A survey of quantum image representations

Quantum image processing (QIMP) is devoted to utilizing the quantum computing technologies to capture, manipulate, and recover quantum images in different formats and for different purposes. Logically, percolating this requires that representations to encode images based on the quantum mechanical composition of any potential quantum computing hardware be conjured. This paper gathers the current mainstream quantum image representations (QIRs) and discusses the advances made in the area. Some similarities, differences, and likely applications for some of the available QIRs are reviewed. We believe this compendium will provide the readership an overview of progress witnessed in the area of QIMP while also simulating further interest to pursue more advanced research in it.

[1]  Kaoru Hirota,et al.  A parallel comparison of multiple pairs of images on quantum computers , 2013 .

[2]  Ping Fan,et al.  Quantum Image Morphology Processing Based on Quantum Set Operation , 2015 .

[3]  Chris Lomont Quantum convolution and quantum correlation algorithms are physically impossible , 2003 .

[4]  Shen Wang,et al.  A Novel Encryption Algorithm for Quantum Images Based on Quantum Wavelet Transform and Diffusion , 2014, ECC.

[5]  Nan Jiang,et al.  Analysis and improvement of the quantum Arnold image scrambling , 2014, Quantum Information Processing.

[6]  M.C. Batouche,et al.  A genetic quantum algorithm for image registration , 2004, Proceedings. 2004 International Conference on Information and Communication Technologies: From Theory to Applications, 2004..

[7]  Ri-Gui Zhou,et al.  Quantum Image Encryption and Decryption Algorithms Based on Quantum Image Geometric Transformations , 2013 .

[8]  Ahmed A. Abd El-Latif,et al.  A dynamic watermarking scheme for quantum images using quantum wavelet transform , 2013, Quantum Information Processing.

[9]  Fei Yan,et al.  Insights into the Viability of Using Available Photonic Quantum Technologies for Efficient Image and Video Processing Applications , 2013, Int. J. Unconv. Comput..

[10]  Nan Jiang,et al.  A Novel Strategy for Quantum Image Steganography Based on Moiré Pattern , 2015 .

[11]  Han Zheng-zhi THE NEW EVOLUTION OF IMAGE ENCRYPTION TECHNIQUES , 2003 .

[12]  E M Fortunato,et al.  Implementation of the quantum Fourier transform. , 2001, Physical review letters.

[13]  Amir Fijany,et al.  Quantum Wavelet Transforms: Fast Algorithms and Complete Circuits , 1998, QCQC.

[14]  Wang Xingmei,et al.  A novel quantum-inspired algorithm for edge detection of sonar image , 2014, Proceedings of the 33rd Chinese Control Conference.

[15]  Siddhartha Bhattacharyya,et al.  Binary image denoising using a quantum multilayer self organizing neural network , 2014, Appl. Soft Comput..

[16]  Tian Li,et al.  Quantum morphology operations based on quantum representation model , 2015, Quantum Inf. Process..

[17]  Lov K. Grover A fast quantum mechanical algorithm for database search , 1996, STOC '96.

[18]  K. Pagiamtzis,et al.  Content-addressable memory (CAM) circuits and architectures: a tutorial and survey , 2006, IEEE Journal of Solid-State Circuits.

[19]  Salwa H. El-Ramly,et al.  A quantum mechanics-based framework for image processing and its application to image segmentation , 2015, Quantum Inf. Process..

[20]  Kaoru Hirota,et al.  Efficient Color Transformations on Quantum Images , 2011, J. Adv. Comput. Intell. Intell. Informatics.

[21]  Abdullah M. Iliyasu,et al.  Strategies for designing geometric transformations on quantum images , 2011, Theor. Comput. Sci..

[22]  Bo Sun,et al.  A duple watermarking strategy for multi-channel quantum images , 2015, Quantum Inf. Process..

[23]  Peng Xu,et al.  Analysis and improvement of the dynamic watermarking scheme for quantum images using quantum wavelet transform , 2014, Quantum Inf. Process..

[24]  Mario Mastriani Quantum Boolean image denoising , 2015, Quantum Inf. Process..

[25]  Nan Jiang,et al.  LSB Based Quantum Image Steganography Algorithm , 2015, International Journal of Theoretical Physics.

[26]  Kaoru Hirota,et al.  A flexible representation of quantum images for polynomial preparation, image compression, and processing operations , 2011, Quantum Inf. Process..

