{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T18:05:12Z","timestamp":1765994712513,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2020,5,20]],"date-time":"2020-05-20T00:00:00Z","timestamp":1589932800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2019YFC1509201"],"award-info":[{"award-number":["2019YFC1509201"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Synthetic Aperture Radar (SAR) Tomography is a technique to provide direct three-dimensional (3D) imaging of the illuminated targets by processing SAR data acquired from different trajectories. In a large part of the literature, 3D imaging is achieved by assuming mono-dimensional (1D) approaches derived from SAR Interferometry, where a vector of pixels from multiple SAR images is transformed into a new vector of pixels representing the vertical profile of scene reflectivity at a given range, azimuth location. However, mono-dimensional approaches are only suited for data acquired from very closely-spaced trajectories, resulting in coarse vertical resolution. In the case of continuous media, such as forests, snow, ice sheets and glaciers, achieving fine vertical resolution is only possible in the presence of largely-spaced trajectories, which involves significant complications concerning the formation of 3D images. The situation gets even more complicated in the presence of irregular trajectories with variable headings, for which the one theoretically exact approach consists of going back to raw SAR data to resolve the targets by 3D back-projection, resulting in a computational burden beyond the capabilities of standard computers. The first aim of this paper is to provide an exhaustive discussion of the conditions under which high-quality tomographic processing can be carried out by assuming a 1D, 2D, or 3D approach to image formation. The case of 3D processing is then further analyzed, and a new processing method is proposed to produce high-quality imaging while largely reducing the computational burden, and without having to process the original raw data. Furthermore, the new method is shown to be easily parallelized and implemented using GPU processing. The analysis is supported by results from numerical simulations as well as from real airborne data from the ESA campaign AlpTomoSAR.<\/jats:p>","DOI":"10.3390\/rs12101638","type":"journal-article","created":{"date-parts":[[2020,5,20]],"date-time":"2020-05-20T10:37:38Z","timestamp":1589971058000},"page":"1638","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Signal Processing Options for High Resolution SAR Tomography of Natural Scenarios"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9227-1091","authenticated-orcid":false,"given":"Yanghai","family":"Yu","sequence":"first","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"},{"name":"Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133 Milan, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1228-9839","authenticated-orcid":false,"given":"Mauro Mariotti","family":"d\u2019Alessandro","sequence":"additional","affiliation":[{"name":"Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133 Milan, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1229-3811","authenticated-orcid":false,"given":"Stefano","family":"Tebaldini","sequence":"additional","affiliation":[{"name":"Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133 Milan, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingsheng","family":"Liao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2142","DOI":"10.1109\/36.868873","article-title":"First demonstration of airborne SAR tomography using multibaseline L-band data","volume":"38","author":"Reigber","year":"2000","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Curlander, J.C., and McDonough, R.N. (1991). Synthetic Aperture Radar, Wiley.","DOI":"10.1016\/0045-8732(91)90094-O"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4132","DOI":"10.1109\/TGRS.2009.2023785","article-title":"Algebraic synthesis of forest scenarios from multibaseline PolInSAR data","volume":"47","author":"Tebaldini","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1109\/TGRS.2011.2159614","article-title":"Multibaseline Polarimetric SAR Tomography of a Boreal Forest at P- and L-Bands","volume":"50","author":"Tebaldini","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1109\/LGRS.2011.2170658","article-title":"Phenomenology of P-Band Scattering From a Tropical Forest Through Three-Dimensional SAR Tomography","volume":"9","author":"Tebaldini","year":"2012","journal-title":"IEEE Geosci. Remote. Sens. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4430","DOI":"10.1109\/TGRS.2013.2246573","article-title":"Phenomenology of ground scattering in a tropical forest through polarimetric synthetic aperture radar tomography","volume":"51","author":"Tebaldini","year":"2013","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.rse.2015.12.037","article-title":"SAR tomography for the retrieval of forest biomass and height: Cross-validation at two tropical forest sites in French Guiana","volume":"175","author":"Minh","year":"2016","journal-title":"Remote. Sens. Environ."