{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T18:59:29Z","timestamp":1771959569808,"version":"3.50.1"},"reference-count":58,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,5,21]],"date-time":"2021-05-21T00:00:00Z","timestamp":1621555200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003407","name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","award":["PRIN2015 U-VIEW, grant number 20152HWRSL"],"award-info":[{"award-number":["PRIN2015 U-VIEW, grant number 20152HWRSL"]}],"id":[{"id":"10.13039\/501100003407","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>A hybrid inversion scheme for through-the-wall imaging is proposed in this paper. The approach is based on a linearized model of the inverse-scattering problem, employing the Green\u2019s function developed for a layered background. The reconstruction is obtained by means of a Landweber-like iterative method performing a regularization in the framework of variable-exponent Lebesgue spaces. Thanks to the non-conventional geometrical properties of such spaces, it is possible to enhance the reconstruction capabilities, e.g., by promoting sparseness and reducing over-smoothing. The exponent function defining the specific space adopted in the inversion procedure is adaptively obtained directly from the measured data, through a truncated-singular value decomposition method. In this way, it is possible to precompute and reuse in both steps, for a given scenario, all the matrices necessary in the inversion process, thus leading to a computationally efficient solving strategy. The effectiveness of the approach is evaluated by using experimental data obtained with a commercial GPR apparatus employing a pulsed source field. A fast Fourier transform is applied to the time-domain measurements to extract frequency-domain data at a set of frequencies in the source spectrum, which are fed in input to the imaging scheme. Very good reconstruction capabilities are obtained both with a single metallic target, as well as in a challenging two targets layout including both a metallic object and a low-permittivity target.<\/jats:p>","DOI":"10.3390\/rs13112028","type":"journal-article","created":{"date-parts":[[2021,5,24]],"date-time":"2021-05-24T00:01:20Z","timestamp":1621814480000},"page":"2028","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Through-the-Wall Imaging Approach Based on a TSVD\/Variable-Exponent Lebesgue-Space Method"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5291-462X","authenticated-orcid":false,"given":"Andrea","family":"Randazzo","sequence":"first","affiliation":[{"name":"Department of Electrical, Electronic, Telecommunications Engineering and Naval Architecture, University of Genoa, 16145 Genoa, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2482-8606","authenticated-orcid":false,"given":"Cristina","family":"Ponti","sequence":"additional","affiliation":[{"name":"Department of Engineering, Roma Tre University, 00146 Rome, Italy"},{"name":"National Interuniversity Consortium for Telecommunications, Roma Tre University, 00146 Rome, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6636-1448","authenticated-orcid":false,"given":"Alessandro","family":"Fedeli","sequence":"additional","affiliation":[{"name":"Department of Electrical, Electronic, Telecommunications Engineering and Naval Architecture, University of Genoa, 16145 Genoa, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0948-6687","authenticated-orcid":false,"given":"Claudio","family":"Estatico","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Genoa, 16146 Genoa, Italy"}]},{"given":"Paolo","family":"D\u2019Atanasio","sequence":"additional","affiliation":[{"name":"Italian National Agency for New Technologies, Energy and Sustainable Economic Development, Casaccia Research Center, 00123 Rome, Italy"}]},{"given":"Matteo","family":"Pastorino","sequence":"additional","affiliation":[{"name":"Department of Electrical, Electronic, Telecommunications Engineering and Naval Architecture, University of Genoa, 16145 Genoa, Italy"}]},{"given":"Giuseppe","family":"Schettini","sequence":"additional","affiliation":[{"name":"Department of Engineering, Roma Tre University, 00146 Rome, Italy"},{"name":"National Interuniversity Consortium for Telecommunications, Roma Tre University, 00146 Rome, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,21]]},"reference":[{"key":"ref_1","unstructured":"Amin, M.G. (2011). Through-the-Wall Radar Imaging, CRC Press."},{"key":"ref_2","unstructured":"Pastorino, M., and Randazzo, A. (2018). Microwave Imaging Methods and Applications, Artech House."