{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T16:31:49Z","timestamp":1775838709366,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2021,8,17]],"date-time":"2021-08-17T00:00:00Z","timestamp":1629158400000},"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>It is difficult to improve image resolution in hardware due to the limitations of technology and too high costs, but most application fields need high resolution images, so super-resolution technology has been produced. This paper mainly uses information redundancy to realize multi-frame super-resolution. In recent years, many researchers have proposed a variety of multi-frame super-resolution methods, but it is very difficult to preserve the image edge and texture details and remove the influence of noise effectively in practical applications. In this paper, a minimum variance method is proposed to select the low resolution images with appropriate quality quickly for super-resolution. The half-quadratic function is used as the loss function to minimize the observation error between the estimated high resolution image and low-resolution images. The function parameter is determined adaptively according to observation errors of each low-resolution image. The combination of a local structure tensor and Bilateral Total Variation (BTV) as image prior knowledge preserves the details of the image and suppresses the noise simultaneously. The experimental results on synthetic data and real data show that our proposed method can better preserve the details of the image than the existing methods.<\/jats:p>","DOI":"10.3390\/s21165533","type":"journal-article","created":{"date-parts":[[2021,8,17]],"date-time":"2021-08-17T21:17:06Z","timestamp":1629235026000},"page":"5533","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Robust Multi-Frame Super-Resolution Based on Adaptive Half-Quadratic Function and Local Structure Tensor Weighted BTV"],"prefix":"10.3390","volume":"21","author":[{"given":"Shanshan","family":"Liu","sequence":"first","affiliation":[{"name":"College of Computer Science, Sichuan University, Chengdu 610065, China"},{"name":"Enrollment and Employment Department, Sichuan Normal University, Chengdu 610066, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Minghui","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Computer Science, Sichuan University, Chengdu 610065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingbin","family":"Huang","sequence":"additional","affiliation":[{"name":"Science and Technology Branch, Southwest Jiaotong University Press, Chengdu 610031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xia","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Computer Science, Sichuan University, Chengdu 610065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2082","DOI":"10.1016\/j.sigpro.2012.01.020","article-title":"A super-resolution reconstruction algorithm for hyperspectral images","volume":"92","author":"Zhang","year":"2012","journal-title":"Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"K\u00f6hler, T., Brost, A., Mogalle, K., Zhang, Q., K\u00f6hler, C., Michelson, G., Hornegger, J., and Tornow, R.P. (2014, January 14\u201318). Multi-frame super-resolution with quality self-assessment for retinal fundus videos. Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention, Boston, MA, USA.","DOI":"10.1007\/978-3-319-10404-1_81"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"848","DOI":"10.1016\/j.sigpro.2009.09.002","article-title":"A super-resolution reconstruction algorithm for surveillance images","volume":"90","author":"Zhang","year":"2010","journal-title":"Signal Process."},{"key":"ref_4","first-page":"317","article-title":"Multi-frame image restoration and registration","volume":"1","author":"Tsaiand","year":"1984","journal-title":"Adv. Comput. Vis. Image Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1109\/TIP.2006.888330","article-title":"Kernel regression for image processing and reconstruction","volume":"16","author":"Takeda","year":"2007","journal-title":"IEEE Trans. Image Process."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Baatz, M., Eichenseer, A., and Kaup, A. (2016, January 25\u201328). Multi-image super resolution using a dual weighting scheme based on voronoi tessellation. Proceedings of the 2016 IEEE International Conference on Image Processing (ICIP), Phoenix, AZ, USA.","DOI":"10.1109\/ICIP.2016.7532874"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1327","DOI":"10.1109\/TIP.2004.834669","article-title":"Fast and robust multiframe super resolution","volume":"13","author":"Farsiu","year":"2004","journal-title":"IEEE Trans. Image Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.dsp.2012.06.013","article-title":"A robust multiframe super-resolution algorithm based on half-quadratic estimation with modified BTV regularization","volume":"23","author":"Zeng","year":"2013","journal-title":"Digit. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1109\/TCI.2016.2516909","article-title":"Robust Multiframe Super-Resolution Employing Iteratively Re-Weighted Minimization","volume":"2","author":"Huang","year":"2016","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4971","DOI":"10.1109\/TIP.2018.2848113","article-title":"Robust Multi-Frame Super-Resolution Based on Spatially Weighted Half-Quadratic Estimation and Adaptive BTV Regularization","volume":"27","author":"Liu","year":"2018","journal-title":"IEEE Trans. Image Process."