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3648","DOI":"10.1109\/TGRS.2011.2125972","article-title":"Analyzing tomographic SAR data of a forest with respect to frequency, polarization, and focusing technique","volume":"49","author":"Frey","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Yang, X., Tebaldini, S., Mariotti d\u2019Alessandro, M., and Liao, M. (2019). Tropical Forest Height Retrieval Based on P-Band Multibaseline SAR Data. IEEE Geosci. Remote. Sens. Lett., 1\u20135.","DOI":"10.1109\/APSAR46974.2019.9048435"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3402","DOI":"10.1109\/JSTARS.2018.2859050","article-title":"Forest Structure Characterization From SAR Tomography at L-Band","volume":"11","author":"Tello","year":"2018","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote. Sens."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Cazcarra-Bes, V., Tello-Alonso, M., Fischer, R., Heym, M., and Papathanassiou, K. (2017). Monitoring of Forest Structure Dynamics by Means of L-Band SAR Tomography. Remote. Sens., 9.","DOI":"10.3390\/rs9121229"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3386","DOI":"10.1109\/JSTARS.2018.2847033","article-title":"L- and P-Band 3-D SAR Reflectivity Profiles Versus Lidar Waveforms: The AfriSAR Case","volume":"11","author":"Pardini","year":"2018","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote. Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1086","DOI":"10.1109\/TGRS.2009.2031101","article-title":"Estimation of forest structure, ground, and canopy layer characteristics from multibaseline polarimetric interferometric SAR data","volume":"48","author":"Neumann","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4752","DOI":"10.1109\/TGRS.2015.2409066","article-title":"Extraction of structural and dynamic properties of forests from polarimetric-interferometric SAR data affected by temporal decorrelation","volume":"53","author":"Lavalle","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1030","DOI":"10.1109\/LGRS.2018.2819884","article-title":"Forest biomass retrieval from l-band sar using tomographic ground backscatter removal","volume":"15","author":"Blomberg","year":"2018","journal-title":"IEEE Geosci. Remote. Sens. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1897","DOI":"10.1109\/LGRS.2018.2865673","article-title":"Multiport vector network analyzer radar for tomographic forest scattering measurements","volume":"15","author":"Ulander","year":"2018","journal-title":"IEEE Geosci. Remote. Sens. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.crhy.2015.12.016","article-title":"Snowpack permittivity profile retrieval from tomographic SAR data","volume":"18","author":"Rekioua","year":"2017","journal-title":"Comptes Rendus Phys."},{"key":"ref_18","unstructured":"Ferro-Famil, L., Leconte, C., Boutet, F., Phan, X., Gay, M., and Durand, Y. (November, January 31). PoSAR: A VHR tomographic GB-SAR system application to snow cover 3-D imaging at X and Ku bands. Proceedings of the 2012 9th European Radar Conference, Amsterdam, The Netherlands."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Frey, O., Werner, C.L., Caduff, R., and Wiesmann, A. (2016, January 6\u20139). A time series of SAR tomographic profiles of a snowpack. Proceedings of the EUSAR 2016: 11th European Conference on Synthetic Aperture Radar, Hamburg, Germany.","DOI":"10.1109\/IGARSS.2016.7728995"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3794","DOI":"10.1109\/JSTARS.2014.2323199","article-title":"Snow height determination by polarimetric phase differences in X-band SAR data","volume":"7","author":"Leinss","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote. Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2832","DOI":"10.1109\/TGRS.2015.2506399","article-title":"Single and multipolarimetric P-band SAR tomography of subsurface ice structure","volume":"54","author":"Banda","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3791","DOI":"10.1109\/TGRS.2011.2132802","article-title":"Ice Sheet Bed Mapping With Airborne SAR Tomography","volume":"49","author":"Wu","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"7197","DOI":"10.1109\/TGRS.2016.2597361","article-title":"Imaging the Internal Structure of an Alpine Glacier via L-Band Airborne SAR Tomography","volume":"54","author":"Tebaldini","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4457","DOI":"10.1109\/JSTARS.2017.2718998","article-title":"Lake and fjord ice imaging using a multifrequency ground-based tomographic SAR system","volume":"10","author":"Yitayew","year":"2017","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote. Sens."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Ponce, O., Prats, P., Scheiber, R., Reigber, A., Hajnsek, I., and Moreira, A. (2015, January 26\u201331). Polarimetric 3-D imaging with airborne holographic SAR tomography over glaciers. Proceedings of the 2015 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Milan, Italy.","DOI":"10.1109\/IGARSS.2015.7327026"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"4389","DOI":"10.1109\/JSTARS.2019.2951026","article-title":"Modeling the Vertical Backscattering Distribution in the Percolation Zone of the Greenland Ice Sheet With SAR Tomography","volume":"12","author":"Fischer","year":"2019","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote. Sens."