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3697","DOI":"10.1109\/TGRS.2016.2525733","article-title":"Unlocking\u2019 the ground: Increasing the detectability of buried objects by depositing passive superstrates","volume":"54","author":"Valagiannopoulos","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5706","DOI":"10.1109\/TAP.2014.2357425","article-title":"Hiding a bump on a PEC plane by using an isotropic lossless dielectric layer","volume":"62","author":"Valagiannopoulos","year":"2014","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1080\/02564602.2017.1364146","article-title":"Through-the-wall radar imaging: A review","volume":"35","author":"Nkwari","year":"2018","journal-title":"IETE Tech. Rev."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Cicchetti, R., Cicchetti, V., Faraone, A., Foged, L., and Testa, O. (2020). A compact high-gain wideband lens vivaldi antenna for wireless communications and through-the-wall imaging. IEEE Trans. Antennas Propag.","DOI":"10.1109\/TAP.2020.3037777"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1109\/TAES.2005.1413761","article-title":"Synthetic aperture beamformer for imaging through a dielectric wall","volume":"41","author":"Ahmad","year":"2005","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1109\/TAP.2013.2287274","article-title":"Three-dimensional synthetic aperture radar imaging through multilayered walls","volume":"62","author":"Zhang","year":"2014","journal-title":"IEEE Trans. Antennas Propagat."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Cicchetti, R., Pisa, S., Piuzzi, E., Pittella, E., D\u2019Atanasio, P., and Testa, O. (2021). Numerical and experimental comparison among a new hybrid FT-MUSIC technique and existing algorithms for through-the-wall radar imaging. IEEE Trans. Microw. Theory Tech.","DOI":"10.1109\/TMTT.2021.3061500"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1109\/TGRS.2008.2010052","article-title":"Through-the-wall imaging using differential SAR","volume":"47","author":"Dehmollaian","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Klibanov, M.V., Smirnov, A.V., Khoa, V.A., Sullivan, A.J., and Nguyen, L.H. (2021). Through-the-wall nonlinear SAR imaging. IEEE Trans. Geosci. Remote Sens., 1\u201312.","DOI":"10.1109\/TGRS.2021.3055805"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1109\/TGRS.2008.916212","article-title":"Refocusing through building walls using synthetic aperture radar","volume":"46","author":"Dehmollaian","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1109\/TGRS.2011.2128331","article-title":"Multipath model and exploitation in through-the-wall and urban radar sensing","volume":"49","author":"Setlur","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_14","first-page":"4","article-title":"A multiarray refocusing approach for through-the-wall imaging","volume":"12","author":"Xin","year":"2015","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TGRS.2020.3035561","article-title":"Clutter reduction and target tracking in through-the-wall radar","volume":"58","author":"Liu","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2108","DOI":"10.1109\/TGRS.2014.2355211","article-title":"A subspace projection approach for wall clutter mitigation in through-the-wall radar imaging","volume":"53","author":"Tivive","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Zhou, Y., Huang, C., Liu, H., Li, D., and Truong, T.-K. (2020). Front-wall clutter removal in through-the-wall radar based on weighted nuclear norm minimization. IEEE Geosci. Remote Sens. Lett., 1\u20135.","DOI":"10.1109\/LGRS.2020.3034568"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1109\/TGRS.2016.2585112","article-title":"All-directions through-the-wall radar imaging using a small number of moving transceivers","volume":"54","author":"Yektakhah","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2618","DOI":"10.1109\/TGRS.2018.2875695","article-title":"All-directions through-the-wall imaging using a small number of moving omnidirectional bi-static FMCW transceivers","volume":"57","author":"Yektakhah","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Yektakhah, B., and Sarabandi, K. (2020). A method for detection of flat walls in through-the-wall SAR imaging. IEEE Geosci. Remote Sens. Lett., 1\u20135.","DOI":"10.1109\/APUSNCURSINRSM.2019.8889357"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1109\/LGRS.2007.900735","article-title":"Through-wall imaging via a linear inverse scattering algorithm","volume":"4","author":"Soldovieri","year":"2007","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1109\/TGRS.2009.2012698","article-title":"Three-dimensional through-wall imaging under ambiguous wall parameters","volume":"47","author":"Solimene","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1109\/TGRS.2007.900994","article-title":"Localization of the interfaces of a slab hidden behind a wall","volume":"45","author":"Soldovieri","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.jcp.2017.06.035","article-title":"A linear sampling method for through-the-wall radar detection","volume":"347","author":"Charnley","year":"2017","journal-title":"J. Comput. