{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T15:43:00Z","timestamp":1781538180880,"version":"3.54.5"},"reference-count":45,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,6,8]],"date-time":"2024-06-08T00:00:00Z","timestamp":1717804800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["202008170016"],"award-info":[{"award-number":["202008170016"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Institute of Earth Sciences, University of Lausanne","award":["202008170016"],"award-info":[{"award-number":["202008170016"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Ground-penetrating radar (GPR) is a popular geophysical tool for mapping the underground. High-resolution 3D GPR data carry a large amount of information and can greatly help to interpret complex subsurface geometries. However, such data require a dense collection along closely spaced parallel survey lines, which is time consuming and costly. In many cases, for the sake of efficiency, a choice is made during 3D acquisitions to use a larger spacing between the profile lines, resulting in a dense measurement spacing along the lines but a much coarser one in the across-line direction. Simple interpolation methods are then commonly used to increase the sampling before interpretation, which can work well when the subsurface structures are already well sampled in the across-line direction but can distort such structures when this is not the case. In this work, we address the latter problem using a novel multiple-point geostatistical (MPS) simulation methodology. For a considered 3D GPR dataset with reduced sampling in the across-line direction, we attempt to reconstruct a more densely spaced, high-resolution dataset using a series of 2D conditional stochastic simulations in both the along-line and across-line directions. For these simulations, the existing profile data serve as training images from which complex spatial patterns are quantified and reproduced. To reduce discontinuities in the generated 3D spatial structures caused by independent 2D simulations, the target profile being simulated is chosen randomly, and simulations in the along-line and across-line directions are performed alternately. We show the successful application of our approach to 100 MHz synthetic and 200 MHz field GPR data under multiple decimation scenarios where survey lines are regularly deleted from a dense 3D reference dataset, and the corresponding reconstructions are compared with the original data.<\/jats:p>","DOI":"10.3390\/rs16122084","type":"journal-article","created":{"date-parts":[[2024,6,10]],"date-time":"2024-06-10T08:49:03Z","timestamp":1718009343000},"page":"2084","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Reconstruction of High-Resolution 3D GPR Data from 2D Profiles: A Multiple-Point Statistical Approach"],"prefix":"10.3390","volume":"16","author":[{"given":"Chongmin","family":"Zhang","sequence":"first","affiliation":[{"name":"Institute of Earth Sciences, University of Lausanne, 1015 Lausanne, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0871-1507","authenticated-orcid":false,"given":"Mathieu","family":"Gravey","sequence":"additional","affiliation":[{"name":"Institute for Interdisciplinary Mountain Research, Austrian Academy of Sciences, 6020 Innsbruck, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8820-2808","authenticated-orcid":false,"given":"Gr\u00e9goire","family":"Mari\u00e9thoz","sequence":"additional","affiliation":[{"name":"Institute of Earth Surface Dynamics, University of Lausanne, 1015 Lausanne, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9833-206X","authenticated-orcid":false,"given":"James","family":"Irving","sequence":"additional","affiliation":[{"name":"Institute of Earth Sciences, University of Lausanne, 1015 Lausanne, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Annan, A.P. (2005). Ground-Penetrating Radar. Near-Surface Geophysics, Society of Exploration Geophysicists.","DOI":"10.1190\/1.9781560801719.ch11"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1146\/annurev.earth.29.1.229","article-title":"Ground Penetrating Radar for Environmental Applications","volume":"29","author":"Knight","year":"2001","journal-title":"Annu. Rev. Earth Planet. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"K12","DOI":"10.1190\/1.1852780","article-title":"Full-resolution 3D GPR imaging","volume":"70","author":"Grasmueck","year":"2005","journal-title":"Geophysics"},{"key":"ref_4","first-page":"290","article-title":"3D GPR survey for the archaeological characterization of the ancient Messapian necropolis in Lecce, South Italy","volume":"7","author":"Leucci","year":"2016","journal-title":"J. Archaeol. Sci. Rep."},{"key":"ref_5","unstructured":"Novo, A., Grasmueck, M., Viggiano, D., and Lorenzo, H. (2008, January 15\u201319). 3D GPR in archaeology: What can be gained from dense data acquisition and processing. Proceedings of the 12th International Conference on Ground Penetrating Radar, Birmingham, UK."