{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T05:28:33Z","timestamp":1778822913060,"version":"3.51.4"},"reference-count":27,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,15]],"date-time":"2021-01-15T00:00:00Z","timestamp":1610668800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, a computer-aided training method for hyperparameter selection of limited data X-ray computed tomography (XCT) reconstruction was proposed. The proposed method employed the ant colony optimisation (ACO) approach to assist in hyperparameter selection for the adaptive-weighted projection-controlled steepest descent (AwPCSD) algorithm, which is a total-variation (TV) based regularisation algorithm. During the implementation, there was a colony of artificial ants that swarm through the AwPCSD algorithm. Each ant chose a set of hyperparameters required for its iterative CT reconstruction and the correlation coefficient (CC) score was given for reconstructed images compared to the reference image. A colony of ants in one generation left a pheromone through its chosen path representing a choice of hyperparameters. Higher score means stronger pheromones\/probabilities to attract more ants in the next generations. At the end of the implementation, the hyperparameter configuration with the highest score was chosen as an optimal set of hyperparameters. In the experimental results section, the reconstruction using hyperparameters from the proposed method was compared with results from three other cases: the conjugate gradient least square (CGLS), the AwPCSD algorithm using the set of arbitrary hyperparameters and the cross-validation method.The experiments showed that the results from the proposed method were superior to those of the CGLS algorithm and the AwPCSD algorithm using the set of arbitrary hyperparameters. Although the results of the ACO algorithm were slightly inferior to those of the cross-validation method as measured by the quantitative metrics, the ACO algorithm was over 10 times faster than cross\u2014Validation. The optimal set of hyperparameters from the proposed method was also robust against an increase of noise in the data and can be applicable to different imaging samples with similar context. The ACO approach in the proposed method was able to identify optimal values of hyperparameters for a dataset and, as a result, produced a good quality reconstructed image from limited number of projection data. The proposed method in this work successfully solves a problem of hyperparameters selection, which is a major challenge in an implementation of TV based reconstruction algorithms.<\/jats:p>","DOI":"10.3390\/s21020591","type":"journal-article","created":{"date-parts":[[2021,1,20]],"date-time":"2021-01-20T03:34:25Z","timestamp":1611113665000},"page":"591","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Ant Colony-Based Hyperparameter Optimisation in Total Variation Reconstruction in X-ray Computed Tomography"],"prefix":"10.3390","volume":"21","author":[{"given":"Manasavee","family":"Lohvithee","sequence":"first","affiliation":[{"name":"Department of Nuclear Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenjuan","family":"Sun","sequence":"additional","affiliation":[{"name":"National Physical Laboratory (NPL), Teddington, Middlesex TW11 0LW, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4544-1315","authenticated-orcid":false,"given":"Stephane","family":"Chretien","sequence":"additional","affiliation":[{"name":"National Physical Laboratory (NPL), Teddington, Middlesex TW11 0LW, UK"},{"name":"Laboratoire ERIC, Universit\u00e9 Lyon 2, 69500 Bron, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manuchehr","family":"Soleimani","sequence":"additional","affiliation":[{"name":"Engineering Tomography Laboratory (ETL), University of Bath, Bath BA2 7AY, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1109\/42.97595","article-title":"Nonstationary filtering of transmission tomograms in high photon counting noise","volume":"10","author":"Sauer","year":"1991","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_2","first-page":"119","article-title":"Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT","volume":"14","author":"Sidky","year":"2006","journal-title":"J. X-ray Sci. Technol."},{"key":"ref_3","first-page":"685618","article-title":"Prior image constrained compressed sensing (PICCS)","volume":"6856","author":"Chen","year":"2008","journal-title":"Proc. SPIE Int. Soc. Opt. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1568","DOI":"10.1109\/PROC.1977.10771","article-title":"The Shannon sampling theorem-Its various extensions and applications: A tutorial review","volume":"65","author":"Jerri","year":"1977","journal-title":"Proc. IEEE"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1007\/s00330-010-1990-5","article-title":"Chest computed tomography using iterative reconstruction vs. filtered back projection (Part 1): Evaluation of image noise reduction in 32 patients","volume":"21","author":"Pontana","year":"2011","journal-title":"Eur. Radiol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"636","DOI":"10.1007\/s00330-010-1991-4","article-title":"Chest computed tomography using iterative reconstruction vs. filtered back projection (Part 2): Image quality of low-dose CT examinations in 80 patients","volume":"21","author":"Pontana","year":"2011","journal-title":"Eur. Radiol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"9295","DOI":"10.1088\/1361-6560\/aa93d3","article-title":"Parameter selection in limited data cone-beam CT reconstruction using edge-preserving total variation algorithms","volume":"62","author":"Lohvithee","year":"2017","journal-title":"Phys. Med. Biol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4777","DOI":"10.1088\/0031-9155\/53\/17\/021","article-title":"Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization","volume":"53","author":"Sidky","year":"2008","journal-title":"Phys. Med. Biol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1757","DOI":"10.1118\/1.3371691","article-title":"GPU-based fast cone beam CT reconstruction from undersampled and noisy projection data via total variation","volume":"37","author":"Jia","year":"2010","journal-title":"Med. