{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:13:44Z","timestamp":1760148824230,"version":"build-2065373602"},"reference-count":57,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,6,8]],"date-time":"2023-06-08T00:00:00Z","timestamp":1686182400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Universit\u00e1 della Campania Luigi Vanvitelli"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>In this paper, we are concerned with microwave subsurface imaging achieved by inverting the linearized scattering operator arising from the Born approximation. In particular, we consider the important question of reducing the required data to achieve imaging. This can help to reduce the radar system\u2019s cost and complexity and mitigate the imaging algorithm\u2019s computational burden and the needed storage resources. To cope with these issues, in the framework of a multi-monostatic\/multi-frequency configuration, we introduce a new spatial sampling scheme, named the warping method, that allows for a significant reduction in spatial measurements compared to other literature approaches. The basic idea is to introduce some variable transformations that \u201cwarp\u201d the measurement space so that the reconstruction point-spread function obtained by adjoint inversion is recast as a Fourier-like transformation, which provides insights into how to achieve the sampling. In our previous contributions, we focused on presenting and checking the theoretical background with simple numerical examples. In this contribution, we briefly review the key components of the warping method and present its experimental validation by considering a realistic subsurface scattering scenario for the case of a buried water pipe. Essentially, we show that the latter succeeds in reducing the number of data compared to other approaches in the literature, without significantly affecting the reconstruction results.<\/jats:p>","DOI":"10.3390\/rs15123012","type":"journal-article","created":{"date-parts":[[2023,6,9]],"date-time":"2023-06-09T02:03:18Z","timestamp":1686276198000},"page":"3012","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An Insight into the Warping Spatial Sampling Method in Subsurface Radar Imaging and Its Experimental Validation"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9266-5880","authenticated-orcid":false,"given":"Maria Antonia","family":"Maisto","sequence":"first","affiliation":[{"name":"Dipartimento di Ingegneria, Universit\u00e0 della Campania, 81031 Aversa, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6310-6959","authenticated-orcid":false,"given":"Chandan","family":"Bhat","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai 600036, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1808-4671","authenticated-orcid":false,"given":"Raffaele","family":"Solimene","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria, Universit\u00e0 della Campania, 81031 Aversa, Italy"},{"name":"National Inter-University Consortium for Telecommunications (CNIT), 43124 Parma, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,8]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"Daniels, D.J. (2004). Ground Penetrating Radar, Institution of Engineering and Technology. [2nd ed.].","key":"ref_1","DOI":"10.1049\/PBRA015E"},{"unstructured":"Pastorino, M., and Randazzo, A. (2018). Microwave Imaging Methods and Applications, Artech House.","key":"ref_2"},{"doi-asserted-by":"crossref","unstructured":"Benedetto, A., and Pajewsky, L. (2015). Civil Engineering Applications of Ground Penetrating Radar, Springer.","key":"ref_3","DOI":"10.1007\/978-3-319-04813-0"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1109\/JSTARS.2011.2161755","article-title":"Holographic Subsurface Radar of RASCAn Type: Development and Applications","volume":"4","author":"Ivashov","year":"2011","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3031","DOI":"10.1109\/TGRS.2008.921959","article-title":"A Kirchhoff-based Shape Reconstruction Algorithm for the Multimonostatic Configuration: The Realistic Case of Buried Pipes","volume":"46","author":"Soldovieri","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4860","DOI":"10.1109\/JSTARS.2014.2321710","article-title":"Autofocusing Techniques for GPR Data from RC Bridge Decks","volume":"7","author":"Wei","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"doi-asserted-by":"crossref","unstructured":"Goodman, D., and Piro, S. (2013). GPR Remote Sensing in Archaeology, Springer.","key":"ref_7","DOI":"10.1007\/978-3-642-31857-3"},{"key":"ref_8","first-page":"291","article-title":"Fast Geophysical Prospecting Applied to Archaeology: Results at \u00abvilla ai Cavallacci\u00bb (Albano Laziale, Rome) site","volume":"50","author":"Urbini","year":"2007","journal-title":"Ann. Geoph."