[27]  A. Akhavan,et al.  An image encryption scheme based on quantum logistic map , 2012 .

[28]  Hirota Kaoru,et al.  Flexible Representation of Quantum Images and Its Computational Complexity Analysis , 2009 .

[29]  Yangyang Li,et al.  SAR image segmentation based on quantum-inspired multiobjective evolutionary clustering algorithm , 2014, Inf. Process. Lett..

[30]  R. S. Jadon,et al.  Quantum methodology for Edge detection: A compelling approach to enhance edge detection in digital image processing , 2014, 2014 5th International Conference - Confluence The Next Generation Information Technology Summit (Confluence).

[31]  Lijiang Chen,et al.  SQR: a simple quantum representation of infrared images , 2014, Quantum Information Processing.

[32]  Hua Zhang,et al.  Novel image encryption/decryption based on quantum Fourier transform and double phase encoding , 2013, Quantum Inf. Process..

[33]  Nan Jiang,et al.  Quantum image pseudocolor coding based on the density-stratified method , 2015, Quantum Inf. Process..

[34]  Mohamed Batouche,et al.  Image processing using quantum computing and reverse emergence , 2009 .

[35]  Chao Yang Pang,et al.  Quantum Discrete Cosine Transform for Image Compression , 2006 .

[36]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[37]  D. Okada,et al.  Digital Image Processing for Medical Applications , 2009 .

[38]  Vijayan K. Asari,et al.  3D Object Classification in Uncalibrated Structure from Motion Models , 2015 .

[39]  D. Deutsch Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[40]  Gilles Brassard,et al.  Tight bounds on quantum searching , 1996, quant-ph/9605034.

[41]  Qingxin Zhu,et al.  Image storage, retrieval, compression and segmentation in a quantum system , 2013, Quantum Inf. Process..

[42]  Huifang Li,et al.  A New Method of Image Compression Based on Quantum Neural Network , 2010, 2010 International Conference of Information Science and Management Engineering.

[43]  周日贵 Quantum image Gray-code and bit-plane scrambling , 2015 .

[44]  Chao-Yang Pang Loading N-Dimensional Vector into Quantum Registers from Classical Memory with O(logN) Steps , 2006 .

[45]  Richard Szeliski,et al.  Computer Vision - Algorithms and Applications , 2011, Texts in Computer Science.

[46]  Li Shan-zhi,et al.  Design of Quantum Comparator Based on Extended General Toffoli Gates with Multiple Targets , 2012 .

[47]  Seyed Mohammad Seyedzadeh,et al.  A novel color image encryption algorithm based on spatial permutation and quantum chaotic map , 2015, Nonlinear Dynamics.

[48]  Peng Xu,et al.  Analysis and improvement of the watermark strategy for quantum images based on quantum Fourier transform , 2013, Quantum Inf. Process..

[49]  Marco Lanzagorta,et al.  Maritime applications of quantum computation , 2015, OCEANS 2015 - MTS/IEEE Washington.

[50]  Yangyang Li,et al.  Quantum evolutionary clustering algorithm based on watershed applied to SAR image segmentation , 2012, Neurocomputing.

[51]  F. Nori,et al.  Quantum Simulation , 2013, Quantum Atom Optics.

[52]  Chris Lomont,et al.  Quantum image processing (QuIP) , 2003, 32nd Applied Imagery Pattern Recognition Workshop, 2003. Proceedings..

[53]  Huamin Yang,et al.  Video Encryption and Decryption on Quantum Computers , 2015, International Journal of Theoretical Physics.

[54]  Kai Lu,et al.  QSobel: A novel quantum image edge extraction algorithm , 2014, Science China Information Sciences.

[55]  Nan Jiang,et al.  The quantum realization of Arnold and Fibonacci image scrambling , 2014, Quantum Inf. Process..

[56]  Lov K. Grover Quantum Mechanics Helps in Searching for a Needle in a Haystack , 1997, quant-ph/9706033.

[57]  Kaoru Hirota,et al.  A Flexible Representation and Invertible Transformations for Images on Quantum Computers , 2011 .

[58]  Kaoru Hirota,et al.  A FRAMEWORK FOR REPRESENTING AND PRODUCING MOVIES ON QUANTUM COMPUTERS , 2011 .

[59]  Simona Caraiman,et al.  Histogram-based segmentation of quantum images , 2014, Theor. Comput. Sci..

