{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T01:00:44Z","timestamp":1785805244879,"version":"3.56.0"},"reference-count":39,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,10,27]],"date-time":"2022-10-27T00:00:00Z","timestamp":1666828800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Rector of the Silesian University of Technology, Gliwice, Poland","award":["09\/010\/RGJ22\/0066"],"award-info":[{"award-number":["09\/010\/RGJ22\/0066"]}]},{"name":"Rector of the Silesian University of Technology, Gliwice, Poland","award":["09\/010\/RGJ22\/0068"],"award-info":[{"award-number":["09\/010\/RGJ22\/0068"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper discusses and compares several computed tomography (CT) algorithms capable of dealing with incomplete data. This type of problem has been proposed for a symmetrical grid and symmetrically distributed transmitters and receivers. The use of symmetry significantly speeds up the process of constructing a system of equations that is the foundation of all CT algebraic algorithms. Classic algebraic approaches are effective in incomplete data scenarios, but suffer from low convergence speed. For this reason, we propose the use of nature-inspired algorithms which are proven to be effective in many practical optimization problems from various domains. The efficacy of nature-inspired algorithms strongly depends on the number of parameters they maintain and reproduce, and this number is usually substantial in the case of CT applications. However, taking into account the specificity of the reconstructed object allows to reduce the number of parameters and effectively use heuristic algorithms in the field of CT. This paper compares the efficacy and suitability of three nature-inspired heuristic algorithms: Artificial BeeColony (ABC), Ant Colony Optimization (ACO), and Clonal Selection Algorithm (CSA) in the CT context, showing their advantages and weaknesses. The best algorithm is identified and some ideas of how the remaining methods could be improved so as to better solve CT tasks are presented.<\/jats:p>","DOI":"10.3390\/sym14112256","type":"journal-article","created":{"date-parts":[[2022,10,27]],"date-time":"2022-10-27T04:35:17Z","timestamp":1666845317000},"page":"2256","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Application of Nature-Inspired Algorithms to Computed Tomography with Incomplete Data"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4971-5360","authenticated-orcid":false,"given":"Mariusz","family":"Pleszczy\u0144ski","sequence":"first","affiliation":[{"name":"Faculty of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3850-8577","authenticated-orcid":false,"given":"Adam","family":"Zielonka","sequence":"additional","affiliation":[{"name":"Faculty of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9073-5347","authenticated-orcid":false,"given":"Marcin","family":"Wo\u017aniak","sequence":"additional","affiliation":[{"name":"Faculty of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Natterer, F. (1986). The Mathematics of Computerized Tomography, Wiley.","DOI":"10.1007\/978-3-663-01409-6"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Malczewski, K. (2020). Image Resolution Enhancement of Highly Compressively Sensed CT\/PET Signals. Algorithms, 13.","DOI":"10.3390\/a13050129"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/S1063-5203(03)00030-7","article-title":"3D Fourier Based Discrete Radon Transform","volume":"15","author":"Averbuch","year":"2003","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1109\/PROC.1983.12597","article-title":"Reconstruction algorithms: Transform methods","volume":"71","author":"Lewitt","year":"1983","journal-title":"Proc. IEEE"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1109\/42.845179","article-title":"Analysis of direct Fourier method for computed tomography","volume":"19","year":"2000","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1177\/016173468400600107","article-title":"Algebraic Reconstruction in CT from limited views. Simultaneous algebraic reconstruction technique (SART): A superior implementation of the ART algorithm","volume":"6","author":"Andersen","year":"1984","journal-title":"Ultrason. Imaging"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1016\/0022-5193(70)90109-8","article-title":"Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography","volume":"29","author":"Gordon","year":"1970","journal-title":"J. Theor. Biol."