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1109\/LGRS.2010.2045473","article-title":"A qualitative inverse scattering method for through-the-wall imaging","volume":"7","author":"Catapano","year":"2010","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1109\/LGRS.2016.2577715","article-title":"Comparative analysis of two approaches for multipath ghost suppression in radar imaging","volume":"13","author":"Gennarelli","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1080\/10589759.2012.707198","article-title":"Through-wall imaging for a metallic cylinder","volume":"28","author":"Chiu","year":"2013","journal-title":"Nondestruct. Test. Eval."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1109\/LGRS.2010.2056912","article-title":"Through-wall shape reconstruction and wall parameters estimation using differential evolution","volume":"8","author":"Dehmollaian","year":"2011","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1967","DOI":"10.1109\/TGRS.2008.916635","article-title":"Shape reconstruction of a perfectly conducting scatterer using differential evolution and particle swarm optimization","volume":"46","author":"Rekanos","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1109\/TGRS.2015.2441957","article-title":"Multiple extended target tracking for through-wall radars","volume":"53","author":"Gennarelli","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.1109\/LGRS.2016.2583795","article-title":"First-order multipath ghosts\u2019 characteristics and suppression in MIMO through-wall imaging","volume":"13","author":"Liu","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"868","DOI":"10.1109\/LGRS.2018.2815042","article-title":"Multipath ghost suppression for through-the-wall imaging radar via array rotating","volume":"15","author":"Guo","year":"2018","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2284","DOI":"10.1109\/TAES.2013.100241","article-title":"Multipath ghost suppression for through-the-wall radar","volume":"50","author":"Tan","year":"2014","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1109\/LAWP.2014.2380787","article-title":"Compressive-sensing-based high-resolution polarimetric through-the-wall radar imaging exploiting target characteristics","volume":"14","author":"Wu","year":"2015","journal-title":"Antennas Wirel. Propag. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1408","DOI":"10.1109\/TGRS.2009.2030321","article-title":"UWB through-wall imaging based on compressive sensing","volume":"48","author":"Huang","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1109\/LGRS.2012.2185679","article-title":"A novel CS-TSVD strategy to perform data reduction in linear inverse scattering problems","volume":"9","author":"Solimene","year":"2012","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"5157","DOI":"10.1109\/TAP.2014.2344673","article-title":"Compressive sensing imaging of non-sparse 2D scatterers by a total-variation approach within the Born approximation","volume":"62","author":"Oliveri","year":"2014","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"4598","DOI":"10.1109\/TIP.2020.2973819","article-title":"Compressive radar imaging of stationary indoor targets with low-rank plus jointly sparse and total variation regularizations","volume":"29","author":"Tang","year":"2020","journal-title":"IEEE Trans. Image Process."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1109\/TCI.2021.3071957","article-title":"Through-the-wall radar imaging based on Bayesian compressive sensing exploiting multipath and target structure","volume":"7","author":"Wu","year":"2021","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Fedeli, A., Pastorino, M., Ponti, C., Randazzo, A., and Schettini, G. (2020). Through-the-wall microwave imaging: Forward and inverse scattering modeling. Sensors, 20.","DOI":"10.3390\/s20102865"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Randazzo, A., Ponti, C., Fedeli, A., Estatico, C., D\u2019Atanasio, P., Pastorino, M., and Schettini, G. (2021). A two-step inverse-scattering technique in variable-exponent Lebesgue spaces for through-the-wall microwave imaging: Experimental results. IEEE