[60]  Fei Yan,et al.  Quantum Image Searching Based on Probability Distributions , 2012 .

[61]  Salvador E. Venegas-Andraca,et al.  Processing images in entangled quantum systems , 2010, Quantum Inf. Process..

[62]  José Ignacio Latorre,et al.  Image compression and entanglement , 2005, ArXiv.

[63]  Xiaojun Bi,et al.  Image Segmentation Algorithm Based on Quantum Immune Programming , 2007, 2007 IEEE International Conference on Integration Technology.

[64]  Alán Aspuru-Guzik,et al.  A study of heuristic guesses for adiabatic quantum computation , 2008, Quantum Inf. Process..

[65]  Pierre Mascarade,et al.  Quantum Image Filtering in the Frequency Domain , 2017 .

[66]  Zhu Gui-liang Research on the New Development of Image Encryption Algorithms , 2012 .

[67]  Simona Caraiman,et al.  Image segmentation on a quantum computer , 2015, Quantum Information Processing.

[68]  Yajuan Sun,et al.  Quantum multidimensional color images similarity comparison , 2015, Quantum Inf. Process..

[69]  Ahmed A. Abd El-Latif,et al.  Dynamic watermarking scheme for quantum images based on Hadamard transform , 2014, Multimedia Systems.

[70]  Milonni,et al.  Quantum logistic map. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[71]  Qingxin Zhu,et al.  Multidimensional color image storage, retrieval, and compression based on quantum amplitudes and phases , 2014, Inf. Sci..

[72]  Nan Jiang,et al.  Quantum image scaling using nearest neighbor interpolation , 2015, Quantum Inf. Process..

[73]  Xiamu Niu,et al.  Multi-Channel Quantum Image Representation Based on Phase Transform and Elementary Transformations , 2014, J. Inf. Hiding Multim. Signal Process..

[74]  Frank Y. Shih,et al.  Image Processing and Pattern Recognition: Fundamentals and Techniques , 2010 .

[75]  Kaoru Hirota,et al.  Watermarking and authentication of quantum images based on restricted geometric transformations , 2012, Inf. Sci..

[76]  Jim H. Chandler,et al.  Photogrammetric Capabilities of the Kodak DC40, DCS420 and DCS460 Digital Cameras , 1999 .

[77]  V. Manta,et al.  Image processing using quantum computing , 2012, 2012 16th International Conference on System Theory, Control and Computing (ICSTCC).

[78]  Kai Lu,et al.  NEQR: a novel enhanced quantum representation of digital images , 2013, Quantum Information Processing.

[79]  Fei Yan,et al.  Bloch Sphere-Based Representation for Quantum Emotion Space , 2015, J. Adv. Comput. Intell. Intell. Informatics.

[80]  Fei Yan,et al.  An RGB Multi-Channel Representation for Images on Quantum Computers , 2013, J. Adv. Comput. Intell. Intell. Informatics.

[81]  Wenquan Zhang,et al.  Quantum Image Encryption Algorithm Based on Image Correlation Decomposition , 2014, International Journal of Theoretical Physics.

[82]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[83]  Nan Jiang,et al.  Quantum Hilbert Image Scrambling , 2014 .

[84]  Qiaoyan Wen,et al.  A Quantum Watermark Protocol , 2013 .

[85]  Fei Yan Quantum Computation based Image Data Searching, Image Watermarking, and Representation of Emotion Space , 2014 .

[86]  Nan Jiang,et al.  Quantum image translation , 2015, Quantum Inf. Process..

[87]  A. Shields Semiconductor quantum light sources , 2007, 0704.0403.

[88]  Sougato Bose,et al.  Storing, processing, and retrieving an image using quantum mechanics , 2003, SPIE Defense + Commercial Sensing.

[89]  R. Feynman Simulating physics with computers , 1999 .

[90]  Mohamed Batouche,et al.  A Quantum-Inspired Genetic Algorithm for Multi-source Affine Image Registration , 2004, ICIAR.

[91]  Huamin Yang,et al.  Moving target detection in multi-channel quantum video , 2015, 2015 IEEE 9th International Symposium on Intelligent Signal Processing (WISP) Proceedings.

[92]  A. Klappenecker,et al.  Discrete cosine transforms on quantum computers , 2001, ISPA 2001. Proceedings of the 2nd International Symposium on Image and Signal Processing and Analysis. In conjunction with 23rd International Conference on Information Technology Interfaces (IEEE Cat..