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"S92","DOI":"10.1088\/1742-2132\/9\/4\/S92","article-title":"Microwave Tomography Enhanced GPR Surveys in Centaur\u2019s Domus\u2014Regio vI of Pompeii","volume":"9","author":"Catapano","year":"2012","journal-title":"J. Geophys. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"8220","DOI":"10.3390\/rs6098220","article-title":"Assessment of Complex Masonry Structures with GPR Compared to other Non-destructive Testing Studies","volume":"6","author":"Caselles","year":"2014","journal-title":"Remote Sens."},{"doi-asserted-by":"crossref","unstructured":"Capozzoli, L., Catapano, I., De Martino, G., Gennarelli, G., Ludeno, G., Rizzo, E., Soldovieri, F., Uliano Scelza, F., and Zuchtriegel, G. (2020). The Discovery of a Buried Temple in Paestum: The Advantages of the Geophysical Multi-Sensor Application. Remote Sens., 12.","key":"ref_11","DOI":"10.3390\/rs12172711"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1109\/MSP.2019.2895121","article-title":"Applying Ground-Penetrating Radar and Microwave Tomography Data Processing in Cultural Heritage: State of the Art and Future Trends","volume":"36","author":"Catapano","year":"2019","journal-title":"IEEE Sign. Proc. Mag."},{"doi-asserted-by":"crossref","unstructured":"Sato, M. (2010, January 25\u201330). GPR Evaluation Test for Humanitarian Demining in Cambodia. Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Honolulu, HI, USA.","key":"ref_13","DOI":"10.1109\/IGARSS.2010.5649837"},{"doi-asserted-by":"crossref","unstructured":"Brancaccio, A., Dell\u2019Aversano, A., Leone, G., and Solimene, R. (2019). Subsurface Detection of Shallow Targets by Undersampled Multifrequency Data and a Non-Cooperative Source. Appl. Sci., 9.","key":"ref_14","DOI":"10.3390\/app9245383"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1080\/01691864.2017.1351393","article-title":"An integrated Aerial System for Landmine Detection: SDR-Based Ground Penetrating Radar Onboard an Autonomous Drone","volume":"31","author":"Colorado","year":"2017","journal-title":"Adv. Robot."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3497","DOI":"10.1109\/TMTT.2018.2804905","article-title":"Microwave Tomography for the Inspection of Wood Materials: Imaging System and Experimental Results","volume":"66","author":"Randazzo","year":"2018","journal-title":"IEEE Trans. Microw. Theory Tech."},{"unstructured":"Chew, W.C. (1995). Waves and Fields in Inhomogeneous Media, Institute of Electrical and Electronics Engineers.","key":"ref_17"},{"doi-asserted-by":"crossref","unstructured":"Benedetto, A., and Pajewsky, L. (2015). Civil Engineering Applications of Ground Penetrating Radar, Springer.","key":"ref_18","DOI":"10.1007\/978-3-319-04813-0"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"8837","DOI":"10.1364\/OE.14.008837","article-title":"A Family of Approximations Spanning the Born and Rytov","volume":"14","author":"Marks","year":"2006","journal-title":"Opt. Express"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1799","DOI":"10.1109\/TGRS.2009.2035053","article-title":"Physical Optics Imaging of 3-D PEC Objects: Vector and Multipolarized Approaches","volume":"48","author":"Solimene","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1150","DOI":"10.1109\/TAP.2014.2387421","article-title":"On the Achievable Imaging Performance in Full 3-D Linear Inverse Scattering","volume":"63","author":"Gennarelli","year":"2015","journal-title":"IEEE Trans. Antenn. Propag."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4836","DOI":"10.1109\/TAP.2021.3060030","article-title":"Near-field Transverse Resolution in Planar Source Reconstructions","volume":"69","author":"Maisto","year":"2021","journal-title":"IEEE Trans. Antenn. Propag."