Trans. Geosci. Remote Sens.","DOI":"10.1109\/TGRS.2021.3052608"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"4155","DOI":"10.1109\/TGRS.2012.2227059","article-title":"Three-dimensional real-time through-the-wall radar imaging with diffraction tomographic algorithm","volume":"51","author":"Zhang","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1138","DOI":"10.1109\/TMTT.2018.2878703","article-title":"Fast microwave through wall imaging method with inhomogeneous background based on levenberg\u2013marquardt algorithm","volume":"67","author":"Chu","year":"2019","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1381","DOI":"10.1109\/TMAG.2003.810526","article-title":"Microwave imaging in the time domain of buried multiple scatterers by using an FDTD-based optimization technique","volume":"39","author":"Rekanos","year":"2003","journal-title":"IEEE Trans. Magn."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1933","DOI":"10.1049\/el.2016.2635","article-title":"Experimental investigation on through-wall imaging based on non-linear inversions","volume":"52","author":"Meng","year":"2016","journal-title":"Electron. Lett."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2793","DOI":"10.1109\/TGRS.2005.857914","article-title":"Through-wall imaging (TWI) by radar: 2-D tomographic results and analyses","volume":"43","author":"Song","year":"2005","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"7282","DOI":"10.1109\/TAP.2018.2869201","article-title":"Quantitative microwave imaging method in Lebesgue spaces with nonconstant exponents","volume":"66","author":"Estatico","year":"2018","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1882","DOI":"10.1109\/TMTT.2019.2963870","article-title":"Variable-exponent Lebesgue-space inversion for brain stroke microwave imaging","volume":"68","author":"Bisio","year":"2020","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_49","unstructured":"Chew, W.C. (1995). Waves and Fields in Inhomogeneous Media, IEEE Press."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1109\/TGRS.2004.839432","article-title":"Shape reconstruction of perfectly conducting objects by multiview experimental data","volume":"43","author":"Soldovieri","year":"2005","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Diening, L., Harjulehto, P., H\u00e4st\u00f6, P., and Ruzicka, M. (2011). Lebesgue and Sobolev Spaces with Variable Exponents, Springer. Lecture Notes in Mathematics.","DOI":"10.1007\/978-3-642-18363-8"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Estatico, C., Fedeli, A., Pastorino, M., and Randazzo, A. (2019). Microwave imaging by means of Lebesgue-space inversion: An overview. Electronics, 8.","DOI":"10.3390\/electronics8090945"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1109\/TCI.2018.2859634","article-title":"Three-dimensional microwave imaging in Lp Banach spaces: Numerical and experimental results","volume":"4","author":"Estatico","year":"2018","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_54","unstructured":"(2021, April 12). PulseEKKO, Overview, Sensors & Software. Available online: https:\/\/www.sensoft.ca\/products\/pulseekkopro\/overview-pulseekko\/."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"3192","DOI":"10.1109\/TGRS.2009.2019728","article-title":"Spatial filtering for wall-clutter mitigation in through-the-wall radar imaging","volume":"47","author":"Yoon","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1109\/MSP.2014.2311271","article-title":"SAR imaging algorithms and some unconventional applications: A unified mathematical overview","volume":"31","author":"Solimene","year":"2014","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1109\/LGRS.2008.915742","article-title":"Three-dimensional wideband beamforming for imaging through a single wall","volume":"5","author":"Ahmad","year":"2008","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1109\/JERM.2018.2878070","article-title":"Comparison between delay and sum and range migration algorithms for image reconstruction in through-the-wall radar imaging systems","volume":"2","author":"Pisa","year":"2018","journal-title":"IEEE J. Electromagn. RF Microw. Med. Biol."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/11\/2028\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:05:20Z","timestamp":1760162720000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/11\/2028"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,21]]},"references-count":58,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["rs13112028"],"URL":"https:\/\/doi.org\/10.3390\/rs13112028","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5,21]]}}}