},{"key":"ref_8","first-page":"1727","article-title":"Computed tomography using algebraic reconstruction techniques with different projection access schemes: A comparison study under practical situation","volume":"41","author":"Guan","year":"1996","journal-title":"J. Theor. Biol."},{"key":"ref_9","unstructured":"Hetmaniok, E., Ludew, J., and Pleszczy\u0144ski, M. (2017). Examination of stability of the computer tomography algorithms in case of the incomplete information for the objects with non-transparent elements. Selected Problems on Experimental Mathematics, Silesian University of Technology Press."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Wo\u017aniak, M., Si\u0142ka, J., and Wieczorek, M. (2021). Deep neural network correlation learning mechanism for CT brain tumor detection. Neural. Comput. Appl., 1\u201316.","DOI":"10.1007\/s00521-021-05841-x"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Sage, A., and Badura, P. (2020). Intracranial Hemorrhage Detection in Head CT Using Double-Branch Convolutional Neural Network, Support Vector Machine, and Random Forest. Appl. Sci., 10.","DOI":"10.3390\/app10217577"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Khan, M.A., Alhaisoni, M., Tariq, U., Hussain, N., Majid, A., Dama\u0161evi\u010dius, R., and Maskeli\u016bnas, R. (2021). COVID-19 Case Recognition from Chest CT Images by Deep Learning, Entropy-Controlled Firefly Optimization, and Parallel Feature Fusion. Sensors, 21.","DOI":"10.3390\/s21217286"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"e339","DOI":"10.7717\/peerj-cs.339","article-title":"Implementation of the computer tomography parallel algorithms with the incomplete set of data","volume":"7","year":"2021","journal-title":"PeerJ Comput. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Pleszczy\u0144ski, M., Zielonka, A., Po\u0142ap, D., Wo\u017aniak, M., and Ma\u0144dziuk, J. (July, January 28). Polar Bear Optimization for Industrial Computed Tomography with Incomplete Data. Proceedings of the 2021 IEEE Congress on Evolutionary Computation (CEC), Krak\u00f3w, Poland.","DOI":"10.1109\/CEC45853.2021.9504750"},{"key":"ref_15","first-page":"244","article-title":"Computed Tomography Image Enhancement Using Cuckoo Search: A Log Transform Based Approach","volume":"6","author":"Ashour","year":"2017","journal-title":"J. Signal Inf. Process."},{"key":"ref_16","first-page":"185","article-title":"Meta-Heuristic Algorithms in Medical Image Segmentation: A Review","volume":"6","author":"Dey","year":"2018","journal-title":"IGI Glob. Adv. Appl. Metaheuristic"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Lohvithee, M., Sun, W., Chretien, S., and Soleimani, M. (2021). Ant Colony-Based Hyperparameter Optimisation in Total Variation Reconstruction in X-ray Computed Tomography. Sensors, 21.","DOI":"10.3390\/s21020591"},{"key":"ref_18","unstructured":"Chen, Y.-C., Wang, H.-C., and Su, T.-J. (September, January 30). Particle Swarm Optimization for Image Noise Cancellation. Proceedings of the First International Conference on Innovative Computing, Information and Control\u2014Volume I (ICICIC\u201906), Beijing, China."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"W\u00fcrfl, T., Ghesu, F.C., Christlein, V., and Maier, A. (2016, January 17\u201321). Deep Learning Computed Tomography. Proceedings of the Medical Image Computing and Computer-Assisted Intervention\u2014MICCAI 2016, Athens, Greece.","DOI":"10.1007\/978-3-319-46726-9_50"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Shahamatnia, E., and Ebadzadeh, M.M. (2011, January 11\u201315). Application of particle swarm optimization and snake model hybrid on medical imaging. Proceedings of the 2011 IEEE Third International Workshop On Computational Intelligence in Medical Imaging, Paris, France.","DOI":"10.1109\/CIMI.2011.5952043"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Ang, L.M., Seng, K.P., and Ge, F.L. (2017). Natural Inspired Intelligent Visual Computing and Its Application to Viticulture. Sensors, 17.","DOI":"10.3390\/s17061186"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1736","DOI":"10.1109\/TMAG.2005.846043","article-title":"A clonal selection algorithm for optimization in electromagnetics","volume":"41","author":"Campelo","year":"2005","journal-title":"IEEE Trans. Magn."