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wang, P., Hu, X., Xuan, B., and Mu, J. (2011, January 18\u201321). Super resolution reconstruction via multiple frames joint learning. Proceedings of the 2011 International Conference on Multimedia and Signal Processing (ICMSP), Seville, Spain.","DOI":"10.1109\/CMSP.2011.79"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.neunet.2015.02.009","article-title":"Multi-frame image super resolution based on sparse coding","volume":"66","author":"Kato","year":"2015","journal-title":"Neural Netw."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Liao, R., Tao, X., Li, R., Ma, Z., and Jia, J. (2015, January 11\u201314). Video super-resolution via deep draft-ensemble learning. Proceedings of the IEEE International Conference on Computer Vision, Berlin, Germany.","DOI":"10.1109\/ICCV.2015.68"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Noor, D.F., Li, L., Li, Z., and Bhattacharyya, S. (2019, January 22\u201325). Multi-frame super resolution with deep residual learning on flow registered non-integer pixel images. Proceedings of the 2019 IEEE International Conference on Image Processing (ICIP), Taipei, Taiwan.","DOI":"10.1109\/ICIP.2019.8803156"},{"key":"ref_15","first-page":"235","article-title":"Bidirectional recurrent convolutional networks for multi-frame super-resolution","volume":"28","author":"Huang","year":"2015","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.1109\/TPAMI.2017.2701380","article-title":"Video super-resolution via bidirectional recurrent convolutional networks","volume":"40","author":"Huang","year":"2018","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Patanavijit, V., and Jitapunkul, S. (2006, January 12\u201315). A robust iterative multiframe super resolution reconstruction using a Huber Bayesian approach with Huber Tikhonov regularization. Proceedings of the IEEE International Symposium on Intelligent Signal Processing and Communications, Yonago, Japan.","DOI":"10.1109\/ISPACS.2006.364825"},{"key":"ref_18","first-page":"1","article-title":"A Lorentzian stochastic estimation for a robust iterative multiframe super-resolution reconstruction with Lorentzian\u2013Tikhonov regularization","volume":"2","author":"Patanavijit","year":"2007","journal-title":"J. Adv. Signal Process."},{"key":"ref_19","first-page":"1","article-title":"Regularized super-resolution image reconstruction employing robust error norms","volume":"48","author":"Anastassopoulos","year":"2009","journal-title":"Opt. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.sigpro.2014.04.031","article-title":"A locally adaptive L1-L2 norm for multi-frame super-resolution of images with mixed noise and outliers","volume":"105","author":"Yue","year":"2014","journal-title":"Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1646","DOI":"10.1109\/83.650118","article-title":"Restoration of a single super resolution image from several blurred, noisy, and undersampled measured images","volume":"6","author":"Elad","year":"1997","journal-title":"IEEE Trans. Image Process."},{"key":"ref_22","first-page":"20","article-title":"Overcoming registration uncertainty in image super-resolution: Maximize or marginalize","volume":"92","author":"Pickup","year":"2007","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_23","unstructured":"Traonmilin, Y., Ladjal, S., and Almansa, A. (2012, January 27\u201331). On the amount of regularization for superresolution interpolation. Proceedings of the 2012 20th European Signal Processing Conference (EUSIPCO), Bucharest, Romania."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3218","DOI":"10.1109\/TIP.2015.2439035","article-title":"No-reference image sharpness assessment in autoregressive parameter space","volume":"24","author":"Gu","year":"2015","journal-title":"IEEE Trans. Image Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3903","DOI":"10.1109\/TIE.2017.2652339","article-title":"A fast reliable image quality predictor by fusing micro-and macro-structures","volume":"64","author":"Gu","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.dsp.2017.09.011","article-title":"Preserving quality in minimum frame selection within multi-frame super-resolution","volume":"72","author":"Rahimi","year":"2018","journal-title":"Digit. Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1109\/83.551699","article-title":"Barlaud Deterministic edge-preserving regularization in computed imaging","volume":"6","author":"Charbonnier","year":"1997","journal-title":"IEEE Trans. Image Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1088\/0266-5611\/4\/4\/010","article-title":"Robust methods in inverse theory","volume":"4","author":"Scales","year":"1988","journal-title":"Inverse Probl."},{"key":"ref_29","unstructured":"Nabney, I.T. (2002). NETLAB: Algorithms for Pattern Recognition, Springer. [1st ed.]."},{"key":"ref_30","unstructured":"Zeyde, R., Elad, M., and Protter, M. (2010). On single image scale-up using sparse-representations. Proceedings of the International Conference on Curves and Surfaces, Springer."},{"key":"ref_31","unstructured":"Farsiu, S. (2021, March 04). MDSP Super-Resolution and Demosaicing Datasets. Available online: https:\/\/users.soe.ucsc.edu\/~milanfar\/software\/sr-datasets.html."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/16\/5533\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:45:56Z","timestamp":1760165156000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/16\/5533"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,17]]},"references-count":31,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2021,8]]}},"alternative-id":["s21165533"],"URL":"https:\/\/doi.org\/10.3390\/s21165533","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,17]]}}}