{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T23:56:34Z","timestamp":1762300594890,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,8]],"date-time":"2024-01-08T00:00:00Z","timestamp":1704672000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42130805","42074151","42074154","42004106"],"award-info":[{"award-number":["42130805","42074151","42074154","42004106"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>A full-waveform inversion (FWI) of ground-penetrating radar (GPR) data can be used to effectively obtain the parameters of a shallow subsurface. Introducing the Markov chain Monte Carlo (MCMC) algorithm into the FWI can reduce the dependence on the initial model and obtain the global optimal solution, but it requires a large number of computations. In order to better detect underground targets based on ground-penetrating radar data, this paper proposes a joint scheme of an improved ResNet and an MCMC full-waveform inversion. This scheme combines the Bayesian MCMC algorithm and an improved ResNet to accurately invert the target dielectric permittivity. The introduction of deep learning networks into the forward calculation part of the MCMC inversion algorithm replaced the complex forward simulation process, greatly improving the inversion speed. It is worth noting that the neural network model was an approximation of complex forward modeling, and, therefore, it contained modeling errors. The MCMC method could quantify and explain modeling errors during the inversion process, reducing the impact of modeling errors on the inversion results. Finally, a simulation dataset was constructed for training and testing, and the errors were statistically analyzed. The results showed that this method can accurately reconstruct underground medium targets, and it has strong robustness and efficiency.<\/jats:p>","DOI":"10.3390\/rs16020243","type":"journal-article","created":{"date-parts":[[2024,1,8]],"date-time":"2024-01-08T07:59:20Z","timestamp":1704700760000},"page":"243","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Monte Carlo Full-Waveform Inversion of Cross-Hole Ground-Penetrating Radar Data Based on Improved Residual Network"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2680-5603","authenticated-orcid":false,"given":"Shengchao","family":"Wang","sequence":"first","affiliation":[{"name":"College of Computer Science, Chengdu University, Chengdu 610000, China"}]},{"given":"Xiangbo","family":"Gong","sequence":"additional","affiliation":[{"name":"College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China"}]},{"given":"Liguo","family":"Han","sequence":"additional","affiliation":[{"name":"College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Daniels, D. (2004). Ground Penetrating Radar, IEE. [2nd ed.].","DOI":"10.1049\/PBRA015E"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1016\/j.conbuildmat.2005.06.007","article-title":"Modelling ground penetrating radar by GprMax","volume":"19","author":"Giannopoulos","year":"2005","journal-title":"Construct. Building Mater."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.jappgeo.2011.12.001","article-title":"Taming the non-linearity problem in GPR full-waveform inversion for high contrast media","volume":"78","author":"Meles","year":"2012","journal-title":"J. Appl. Geophys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jappgeo.2014.05.008","article-title":"Application of pre-stack reverse time migration based on FWI velocity estimation to ground penetrating radar data","volume":"107","author":"Liu","year":"2014","journal-title":"J. Appl. Geophys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1093\/gji\/ggt528","article-title":"Twodimensional permittivity and conductivity imaging by full waveform inversion of multioffset GPR data: A frequency-domain quasi-Newton approach","volume":"197","author":"Brossier","year":"2014","journal-title":"Geophys. J. Int."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1387","DOI":"10.1190\/1.1442188","article-title":"Two-dimensional nonlinear inversion of seismic wave-forms\u2014Numerical results","volume":"51","author":"Gauthier","year":"1986","journal-title":"Geophysics"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1190\/1.1441754","article-title":"Inversion of seismic reflection data in the acoustic approximation","volume":"49","author":"Tarantola","year":"1984","journal-title":"Geophysics"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1111\/j.1365-2478.1990.tb01846.x","article-title":"Inverse theory applied to multi-source cross-hole tomography. Part 1: Acoustic wave-equation method1","volume":"38","author":"Pratt","year":"1990","journal-title":"Geophys. Prospect."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1046\/j.1365-246X.1998.00498.x","article-title":"Hicks, Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion","volume":"133","author":"Pratt","year":"1998","journal-title":"Geophys. J. Int."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2807","DOI":"10.1109\/TGRS.2007.901048","article-title":"Full-waveform inversion of crosshole radar data based on 2-D finite-difference time domain solutions of Maxwell\u2019s equations","volume":"45","author":"Ernst","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"H79","DOI":"10.1190\/geo2012-0045.1","article-title":"Quantitative conductivity and permittivity estimation using full-waveform inversion of on-ground GPR data","volume":"77","author":"Busch","year":"2012","journal-title":"Geophysics"},{"key":"ref_12","unstructured":"Watson, F.M. (2016). Better Imaging for Landmine Detection: An Exploration of 3D Full-Wave Inversion for Ground-Penetrating Radar. [Ph.D. Dissertation, Department of Mathematics, The University of Manchester]."