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"105674","DOI":"10.1016\/j.enggeo.2020.105674","article-title":"Which fractures are imaged with Ground Penetrating Radar? Results from an experiment in the \u00c4sp\u00f6 Hardrock Laboratory, Sweden","volume":"273","author":"Molron","year":"2020","journal-title":"Eng. Geol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3975","DOI":"10.5194\/tc-15-3975-2021","article-title":"Ground-penetrating radar imaging reveals glacier\u2019s drainage network in 3D","volume":"15","author":"Church","year":"2021","journal-title":"Cryosphere"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1017\/jog.2021.26","article-title":"Characterization of subglacial marginal channels using 3-D analysis of high-density ground-penetrating radar data","volume":"67","author":"Egli","year":"2021","journal-title":"J. Glaciol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"104689","DOI":"10.1016\/j.autcon.2022.104689","article-title":"Automatic pixel-level detection of vertical cracks in asphalt pavement based on GPR investigation and improved mask R-CNN","volume":"146","author":"Liu","year":"2023","journal-title":"Autom. Constr."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Liu, Z., Wu, W., Gu, X., Li, S., Wang, L., and Zhang, T. (2021). Application of combining YOLO models and 3D GPR images in road detection and maintenance. Remote Sens., 13.","DOI":"10.3390\/rs13061081"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1002\/nsg.12039","article-title":"High-resolution imaging and monitoring of animal tunnels using 3D ground-penetrating radar","volume":"17","author":"Allroggen","year":"2019","journal-title":"Near Surf. Geophys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.apsoil.2014.03.019","article-title":"Reconstructing mole tunnels using frequency-domain ground penetrating radar","volume":"80","author":"Saey","year":"2014","journal-title":"Appl. Soil Ecol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s11220-018-0209-8","article-title":"Characterizing subsurface archaeological structures with full resolution 3D GPR at the early dynastic foundations of Saqqara Necropolis, Egypt","volume":"19","author":"Gaballah","year":"2018","journal-title":"Sens. Imaging"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1002\/arp.327","article-title":"Three-dimensional, multi-offset ground-penetrating radar imaging of archaeological targets","volume":"15","author":"Booth","year":"2008","journal-title":"Archaeol. Prospect."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1190\/1.1443096","article-title":"Seismic trace interpolation in the FX domain","volume":"56","author":"Spitz","year":"1991","journal-title":"Geophysics"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1057\/palgrave.jba.2950060","article-title":"Practical implications of GPR investigation using 3D data reconstruction and transmission tomography","volume":"3","author":"Topczewski","year":"2007","journal-title":"J. Build. Apprais."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/j.jappgeo.2017.04.003","article-title":"Using interpolation techniques to determine the optimal profile interval in ground-penetrating radar applications","volume":"140","author":"Samet","year":"2017","journal-title":"J. Appl. Geophys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"107494","DOI":"10.1016\/j.measurement.2020.107494","article-title":"Interpolation methods in GPR tomographic imaging of linear and volume anomalies for cultural heritage diagnostics","volume":"154","author":"Rucka","year":"2020","journal-title":"Measurement"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Goodman, D., and Piro, S. (2013). GPR Remote Sensing in Archaeology, Springer.","DOI":"10.1007\/978-3-642-31857-3"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.jappgeo.2019.04.008","article-title":"GPR imaging criteria","volume":"165","author":"Luo","year":"2019","journal-title":"J. Appl. Geophys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1002\/arp.1501","article-title":"The Impact of Spatial Sampling and Migration on the Interpretation of Complex Archaeological Ground-penetrating Radar Data","volume":"22","author":"Verdonck","year":"2015","journal-title":"Archaeol. Prospect."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"E91","DOI":"10.1190\/1.2356088","article-title":"3D interpolation of irregular data with a POCS algorithm","volume":"71","author":"Abma","year":"2006","journal-title":"Geophysics"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1190\/1.1543221","article-title":"Seismic trace interpolation in the Fourier transform domain","volume":"68","year":"2003","journal-title":"Geophysics"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1111\/j.1365-2478.1995.tb00257.x","article-title":"Restoration of missing offsets by parabolic radon transform","volume":"43","author":"Kabir","year":"1995","journal-title":"Geophys. Prospect."