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3839","DOI":"10.1109\/TGRS.2010.2048117","article-title":"Tomographic SAR Inversion by L1 -Norm Regularization\u2014The Compressive Sensing Approach","volume":"48","author":"Zhu","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1109\/TGRS.2010.2054099","article-title":"Three-Dimensional SAR Focusing From Multipass Signals Using Compressive Sampling","volume":"49","author":"Budillon","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1109\/MAES.2005.1499278","article-title":"Multibaseline cross-track SAR interferometry: A signal processing perspective","volume":"20","author":"Gini","year":"2005","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"5283","DOI":"10.1109\/TGRS.2012.2231081","article-title":"Wavelet-Based Compressed Sensing for SAR Tomography of Forested Areas","volume":"51","author":"Aguilera","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1454","DOI":"10.1109\/LGRS.2017.2709839","article-title":"Three-Dimensional Imaging of Objects Concealed Below a Forest Canopy Using SAR Tomography at L-Band and Wavelet-Based Sparse Estimation","volume":"14","author":"Huang","year":"2017","journal-title":"IEEE Geosci. Remote. Sens. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"5884","DOI":"10.3390\/s8095884","article-title":"Tomographic imaging of a forested area by airborne multi-baseline P-band SAR","volume":"8","author":"Frey","year":"2008","journal-title":"Sensors"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3074","DOI":"10.1109\/TGRS.2013.2269194","article-title":"Fully Polarimetric High-Resolution 3-D Imaging With Circular SAR at L-Band","volume":"52","author":"Ponce","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"6170","DOI":"10.1109\/TGRS.2016.2582959","article-title":"First Airborne Demonstration of Holographic SAR Tomography With Fully Polarimetric Multicircular Acquisitions at L-Band","volume":"54","author":"Ponce","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1844","DOI":"10.1109\/TGRS.2008.2007591","article-title":"Focusing of Airborne Synthetic Aperture Radar Data From Highly Nonlinear Flight Tracks","volume":"47","author":"Frey","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1109\/TGRS.2018.2864243","article-title":"SAR Processing Without a Motion Measurement System","volume":"57","author":"Torgrimsson","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_37","unstructured":"Cumming, I.G., Dettwiler, M., and Wong, F.H. (2004). Digital signal Processing of Synthetic Aperture Radar Data: Algorithms and Implementation, ArtechHouse."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1775","DOI":"10.1109\/TGRS.2015.2488358","article-title":"Phase Calibration of Airborne Tomographic SAR Data via Phase Center Double Localization","volume":"54","author":"Tebaldini","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"R1","DOI":"10.1088\/0266-5611\/14\/4\/001","article-title":"Synthetic aperture radar interferometry","volume":"14","author":"Bamler","year":"1998","journal-title":"Inverse Probl."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Tebaldini, S., Minh, D.H.T., d\u2019Alessandro, M.M., Villard, L., Le Toan, T., and Chave, J. (2019). The status of technologies to measure forest biomass and structural properties: State of the art in SAR tomography of tropical forests. Surv. Geophys., 1\u201323.","DOI":"10.1007\/s10712-019-09539-7"},{"key":"ref_41","unstructured":"Stoica, P., and Moses, R.L. (2005). Spectral Analysis of Signals, Prince-Hall."},{"key":"ref_42","first-page":"8","article-title":"Nvidia cuda c programming guide","volume":"120","author":"Nvidia","year":"2011","journal-title":"Nvidia Corp."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"3956","DOI":"10.1109\/JSTARS.2014.2330333","article-title":"Accelerating Time-Domain SAR Raw Data Simulation for Large Areas Using Multi-GPUs","volume":"7","author":"Zhang","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote. Sens."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.cageo.2019.04.010","article-title":"GPU accelerated interferometric SAR processing for Sentinel-1 TOPS data","volume":"129","author":"Yu","year":"2019","journal-title":"Comput. Geosci."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/10\/1638\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:30:49Z","timestamp":1760175049000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/10\/1638"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,20]]},"references-count":44,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2020,5]]}},"alternative-id":["rs12101638"],"URL":"https:\/\/doi.org\/10.3390\/rs12101638","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2020,5,20]]}}}