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"H27","DOI":"10.1190\/geo2017-0617.1","article-title":"Improving estimates of buried pipe diameter and infilling material from ground-penetrating radar profiles with full-waveform inversion","volume":"83","author":"Jazayeri","year":"2018","journal-title":"Geophysics"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Nilot, E., Feng, X., Zhang, Y., Zhang, M., Dong, Z., Zhou, H., and Zhang, X. (2018, January 18\u201321). Multiparameter full-waveform inversion of on-ground GPR using memoryless quasi-Newton (MLQN) method. Proceedings of the 2018 17th International Conference on Ground Penetrating Radar (GPR), Rapperswil, Switzerland.","DOI":"10.1109\/ICGPR.2018.8441534"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.jappgeo.2018.02.025","article-title":"Inverts permittivity and conductivity with structural constraint in GPR FWI based on truncated Newton method","volume":"151","author":"Ren","year":"2018","journal-title":"J. Appl. Geophys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"WCC1","DOI":"10.1190\/1.3238367","article-title":"An overview of full-waveform inversion in exploration geophysics","volume":"74","author":"Virieux","year":"2009","journal-title":"Geophysics"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1029\/94JB03097","article-title":"Monte Carlo sampling of solutions to inverse problems","volume":"100","author":"Mosegaard","year":"1995","journal-title":"J. Geophys. Res."},{"key":"ref_18","unstructured":"Ortiz, J.M., and Emery, X. (2008). Using Geostatisticsto Describe Complex a Priori Information for Inverse Problems, GEOSTATS 2008."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1007\/s10596-011-9271-1","article-title":"Inverse problems with non-trivial priors: Efficient solution through sequential Gibbs sampling","volume":"16","author":"Hansen","year":"2012","journal-title":"Comput. Geosci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"H19","DOI":"10.1190\/geo2011-0170.1","article-title":"Monte Carlo full-waveform inversion of crosshole GPR data using multi-ple-point geostatistical a priori information","volume":"77","author":"Cordua","year":"2012","journal-title":"Geophysics"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2135","DOI":"10.1109\/TGRS.2019.2953473","article-title":"Deep-learning inversion of seismic data","volume":"58","author":"Li","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2225","DOI":"10.1109\/LAWP.2019.2916369","article-title":"DNNs as applied to electromagnetics, antennas, and propagation\u2014A review","volume":"18","author":"Massa","year":"2019","journal-title":"IEEE Antennas Wireless Propag. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/0893-6080(91)90009-T","article-title":"Approximation capabilities of multilayer feedforward networks","volume":"4","author":"Hornik","year":"1991","journal-title":"Neural Netw."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"8172","DOI":"10.1109\/JSEN.2021.3050618","article-title":"Deep neural network-based permittivity inversions for ground penetrating radar data","volume":"21","author":"Ji","year":"2021","journal-title":"IEEE Sensors J."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"8305","DOI":"10.1109\/TGRS.2020.3046454","article-title":"GPRInvNet: Deep learning-based ground-penetrating radar data inversion for tunnel linings","volume":"59","author":"Liu","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., and Sun, J. (2016, January 27\u201330). Deep Residual Learning for Image Recognition. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/j.isprsjprs.2018.02.014","article-title":"Multi-class geospatial object detection based on a position-sensitive balancing framework for high spatial resolution remote sensing imagery","volume":"138","author":"Zhong","year":"2018","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Xu, Z., Xu, X., Wang, L., Yang, R., and Pu, F. (2017). Deformable convnet with aspect ratio constrained NMS for object detection in remote sensing imagery. Remote Sens., 9.","DOI":"10.3390\/rs9121312"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Mahdianpari, M., Salehi, B., Rezaee, M., Mohammadimanesh, F., and Zhang, Y. (2018). Very deep convolutional neural networks for complex land cover mapping using multispectral remote sensing imagery. Remote Sens., 10.","DOI":"10.3390\/rs10071119"},{"key":"ref_30","first-page":"1","article-title":"Pavement Moisture Content Prediction: A Deep Residual Neural Network Approach for Analyzing Ground Penetrating Radar","volume":"60","author":"Cao","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_31","unstructured":"Alvarez, J.K., and Kodagoda, S. (June, January 31). Application of deep learning imageto-image transformation networks to GPR radargrams for sub-surface imaging in infrastructure monitoring. Proceedings of the 13th IEEE Conference on Industrial Electronics and Applications (ICIEA), Wuhan, China."},{"key":"ref_32","first-page":"159","article-title":"Inverse problems = quest for information","volume":"50","author":"Tarantola","year":"1982","journal-title":"J. Geophys."},{"key":"ref_33","unstructured":"Taflove, A., and Hagness, S.C. (2000). Computational Electrodynamics the Finite-Difference Time-Domain Method, Artech House. [2nd ed.]."},{"key":"ref_34","first-page":"302","article-title":"Numerical solution of initial boundary value problems involving Maxwell\u2019s equations in isotropic media","volume":"AP-14","author":"Yee","year":"1966","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4133\/JEEG6.1.1","article-title":"Pre-inversion correction and analysis of radar tomographic data","volume":"6","author":"Peterson","year":"2001","journal-title":"J. Environ. Eng. Geophys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"H1","DOI":"10.1190\/geo2013-0215.1","article-title":"Accounting for imperfect forward modeling in geophysical inverse problems-exemplified for crosshole tomography","volume":"79","author":"Hansen","year":"2014","journal-title":"Geophysics"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/2\/243\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:42:16Z","timestamp":1760103736000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/2\/243"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,8]]},"references-count":36,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,1]]}},"alternative-id":["rs16020243"],"URL":"https:\/\/doi.org\/10.3390\/rs16020243","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2024,1,8]]}}}