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Mariethoz, G., and Caers, J. (2014). Multiple-Point Geostatistics: Stochastic Modeling with Training Images, John Wiley & Sons.","DOI":"10.1002\/9781118662953"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.cageo.2011.07.009","article-title":"3D multiple-point statistics simulation using 2D training images","volume":"40","author":"Comunian","year":"2012","journal-title":"Comput. Geosci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1014009426274","article-title":"Conditional simulation of complex geological structures using multiple-point statistics","volume":"34","author":"Strebelle","year":"2002","journal-title":"Math. Geol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/s11004-019-09818-4","article-title":"Downscaling images with trends using multiple-point statistics simulation: An application to digital elevation models","volume":"52","author":"Rasera","year":"2020","journal-title":"Math. Geosci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4922","DOI":"10.1109\/JSTARS.2015.2438299","article-title":"Digital elevation data fusion using multiple-point geostatistical simulation","volume":"8","author":"Tang","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Hadjipetrou, S., Mariethoz, G., and Kyriakidis, P. (2023). Gap-filling sentinel-1 offshore wind speed image time series using multiple-point geostatistical simulation and reanalysis data. Remote Sens., 15.","DOI":"10.3390\/rs15020409"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Yin, G., Mariethoz, G., and McCabe, M.F. (2016). Gap-filling of landsat 7 imagery using the direct sampling method. Remote Sens., 9.","DOI":"10.3390\/rs9010012"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3015","DOI":"10.5194\/hess-18-3015-2014","article-title":"Simulation of rainfall time series from different climatic regions using the direct sampling technique","volume":"18","author":"Oriani","year":"2014","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_33","first-page":"1","article-title":"Reconstruction of missing GPR data using multiple-point statistical simulation","volume":"62","author":"Zhang","year":"2024","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Guardiano, F.B., and Srivastava, R.M. (1993). Multivariate geostatistics: Beyond bivariate moments. Geostatistics Tr\u00f3ia\u201992: Volume 1, Springer.","DOI":"10.1007\/978-94-011-1739-5_12"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/s11004-011-9328-7","article-title":"An improved parallel multiple-point algorithm using a list approach","volume":"43","author":"Straubhaar","year":"2011","journal-title":"Math. Geosci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"W11536","DOI":"10.1029\/2008WR007621","article-title":"The direct sampling method to perform multiple-point geostatistical simulations","volume":"46","author":"Mariethoz","year":"2010","journal-title":"Water Resour. Res."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2611","DOI":"10.5194\/gmd-13-2611-2020","article-title":"QuickSampling v1. 0: A robust and simplified pixel-based multiple-point simulation approach","volume":"13","author":"Gravey","year":"2020","journal-title":"Geosci. Model Dev."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/s11004-017-9694-x","article-title":"Reconstruction of three-dimensional aquifer heterogeneity from two-dimensional geophysical data","volume":"50","author":"Gueting","year":"2018","journal-title":"Math. Geosci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1109\/TIP.2003.819861","article-title":"Image quality assessment: From error visibility to structural similarity","volume":"13","author":"Wang","year":"2004","journal-title":"IEEE Trans. Image Process."},{"key":"ref_40","unstructured":"Isaaks, E.H., and Srivastava, R.M. (1989). An Introduction to Applied Geostatistics, Oxford University Press."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.jhydrol.2011.03.037","article-title":"Three-dimensional high resolution fluvio-glacial aquifer analog\u2013Part 2: Geostatistical modeling","volume":"405","author":"Comunian","year":"2011","journal-title":"J. Hydrol."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"104422","DOI":"10.1016\/j.cageo.2020.104422","article-title":"3D modeling of ground-penetrating radar data across a realistic sedimentary model","volume":"137","author":"Koyan","year":"2020","journal-title":"Comput. Geosci."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/j.cpc.2016.08.020","article-title":"gprMax: Open source software to simulate electromagnetic wave propagation for Ground Penetrating Radar","volume":"209","author":"Warren","year":"2016","journal-title":"Comput. Phys. Commun."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"W00D26","DOI":"10.1029\/2008WR006960","article-title":"Estimating porosity with ground-penetrating radar reflection tomography: A controlled 3-D experiment at the Boise Hydrogeophysical Research Site","volume":"45","author":"Bradford","year":"2009","journal-title":"Water Resour. Res."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Ruols, B., Baron, L., and Irving, J. (2023). Development of a drone-based ground-penetrating radar system for efficient and safe 3D and 4D surveying of alpine glaciers. J. Glaciol., 1\u201312.","DOI":"10.1017\/jog.2023.83"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/12\/2084\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:56:02Z","timestamp":1760108162000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/12\/2084"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,8]]},"references-count":45,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2024,6]]}},"alternative-id":["rs16122084"],"URL":"https:\/\/doi.org\/10.3390\/rs16122084","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,8]]}}}