[93]  Hui Chen,et al.  A watermark strategy for quantum images based on quantum fourier transform , 2012, Quantum Information Processing.

[94]  Abdullah M. Iliyasu,et al.  A Multi-Channel Representation for images on quantum computers using the RGBα color space , 2011, 2011 IEEE 7th International Symposium on Intelligent Signal Processing.

[95]  Jack Ireland,et al.  Solar Image Analysis and Visualization , 2009 .

[96]  Deqing Sun,et al.  A Bayesian approach to adaptive video super resolution , 2011, CVPR 2011.

[97]  Abdullah M. Iliyasu,et al.  Fast Geometric Transformations on Quantum Images , 2010 .

[98]  Barenco,et al.  Quantum networks for elementary arithmetic operations. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[99]  K. Benatchba,et al.  Image segmentation using quantum genetic algorithms , 2006, IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics.

[100]  Qun Wan,et al.  A theoretical framework for quantum image representation and data loading scheme , 2013, Science China Information Sciences.

[101]  Yu-Guang Yang,et al.  Quantum cryptographic algorithm for color images using quantum Fourier transform and double random-phase encoding , 2014, Inf. Sci..

[102]  Shiyan Hu,et al.  Quantum Neural Network for Image Watermarking , 2004, ISNN.

[103]  Kai Xu,et al.  Local feature point extraction for quantum images , 2015, Quantum Inf. Process..

[104]  Salvador E. Venegas-Andraca,et al.  Region-based approach for the spectral clustering Nyström approximation with an application to burn depth assessment , 2015, Machine Vision and Applications.

[105]  Abdullah M. Iliyasu Towards Realising Secure and Efficient Image and Video Processing Applications on Quantum Computers , 2013, Entropy.

[106]  Zhengang Jiang,et al.  Quantum Computation-Based Image Representation, Processing Operations and Their Applications , 2014, Entropy.

[107]  Salvador Elías Venegas-Andraca,et al.  Introductory words: Special issue on quantum image processing published by Quantum Information Processing , 2015, Quantum Inf. Process..

[108]  Fei Yan,et al.  Multi-Channel Information Operations on Quantum Images , 2014, J. Adv. Comput. Intell. Intell. Informatics.

[109]  Kai Xu,et al.  A novel quantum representation for log-polar images , 2013, Quantum Information Processing.

[110]  Fei Yan,et al.  Hybrid Quantum-Classical Protocol for Storage and Retrieval of Discrete-Valued Information , 2014, Entropy.

[111]  Shen Wang,et al.  Least significant qubit (LSQb) information hiding algorithm for quantum image , 2015 .

[112]  Qingxin Zhu,et al.  Multi-dimensional color image storage and retrieval for a normal arbitrary quantum superposition state , 2014, Quantum Inf. Process..

[113]  C. Tseng,et al.  Quantum circuit design of 8/spl times/8 discrete cosine transform using its fast computation flow graph , 2005, 2005 IEEE International Symposium on Circuits and Systems.

[114]  Ahmed A. Abd El-Latif,et al.  Quantum image encryption based on restricted geometric and color transformations , 2014, Quantum Information Processing.

[115]  Guo Guang-Can,et al.  A hybrid quantum encoding algorithm of vector quantization for image compression , 2006 .

[116]  V. V.D. Shah Image Processing and its Military Applications , 1987 .

[117]  Kaoru Hirota,et al.  A two-tier scheme for greyscale quantum image watermarking and recovery , 2013 .

[118]  Marco Lanzagorta,et al.  Quantum Radar , 2011, Quantum Radar.

[119]  Ben-Qiong Hu,et al.  Quantum Pattern Recognition of Classical Signal , 2007 .

[120]  Michelle A. Borkin,et al.  What Makes a Visualization Memorable? , 2013, IEEE Transactions on Visualization and Computer Graphics.

[121]  Anders Eklund,et al.  Medical image processing on the GPU - Past, present and future , 2013, Medical Image Anal..

[122]  Sean Hallgren,et al.  An improved quantum Fourier transform algorithm and applications , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[123]  Bo Sun,et al.  Assessing the similarity of quantum images based on probability measurements , 2012, 2012 IEEE Congress on Evolutionary Computation.