{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T14:36:33Z","timestamp":1773930993285,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2018,11,30]],"date-time":"2018-11-30T00:00:00Z","timestamp":1543536000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006245","name":"Ministry of Science and Technology, Israel","doi-asserted-by":"publisher","award":["3-12473"],"award-info":[{"award-number":["3-12473"]}],"id":[{"id":"10.13039\/501100006245","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>A new method to invert X-band radar images for linear shoaling conditions is proposed. The commonly used approach for this type of inverse problems is the Fourier transform. Unlike in deep water conditions, in the shoaling region, waves are modulated both in terms of wavelength and amplitude. However, Fourier analysis assumes spacial and temporal periodicity, and homogeneity limiting its applicability to this region. In order to overcome these limitations, a wavelet based technique is developed. The proposed technique treats every spatial radar image within the time sequence individually, so no information on the dispersion relation is required. For validation purposes, surface elevation range-time shoaling realizations based on the mild slope equation are prepared. A radar imaging model including tilt and shadowing modulations, speckle noise, and the radar equation is applied to these realizations to provide modeled grazing incidence radar images. The inversion process starts with the application of the continuous wavelet transform independently for each spacial image. The procedure continues with employing a successive range independent modulation transfer function to the wavelet spectra in the wavenumber domain. Then, after a phase shift correction, an inverse continuous wavelet transform is applied. The procedure is finalized by a calibration of the retrieved maps. After the calibration, a thorough comparison between the original and the reconstructed surface elevations is performed. It shows high efficiency of the proposed method in treating wave number and amplitude modulated signals, as well as in addressing local phase shifts due to tilt modulation and noise contamination. The new inversion method is proven to have high accuracy in inhomogeneous conditions. It shows high potential to be implemented for individual wave reconstruction using real aperture radars.<\/jats:p>","DOI":"10.3390\/rs10121919","type":"journal-article","created":{"date-parts":[[2018,11,30]],"date-time":"2018-11-30T12:13:17Z","timestamp":1543579997000},"page":"1919","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Inversion of Nearshore X-Band Radar Images to Sea Surface Elevation Maps"],"prefix":"10.3390","volume":"10","author":[{"given":"Pavel","family":"Chernyshov","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Tel Aviv University, Tel Aviv 6997801, Israel"}]},{"given":"Teodor","family":"Vrecica","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Tel Aviv University, Tel Aviv 6997801, Israel"}]},{"given":"Yaron","family":"Toledo","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Tel Aviv University, Tel Aviv 6997801, Israel"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/S0378-3839(99)00032-0","article-title":"Use of nautical radar as a wave monitoring instrument","volume":"37","author":"Borge","year":"1999","journal-title":"Coast. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1049\/iet-rsn:20070027","article-title":"Signal-to-noise ratio analysis to estimate ocean wave heights from X-band marine radar image time series","volume":"2","author":"Hessner","year":"2008","journal-title":"IET Radar Sonar Navig."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2267","DOI":"10.1109\/TGRS.2008.916474","article-title":"Determination of bathymetric and current maps by the method DiSC based on the analysis of nautical X-band radar image sequences of the sea surface (November 2007)","volume":"46","author":"Senet","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"6522","DOI":"10.3390\/s100706522","article-title":"Bathymetry determination via X-band radar data: A new strategy and numerical results","volume":"10","author":"Serafino","year":"2010","journal-title":"Sensors"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"13697","DOI":"10.1029\/1998JC900029","article-title":"Rainfall measurements with navigational radar","volume":"104","author":"Lebedev","year":"1999","journal-title":"J. Geophys. Res. Ocean."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Dankert, H., Horstmann, J., and Rosenthal, W. (2003). Ocean wind fields retrieved from radar-image sequences. J. Geophys. Res., 108.","DOI":"10.1029\/2003JC002056"},{"key":"ref_7","unstructured":"Kanevsky, M.B. (2008). Radar Imaging of the Ocean Waves, Elsevier."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/BF00913863","article-title":"Theories for the interaction of electromagnetic and oceanic waves\u2014A review","volume":"13","author":"Valenzuela","year":"1978","journal-title":"Bound.-Layer Meteorol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1291","DOI":"10.1175\/1520-0426(2004)021<1291:IOMRIF>2.0.CO;2","article-title":"Inversion of marine radar images for surface wave analysis","volume":"21","author":"Borge","year":"2004","journal-title":"J. Atmos. Ocean. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1016\/j.oceaneng.2015.04.041","article-title":"Significant wave height estimation using SVR algorithms and shadowing information from simulated and real measured X-band radar images of the sea surface","volume":"101","author":"Borge","year":"2015","journal-title":"Ocean Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/BF00913873","article-title":"The two-frequency microwave technique for measuring ocean-wave spectra from an airplane or satellite","volume":"13","author":"Alpers","year":"1978","journal-title":"Bound.