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Donati, A.V., Krause, J., Thiel, C., White, B., and Hill, N. (2020). An Ant Colony Algorithm for Improving Energy Efficiency of Road Vehicles. Energies, 13.","DOI":"10.3390\/en13112850"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Guo, X., Yuan, X., Hou, G., Zhang, Z., and Liu, G. (2022). Natural Aging Life Prediction of Rubber Products Using Artificial Bee Colony Algorithm to Identify Acceleration Factor. Polymers, 14.","DOI":"10.3390\/polym14173439"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Kubicek, J., Varysova, A., Cerny, M., Hancarova, K., Oczka, D., Augustynek, M., Penhaker, M., Prokop, O., and Scurek, R. (2022). Performance and Robustness of Regional Image Segmentation Driven by Selected Evolutionary and Genetic Algorithms: Study on MR Articular Cartilage Images. Sensors, 22.","DOI":"10.3390\/s22176335"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Muniyan, R., Ramalingam, R., Alshamrani, S.S., Gangodkar, D., Dumka, A., Singh, R., Gehlot, A., and Rashid, M. (2022). Artificial Bee Colony Algorithm with Nelder\u2013Mead Method to Solve Nurse Scheduling Problem. Mathematics, 10.","DOI":"10.3390\/math10152576"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Mohsin, S.A., Younes, A., and Darwish, S.M. (2021). Dynamic Cost Ant Colony Algorithm to Optimize Query for Distributed Database Based on Quantum-Inspired Approach. Symmetry, 13.","DOI":"10.3390\/sym13010070"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Paprocka, I., Krenczyk, D., and Burduk, A. (2021). The Method of Production Scheduling with Uncertainties Using the Ants Colony Optimisation. Appl. Sci., 11.","DOI":"10.3390\/app11010171"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Rokicki, \u0141. (2021). Optimization of the Configuration and Operating States of Hybrid AC\/DC Low Voltage Microgrid Using a Clonal Selection Algorithm with a Modified Hypermutation Operator. Energies, 14.","DOI":"10.3390\/en14196351"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Tao, W., Ma, Y., Xiao, S., Cheng, Q., Wang, Y., and Chen, Z. (2022). An Active Indoor Noise Control System Based on CS Algorithm. Appl. Sci., 12.","DOI":"10.3390\/app12189253"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Xu, B., Ma, W., Ke, H., Yang, W., and Zhang, H. (2022). An Efficient Ant Colony Algorithm Based on Rank 2 Matrix Approximation Method for Aircraft Arrival\/Departure Scheduling Problem. Processes, 10.","DOI":"10.3390\/pr10091825"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1759","DOI":"10.1016\/j.patrec.2009.11.018","article-title":"Artificial bee colony (ABC) optimized edge potential function (EPF) approach to target recognition for low-altitude aircraft","volume":"31","author":"Xu","year":"2010","journal-title":"Pattern Recognit. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Zamri, N.E., Mansor, M.A., Mohd Kasihmuddin, M.S., Alway, A., Mohd Jamaludin, S.Z., and Alzaeemi, S.A. (2020). Amazon Employees Resources Access Data Extraction via Clonal Selection Algorithm and Logic Mining Approach. Entropy, 22.","DOI":"10.3390\/e22060596"},{"key":"ref_34","first-page":"1","article-title":"Die t\u00e4nze der bienen","volume":"1","year":"1948","journal-title":"\u00d6sterr. Zool. Z."},{"key":"ref_35","unstructured":"(2022, September 24). Available online: https:\/\/www.youtube.com\/watch?v=1MX2WN-7Xzc."},{"key":"ref_36","unstructured":"Karaboga, D. (2005). An Idea Based on Honey Bee Swarm for Numerical Optimization, Computer Engineering Department, Engineering Faculty, Erciyes University. Technical Report\u2014TR06."},{"key":"ref_37","first-page":"308","article-title":"Ant colony optimization for finding the global minimum","volume":"176","author":"Toksari","year":"2006","journal-title":"Appl. Math. Comput."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1155","DOI":"10.1016\/j.ejor.2006.06.046","article-title":"Ant colony optimization for continuous domains","volume":"185","author":"Socha","year":"2008","journal-title":"Eur. J. Oper. Res."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1109\/TEVC.2002.1011539","article-title":"Learning and optimization using the clonal selection principle","volume":"6","year":"2002","journal-title":"IEEE Trans. Evol. Comput."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/11\/2256\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:03:47Z","timestamp":1760144627000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/11\/2256"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,27]]},"references-count":39,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["sym14112256"],"URL":"https:\/\/doi.org\/10.3390\/sym14112256","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,27]]}}}