{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T17:51:17Z","timestamp":1772041877228,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2016,10,9]],"date-time":"2016-10-09T00:00:00Z","timestamp":1475971200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Prince Sattam Bin Abdul Aziz University, Saudi Arabia via the Deanship for Scientific Research Project Number","award":["2015\/01\/3983"],"award-info":[{"award-number":["2015\/01\/3983"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>An enhanced quantum-based image fidelity metric, the QIFM metric, is proposed as a tool to assess the \u201ccongruity\u201d between two or more quantum images. The often confounding contrariety that distinguishes between classical and quantum information processing makes the widely accepted peak-signal-to-noise-ratio (PSNR) ill-suited for use in the quantum computing framework, whereas the prohibitive cost of the probability-based similarity score makes it imprudent for use as an effective image quality metric. Unlike the aforementioned image quality measures, the proposed QIFM metric is calibrated as a pixel difference-based image quality measure that is sensitive to the intricacies inherent to quantum image processing (QIP). As proposed, the QIFM is configured with in-built non-destructive measurement units that preserve the coherence necessary for quantum computation. This design moderates the cost of executing the QIFM in order to estimate congruity between two or more quantum images. A statistical analysis also shows that our proposed QIFM metric has a better correlation with digital expectation of likeness between images than other available quantum image quality measures. Therefore, the QIFM offers a competent substitute for the PSNR as an image quality measure in the quantum computing framework thereby providing a tool to effectively assess fidelity between images in quantum watermarking, quantum movie aggregation and other applications in QIP.<\/jats:p>","DOI":"10.3390\/e18100360","type":"journal-article","created":{"date-parts":[[2016,10,10]],"date-time":"2016-10-10T10:35:19Z","timestamp":1476095719000},"page":"360","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Metric for Estimating Congruity between Quantum Images"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4964-6609","authenticated-orcid":false,"given":"Abdullah","family":"Iliyasu","sequence":"first","affiliation":[{"name":"Electrical Engineering Department, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fei","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Changchun University of Science and Technology, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kaoru","family":"Hirota","sequence":"additional","affiliation":[{"name":"School of Automation, Beijing Institute of Technology, Haidian District, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,10,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Iliyasu, A.M., Yan, F., and Abuhasel, K.A. (2015, January 28\u201330). A quantum-based image fidelity metric. Proceedings of the Science and Information Conference, London, UK.","DOI":"10.1109\/SAI.2015.7237213"},{"key":"ref_2","unstructured":"Nielsen, M.A., and Chuang, I.L. (2000). Quantum Computation and Quantum Information, Cambridge University Press. [5th ed.]."},{"key":"ref_3","unstructured":"Vlasov, A.Y. (1997). Quantum Computations and Images Recognition."},{"key":"ref_4","unstructured":"Rastegari, M. Quantum Approach to Image Processing. Available online: http:\/\/www.umiacs.umd.edu\/~mrastega\/paper\/final3.pdf."},{"key":"ref_5","first-page":"062311","article-title":"Pattern recognition on a quantum computer","volume":"67","year":"2002","journal-title":"Phys. Rev. A"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1109\/MSP.2002.1043298","article-title":"Quantum signal processing","volume":"19","author":"Eldar","year":"2002","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"S176","DOI":"10.1088\/1464-4266\/4\/3\/372","article-title":"Quantum Imaging","volume":"4","author":"Lugiato","year":"2002","journal-title":"J. Opt. B"},{"key":"ref_8","unstructured":"Beach, G., Lomont, C., and Cohen, C. (2003, January 15\u201317). Quantum image processing. Proceedings of the 32nd IEEE Conference on Applied Imagery and Pattern Recognition, Bellingham, WA, USA."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Venegas-Andraca, S.E., and Bose, S. (2003, January 2\u20134). Storing processing and retrieving an image using quantum mechanics. Proceedings of the SPIE Conference Quantum Information and Computation, Bellingham, WA, USA.","DOI":"10.1117\/12.485960"},{"key":"ref_10","unstructured":"Latorre, J.I. Image Compression and Entanglement. Available online: http:\/\/arxiv.org\/abs\/quantph\/0510031."},{"key":"ref_11","first-page":"63","article-title":"A flexible representation of quantum images for polynomial preparation, image compression and processing operations","volume":"11","author":"Le","year":"2012","journal-title":"Quantum Inf. Process."