-Layer Meteorol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"68","DOI":"10.21046\/2070-7401-2016-13-5-68-78","article-title":"Accuracy analysis of individual waves retrieval from X-band radar brightness images by implementation of stochastic modeling of rough sea surface","volume":"13","author":"Chernyshov","year":"2016","journal-title":"Sovremmennie Probl. Distansionnogo Zondirovaniya Zemli Iz Kosmosa"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Wei, Y., Zhang, J.K., and Lu, Z. (2016). A Novel Successive Cancellation Method to Retrieve Sea Wave Components from Spatio-Temporal Remote Sensing Image Sequences. Remote Sens., 8.","DOI":"10.3390\/rs8070607"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"961","DOI":"10.1109\/18.57199","article-title":"The wavelet transform, time-frequency localization and signal analysis","volume":"36","author":"Daubechies","year":"1990","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"8779","DOI":"10.1080\/01431161.2010.534511","article-title":"Ocean remotely sensed image analysis using two-dimensional continuous wavelet transforms","volume":"32","author":"Wu","year":"2011","journal-title":"Int. J. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1109\/TGRS.2014.2325782","article-title":"A self-adaptive wavelet-based algorithm for wave measurement using nautical radar","volume":"53","author":"An","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.1016\/j.oceaneng.2008.02.008","article-title":"Two-dimensional continuous wavelet transform of simulated spatial images of waves on a slowly varying topography","volume":"35","author":"Chuang","year":"2008","journal-title":"Ocean Eng."},{"key":"ref_18","unstructured":"Doong, D.J., Wu, L.C., Kao, C.C., Chuang, H., and Zsu, L. (2003, January 25\u201330). Wavelet spectrum extracted from coastal marine radar images. Proceedings of the The Thirteenth International Offshore and Polar Engineering Conference, Honolulu, HI, USA."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3011","DOI":"10.1109\/JSTARS.2014.2321048","article-title":"Remocean system for the detection of the reflected waves from the costa concordia ship wreck","volume":"7","author":"Ludeno","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Dean, R.G., and Dalrymple, R.A. (1991). Water Wave Mechanics for Engineers and Scientists, World Scientific Publishing Co Inc.","DOI":"10.1142\/9789812385512"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/0378-3839(93)90054-C","article-title":"Nonlinear evolution of a unidirectional shoaling wave field","volume":"20","author":"Agnon","year":"1993","journal-title":"Coast. Eng."},{"key":"ref_22","unstructured":"Hasselmann, K., Barnett, T., Bouws, E., Carlson, H., Cartwright, D., Enke, K., Ewing, J., Gienapp, H., Hasselmann, D., and Kruseman, P. (1973). Measurements of Wind-Wave Growth and Swell Decay During the Joint North Sea Wave Project (JONSWAP), Deutches Hydrographisches Institut. Technical Report."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Daubechies, I. (1992). Ten Lectures on Wavelets, SIAM.","DOI":"10.1137\/1.9781611970104"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"6481","DOI":"10.1029\/JC086iC07p06481","article-title":"On the detectability of ocean surface waves by real and synthetic aperture radar","volume":"86","author":"Alpers","year":"1981","journal-title":"J. Geophys. Res. Ocean."},{"key":"ref_25","unstructured":"Skolnik, M.I. (1970). Radar Handbook, McGraw-Hill Book Co."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/2012JC007912","article-title":"Wave shadowing and modulation of microwave backscatter from the ocean","volume":"117","author":"Plant","year":"2012","journal-title":"J. Geophys. Res. Ocean."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3373","DOI":"10.1109\/TGRS.2013.2272701","article-title":"An algorithm for estimation of wave height from shadowing in X-band radar sea surface images","volume":"52","author":"Gangeskar","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1080\/07038992.2016.1177450","article-title":"Comparison of Wave Height Measurement Algorithms for Ship-Borne X-Band Nautical Radar","volume":"42","author":"Liu","year":"2016","journal-title":"Canadian J. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Forouzanfar, M., Moghaddam, H.A., and Dehghani, M. (2007, January 11\u201313). Speckle reduction in medical ultrasound images using a new multiscale bivariate Bayesian MMSE-based method. Proceedings of the IEEE 15th Signal Processing and Communications Applications, Eskisehir, Turkey.","DOI":"10.1109\/SIU.2007.4298552"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"668","DOI":"10.1109\/TAP.1967.1138991","article-title":"Geometrical shadowing of a random rough surface","volume":"15","author":"Smith","year":"1967","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_31","unstructured":"Bass, F., and Fuks, I. (2013). Wave Scattering from Statistically Rough Surfaces: International Series in Natural Philosophy, Elsevier."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Naaijen, P., and Blondel-Couprie, E. (2012, January 1\u20136). Reconstruction and Prediction of Short-Crested Seas Based on the Application of a 3D-FFT on Synthetic Waves. Part 1: Reconstruction. Proceedings of the ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering, Rio de Janeiro, Brazil.","DOI":"10.1115\/OMAE2012-83093"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Blondel-Couprie, E., and Naaijen, P. (2012, January 1\u20136). Reconstruction and Prediction of Short-Crested Seas Based on the Application of a 3D-FFT on Synthetic Waves. Part 2: Prediction. Proceedings of the ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering, Rio de Janeiro, Brazil.","DOI":"10.1115\/OMAE2012-83096"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/S0378-3839(00)00019-3","article-title":"Analysis of directional wave fields using X-band navigation radar","volume":"40","year":"2000","journal-title":"Coast. Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1132","DOI":"10.1007\/s00343-015-4147-1","article-title":"A new modulation transfer function for ocean wave spectra retrieval from X-band marine radar imagery","volume":"33","author":"Chen","year":"2015","journal-title":"Chin. J. Oceanol. Limnol."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/12\/1919\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:33:34Z","timestamp":1760196814000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/12\/1919"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,30]]},"references-count":35,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2018,12]]}},"alternative-id":["rs10121919"],"URL":"https:\/\/doi.org\/10.3390\/rs10121919","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,30]]}}}