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"145","DOI":"10.2528\/PIERM19080301","article-title":"Transverse Resolution in Microwave Imaging for Strip Objects Buried in a Half-Space Medium","volume":"88","author":"Maisto","year":"2020","journal-title":"Progress Electrom. Res. M"},{"doi-asserted-by":"crossref","unstructured":"Bertero, M., and Boccacci, P. (1998). Introduction to Inverse Problems in Imaging, CRC Press.","key":"ref_24","DOI":"10.1887\/0750304359"},{"doi-asserted-by":"crossref","unstructured":"Brancaccio, A., Leone, G., Pierri, R., and Solimene, R. (2021). Experimental Validation of a Microwave Imaging Method for Shallow Buried Target Detection by Under-Sampled Data and a Non-Cooperative Source. Sensors, 21.","key":"ref_25","DOI":"10.20944\/preprints202106.0563.v1"},{"doi-asserted-by":"crossref","unstructured":"Noviello, C., Gennarelli, G., Esposito, G., Ludeno, G., Fasano, G., Capozzoli, L., Soldovieri, F., and Catapano, I. (2022). An Overview on Down-Looking UAV-Based GPR Systems. Remote Sens., 14.","key":"ref_26","DOI":"10.3390\/rs14143245"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1109\/MGRS.2021.3082170","article-title":"Contactless Ground Penetrating Radar Imaging: State of the Art, Challenges, and Microwave Tomography-based Data Processing","volume":"10","author":"Catapano","year":"2022","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"doi-asserted-by":"crossref","unstructured":"Catapano, I., Noviello, C., and Soldovieri, F. (2021). Down-Looking Airborne Radar Imaging Performance: The Multi-Line and Multi-Frequency. Remote Sens., 13.","key":"ref_28","DOI":"10.3390\/rs13234897"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1109\/78.370637","article-title":"Selection of Observations in Signal Reconstruction","volume":"43","author":"Reeves","year":"1995","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1109\/TSP.2008.2007095","article-title":"Sensor Selection via Convex Optimization","volume":"57","author":"Joshi","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"doi-asserted-by":"crossref","unstructured":"Naeem, M., Xue, S., and Lee, D.C. (2009, January 28\u201330). Cross-Entropy Optimization for Sensor Selection Problems. Proceedings of the 9th International Symposium on Communications and Information Technology, Icheon, Republic of Korea.","key":"ref_31","DOI":"10.1109\/ISCIT.2009.5341219"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1109\/TSP.2014.2299518","article-title":"Near-Optimal Sensor Placement for Linear Inverse Problems","volume":"62","author":"Ranieri","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"5595","DOI":"10.1109\/TSP.2016.2573767","article-title":"Sensor Placement by Maximal Projection on Minimum Eigenspace for Linear Inverse Problems","volume":"64","author":"Jiang","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1608","DOI":"10.1109\/83.799888","article-title":"Depth-Focused Interior Echo Imaging","volume":"8","author":"Soumekh","year":"1999","journal-title":"IEEE Trans. Image Process."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"728","DOI":"10.1109\/8.855491","article-title":"3-D Radar Imaging Using Range Migration Techniques","volume":"48","year":"2000","journal-title":"IEEE Trans. Antenn. Propag."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1434","DOI":"10.1109\/8.954932","article-title":"Extension of the 3-D Range Migration Algorithm to Cylindrical and Spherical Scanning Geometries","volume":"49","year":"2001","journal-title":"IEEE Trans. Antenn. Propag."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/LGRS.2020.3028938","article-title":"Spatial Sampling in Monostatic Radar Imaging","volume":"19","author":"Maisto","year":"2020","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"82336","DOI":"10.1109\/ACCESS.2022.3196384","article-title":"Non-Uniform Warping Sampling for Data Reduction in Planar Array Diagnostics","volume":"10","author":"Maisto","year":"2022","journal-title":"IEEE Access"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1109\/OJAP.2020.3037678","article-title":"Sensor Arrangement in Monostatic Subsurface Radar Imaging","volume":"2","author":"Maisto","year":"2020","journal-title":"IEEE Open J. Antenn. Propag."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1109\/OJAP.2022.3159279","article-title":"Sensor Arrangement in Through-the Wall Radar Imaging","volume":"3","author":"Maisto","year":"2022","journal-title":"IEEE Open J. Antenn. Propag."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2528\/PIER10050705","article-title":"3D Sliced Tomographic Inverse Scattering Experimental Results","volume":"105","author":"Solimene","year":"2010","journal-title":"Progress Electrom. Res."