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ruano, A.E., and Varkonyi-Koczy, A.R. (2011). New Advances in Intelligent Signal Processing, Springer.","DOI":"10.1007\/978-3-642-11739-8"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.ins.2011.09.028","article-title":"Watermarking and Authentication of Quantum Images based on Restricted Geometric Transformations","volume":"186","author":"Iliyasu","year":"2012","journal-title":"Inf. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1459","DOI":"10.1142\/S0219749911008015","article-title":"A framework for representing and producing movies on quantum computers","volume":"9","author":"Iliyasu","year":"2011","journal-title":"Int. J. Quantum Inf."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"55","DOI":"10.4236\/jqis.2012.23010","article-title":"Quantum Image Searching Based on Probability Distributions","volume":"2","author":"Yan","year":"2012","journal-title":"J. Quantum Inf. Sci."},{"key":"ref_16","first-page":"125","article-title":"Insights into the Viability of Using Available Photonic Quantum Technologies for Efficient Image and Video Processing Applications","volume":"9","author":"Iliyasu","year":"2013","journal-title":"Int. J. Unconv. Comput."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2874","DOI":"10.3390\/e15082874","article-title":"Towards the Realisation of Secure and Efficient Image and Video Processing Applications on Quantum Computers","volume":"15","author":"Iliyasu","year":"2013","journal-title":"Entropy"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11128-015-1195-6","article-title":"A survey of quantum image representations","volume":"15","author":"Yan","year":"2016","journal-title":"Quantum Inf. Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5290","DOI":"10.3390\/e16105290","article-title":"Quantum Computation-Based Image Representation, Processing Operations and Their Applications","volume":"16","author":"Yan","year":"2014","journal-title":"Entropy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1504\/IJICA.2013.053179","article-title":"A two-tier scheme for Greyscale Quantum Image Watermarking and Recovery","volume":"5","author":"Iliyasu","year":"2013","journal-title":"Int. J. Innov. Comput. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1675","DOI":"10.1007\/s11128-014-0912-x","article-title":"A duple watermarking strategy for multi-channel quantum images","volume":"14","author":"Yan","year":"2015","journal-title":"Quantum Inf. Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2893","DOI":"10.1007\/s10773-015-2524-3","article-title":"Video encryption and decryption on quantum computers","volume":"54","author":"Yan","year":"2015","journal-title":"Int. J. Theor. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1504\/IJICA.2013.062955","article-title":"A Parallel Comparison of Multiple Pairs of Images on Quantum Computers","volume":"5","author":"Yan","year":"2013","journal-title":"Int. J. Innov. Comput. Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"020301","DOI":"10.1103\/PhysRevA.82.020301","article-title":"Ancilla-driven universal quantum computation","volume":"82","author":"Anders","year":"2010","journal-title":"Phys. Rev. A"},{"key":"ref_25","unstructured":"Navas, K.A., and Sasikumar, M. (2011, January 22\u201324). Image Fidelity Metrics: Future Directions. Proceedings of the IEEE International Conference on Recent Advances in Intelligent Computational Systems (RAICS), Trivandrum, India."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"800","DOI":"10.1049\/el:20080522","article-title":"Scope of validity of PSNR in image\/video quality assessment","volume":"44","author":"Huynh","year":"2008","journal-title":"Electron. Lett."},{"key":"ref_27","unstructured":"Iliyasu, A.M., Le, P.Q., Dong, F., and Hirota, K. (2010, January 18\u201319). Restricted geometric transformations and their applications for quantum image watermarking and authentication. Proceedings of the 10th Asian Conference on Quantum Information Science, Tokyo, Japan."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1177\/1094428104264024","article-title":"Testing dependent correlation coefficient via structural equation modeling","volume":"7","author":"Cheung","year":"2004","journal-title":"Organ. Res. Methods"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3537","DOI":"10.3390\/e16063537","article-title":"Hybrid Quantum-Classical Protocol for Storage and Retrieval of Discrete-Valued Information","volume":"16","author":"Iliyasu","year":"2014","journal-title":"Entropy"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/j.neulet.2009.06.052","article-title":"SVM-based computer-aided diagnosis of the Alzheimer\u2019s disease using t-test NMSE feature selection with feature correlation weighting","volume":"461","author":"Chaves","year":"2009","journal-title":"Neurosci. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/10\/360\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:32:33Z","timestamp":1760211153000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/10\/360"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,9]]},"references-count":30,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2016,10]]}},"alternative-id":["e18100360"],"URL":"https:\/\/doi.org\/10.3390\/e18100360","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,10,9]]}}}