlation decomposition”,Int.J.Theor.Phys.,Vol.54,No.2,pp.526-537,2015.
[39]S.Wang,X.H.Song and X.M.Niu,“A novel encryption algorithm for quantum images based on quantum wavelet transform and diffusion”,Intelligent Data Analysis and Its Applications,Vol.II,No.298,pp.243-250,2014.
[40]X.H.Song,S.Wang,A.Ahmed,et al.,“Quantum image encryption based on restricted geometric and color transformations”,Quantum Inf.Proc.,Vol.13,No.8,pp.1765-1787,2014.
[41]R.G.Zhou,Q.Wu and M.Q.Zhang,“A Quantum image encryption algorithm based on quantum image geometric transformations”,Proc.of the Chinese Conference on Pattern Recognition,Beijing,China,pp.480-487,2012.
[42]R.G.Zhou,Q.Wu and M.Q.Zhang,“Quantum image encryption and decryption algorithms based on quantum image geometric transformations”,International Journal of Theoretical Physics,Vol.52,No.6,pp.1802-1817,2013.
[43]A.Akhshani,A.Akhavan,S.C.Lim,et al.,“An image encryption scheme based on quantum logistic map”,Communications in Nonlinear Science and Numerical Simulation,Vol.17,No.12,pp.4653-4661,2012.
[44]Y.G.Yang,J.Xia,X.Jia,et al.,“Novel image encryption/decryption based on quantum Fourier transform and double phase encoding”,Quantum Inf.Proc.,Vol.12,No.11,pp.3477-3493,2013.
[45]Y.G.Yang,J.Tian,H.Lei,et al.,“Novel quantum image encryption using one-dimensional quantum cellular automata”,Information Sciences,Vol.345,pp.257-270,2016.
[46]A.M.Iliyasu,P.Q.Le,F.Dong,et al.,“Watermarking and authentication of quantum images based on restricted geometric transformations”,Information Sciences,Vol.186,pp.126-149,2012.
[47]F.Yan,A.M.Iliyasu,B.Sun,et al.,“A duple watermarking strategy for multi-channel quantum images”,Quantum Information Processing,Vol.14,No.5,pp.1675-1692,2015.
[48]W.W.Zhang,F.Gao and B.Liu,“A watermark strategy for quantum images based on quantum Fourier transform”,Quantum Information Processing,Vol.12,No.4,pp.793-803,2013.
[49]W.W.Zhang,F.Gao and B.Liu,“A quantum watermark protocol”,Int.J.Theor.Phys.,Vol.52,No.2,pp.504-513,2013.
[50]X.H.Song,S.Wang,S.Liu,et al.,“A dynamic watermarking scheme for quantum images using quantum wavelet transform”,Quantum Inf.Proc.,Vol.12,No.12,pp.3689-3706,2013.
[51]X.H.Song,S.Wang,S.Liu,et al.,“Dynamic watermarking scheme for quantum images based on Hadamard transform”,Multimedia Systems,Vol.20,No.4,pp.379-388,2014.
[52]S.Wang,X.H.Song and X.M.Niu,“Quantum Cosine transform based watermarking scheme for quantum images”,Chinese Journal of Electronics,Vol.24,No.2,pp.321-325,2015.
[53]N.Jiang and L.Wang,“A novel strategy for quantum image steganography based on Moir′e pattern”,International Journal of Theoretical Physics,Vol.54,No.3,pp.1021-1032,2015.
[54]N.Jiang,N.Zhao and L.Wang,“LSB based quantum image steganography algorithm”,International Journal of Theoretical Physics,Vol.55,No.1,pp.107-123,2016.
[55]S.Heidari and M.Naseri,“A novel LSB based quantum watermarking”,Int.J.Theor.Phys.,Vol.55,No.10,pp.4205-4218,2016.
[56]S.Miyake and K.Nakamae,“A quantum watermarking scheme using simple and small-scale quantum circuits”,Quantum Information Processing,Vol.15,No.5,pp.1849-1864,2016.
[57]Z.H.Wei,X.B.Chen,S.J.Xu,et al.,“A spatial domain quantum watermarking scheme”,Communications in Theoretical Physics,Vol.66,No.1,pp.66-76,2016.
[58]S.Yuan,X.Mao,T.Li,et al.,“Quantum morphology operations based on quantum representation model”,Quantum Inf.Proc.,Vol.14,No.5,pp.1625-1645,2015.
[59]R.Zhou,Z.Chang,P.Fan,et al.,“Quantum image morphology processing based on quantum set operation”,Int.J.Theor.Phys.,Vol.54,No.6,pp.1974-1986,2015.
[60]S.Caraiman and V.Manta,“Quantum image filtering in the frequency domain”,Advances in Electrical and Computer Engineering,Vol.13,No.3,pp.77-84,2013.
[61]M.Mastriani,“Quantum boolean image denoising”,Quantum Inf.Proc.,Vol.14,No.5,pp.1647-1673,2015.
[62]F.Yan,A.Iliyasu,P.Le,et al.,“A parallel comparison of multiple pairs of images on quantum computers”,International Journal of Innovative Computing and Applications,Vol.5,No.4,pp.199-212,2013.
[63]R.Zhou and Y.Sun,“Quantum multidimensional color images similarity comparison”,Quantum Information Processing,Vol.14,No.5,pp.1605-1624,2015.
[64]F.Yan,A.Iliyasu,C.Fatichah,et al.,“Quantum image searching based on probability distributions”,Journal of Quantum Information Science,Vol.2,No.3,pp.55-60,2012.
[65]N.Jiang,Y.J.Dang and J.Wang,“Quantum image matching”,Quantum Inf.Proc.,Vol.15,No.9,pp.3543-3572,2016.
[66]N.Jiang,Y.J.Dang and N.Zhao,“Quantum image location”,Int.J.Theor.Phys.,Vol.55,No.10,pp.4501-4512,2016.
[67]Y.Zhao,X.Chen,Z.Shi,et al.,“Implementation of one-way quantum computing with a hybrid solid-state quantum system”,Chinese Journal of Electronics,Vol.26,No.1,pp.27-34,2017.
[68]H.Xiong,“Multi-level Bell-type inequality from information causality and noisy computations”,Chinese Journal of Electronics,Vol.24,No.2,pp.408-413,2015.
[69]A.Iliyasu,“Towards realising secure and efficient image and video processing applications on quantum computers”,Entropy,Vol.15,No.8,pp.2874-2974,2013.