},{"doi-asserted-by":"crossref","unstructured":"Gennarelli, G., Ludeno, G., Carlo, N., Catapano, I., and Soldovieri, F. (2022). The Role of Model Dimensionality in Linear Inverse Scattering from Dielectric Objects. Remote Sens., 14.","key":"ref_42","DOI":"10.3390\/rs14010222"},{"doi-asserted-by":"crossref","unstructured":"Persico, R., Ludeno, G., Soldovieri, F., De Coster, A., and Lambot, S. (2017). Two-Dimensional Linear Inversion of GPR Data with a Shifting Zoom along the Observation Line. Remote Sens., 9.","key":"ref_43","DOI":"10.3390\/rs9100980"},{"doi-asserted-by":"crossref","unstructured":"Devaney, A.J. (2012). Mathematical Foundations of Imaging, Tomography and Wavefield Inversion, Cambridge University Press.","key":"ref_44","DOI":"10.1017\/CBO9781139047838"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1109\/58.156176","article-title":"Time-Reversal of Ultrasonic Fields. III. Theory of the Closed Time-Reversal Cavity","volume":"39","author":"Cassereau","year":"1992","journal-title":"IEEE Trans. Ultrason. Ferroelect. Freq. Control"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"105010","DOI":"10.1088\/1361-6420\/aa7ad1","article-title":"Back-propagation Imaging by Exploiting Multipath from Point Scatterers","volume":"33","author":"Solimene","year":"2017","journal-title":"Inv. Problems"},{"doi-asserted-by":"crossref","unstructured":"Maisto, M.A., Masoodi, M., Leone, G., Solimene, R., and Pierri, R. (2021). Scattered Far-Field Sampling in Multi-Static Multi-Frequency Configuration. Sensors, 21.","key":"ref_47","DOI":"10.3390\/s21144724"},{"unstructured":"Soumekh, M. (1999). Synthetic Aperture Radar Signal Processing, Wiley.","key":"ref_48"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1364\/JOSAA.36.000353","article-title":"Sampling Approach for Singular System Computation of a Radiation Operator","volume":"36","author":"Solimene","year":"2019","journal-title":"J. Opt. Soc. Am. A"},{"unstructured":"Raymond, X.S. (1991). Elementary Introduction to the Theory of Pseudodifferential Operators, CRC.","key":"ref_50"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/S0019-9958(68)90787-0","article-title":"Sampling Principle for Continuous Signals with Time-Varying Bands","volume":"13","author":"Horiuchi","year":"1968","journal-title":"Inf. Control"},{"unstructured":"Gebremichael, T., Mali, D., and Zoubir, A.M. (2011, January 21\u201322). Clutter Reduction Techniques for GPR Based Buried Landmine Detection. Proceedings of the IEEE 2011 International Conference on Signal Processing, Communication, Computing and Networking Technologies, Thuckalay, India.","key":"ref_52"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1104","DOI":"10.1109\/TGRS.2007.910223","article-title":"Effects of Background Removal in Linear Inverse Scattering","volume":"46","author":"Persico","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TGRS.2008.2010052","article-title":"Through-thewall Imaging Using Differential SAR","volume":"47","author":"Dehmollaian","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"doi-asserted-by":"crossref","unstructured":"Khan, U.S., and Al-Nuaimy, W. (2010, January 21\u201325). Background Removal from GPR Data Using Eigenvalues. Proceedings of the IEEE XIII International Conference on Ground Penetrating Radar, Lecce, Italy.","key":"ref_55","DOI":"10.1109\/ICGPR.2010.5550079"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1109\/JSTARS.2013.2287016","article-title":"Ground Clutter Removal in GPR Surveys","volume":"7","author":"Solimene","year":"2013","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"62255","DOI":"10.1109\/ACCESS.2021.3074786","article-title":"Efficient planar near-field measurements for radiation pattern evaluation by a warping strategy","volume":"9","author":"Maisto","year":"2021","journal-title":"IEEE Access"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/12\/3012\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:51:16Z","timestamp":1760125876000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/12\/3012"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,8]]},"references-count":57,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["rs15123012"],"URL":"https:\/\/doi.org\/10.3390\/rs15123012","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2023,6,8]]}}}