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3787","DOI":"10.1088\/0031-9155\/56\/13\/004","article-title":"GPU-based iterative cone-beam CT reconstruction using tight frame regularization","volume":"56","author":"Jia","year":"2011","journal-title":"Phys. Med. Biol."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Chr\u00e9tien, S., Lohvithee, M., Sun, W., and Soleimani, M. (2020). Efficient Hyper-Parameter Selection in Total Variation-Penalised XCT Reconstruction Using Freund and Shapire\u2019s Hedge Approach. Mathematics, 8.","DOI":"10.3390\/math8040493"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1430","DOI":"10.1109\/TMI.2018.2823679","article-title":"Intelligent parameter tuning in optimization-based iterative CT reconstruction via deep reinforcement learning","volume":"37","author":"Shen","year":"2018","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1162\/106454699568728","article-title":"Ant Algorithms for Discrete Optimization","volume":"5","author":"Dorigo","year":"1999","journal-title":"Artif. Life"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"7857","DOI":"10.1088\/0031-9155\/58\/21\/7857","article-title":"DQS advisor: A visual interface and knowledge-based system to balance dose, quality, and reconstruction speed in iterative CT reconstruction with application to NLM regularization","volume":"58","author":"Zheng","year":"2013","journal-title":"Phys. Med. Biol."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Bj\u00f6rck, \u00c5. (1996). Numerical Methods for Least Squares Problems, Society for Industrial and Applied Mathematics.","DOI":"10.1137\/1.9781611971484"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4902","DOI":"10.1118\/1.3480985","article-title":"4D XCAT phantom for multimodality imaging research","volume":"37","author":"Segars","year":"2010","journal-title":"Med. Phys."},{"key":"ref_17","unstructured":"(2018, August 12). 4D Extended Cardiac-Torso (XCAT) Phantom Version 2.0. Available online: Olv.duke.edu\/technologies\/4dextended-cardiac-torso-xcat-phantom-version-2-0\/."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"5949","DOI":"10.1088\/0031-9155\/56\/18\/011","article-title":"Low-dose CT reconstruction via edge preserving total variation regularization","volume":"56","author":"Tian","year":"2011","journal-title":"Phys. Med. Biol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"7923","DOI":"10.1088\/0031-9155\/57\/23\/7923","article-title":"Adaptive-weighted total variation minimization for sparse data toward low-dose x-ray computed tomography image reconstruction","volume":"57","author":"Liu","year":"2012","journal-title":"Phys. Med. Biol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"055010","DOI":"10.1088\/2057-1976\/2\/5\/055010","article-title":"TIGRE: A MATLAB-GPU toolbox for CBCT image reconstruction","volume":"2","author":"Biguri","year":"2016","journal-title":"Biomed. Phys. Eng. Express"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1177\/016173468400600107","article-title":"Simultaneous Algebraic Reconstruction Technique (SART): A superior implementation of the ART algorithm","volume":"6","author":"Anderson","year":"1984","journal-title":"Ultrason. Imaging"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1109\/34.56205","article-title":"Scale-Space and edge detection using anisotropic diffusion","volume":"12","author":"Perona","year":"1990","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_23","unstructured":"Dorigo, M., Maniezzo, V., and Colorni, A. (1991). The Ant System: An Autocatalytic Optimizing Process, Politecnico di Milano. Technical Report 91-016."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/3477.484436","article-title":"Ant system: Optimization by a colony of cooperating agents","volume":"26","author":"Dorigo","year":"1996","journal-title":"IEEE Trans. Syst. Man Cybern. Part B"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1228","DOI":"10.1109\/TIP.2009.2017139","article-title":"Electronic noise modeling in statistical iterative reconstruction","volume":"18","author":"Xu","year":"2009","journal-title":"IEEE Trans. Image Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"4051","DOI":"10.1118\/1.4722751","article-title":"Variance analysis of x-ray CT sinograms in the presence of electronic noise background","volume":"39","author":"Ma","year":"2012","journal-title":"Med. Phys."},{"key":"ref_27","first-page":"1137","article-title":"A study of cross-validation and bootstrap for accuracy estimation and model selection","volume":"14","author":"Kohavi","year":"1995","journal-title":"Int. Joint Conf. Artif. Intell. (IJCAI)"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/2\/591\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:11:39Z","timestamp":1760159499000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/2\/591"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,15]]},"references-count":27,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["s21020591"],"URL":"https:\/\/doi.org\/10.3390\/s21020591","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,15]]}}}