{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T15:17:49Z","timestamp":1771514269809,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2022,7,8]],"date-time":"2022-07-08T00:00:00Z","timestamp":1657238400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science","award":["62071231"],"award-info":[{"award-number":["62071231"]}]},{"name":"Natural Science","award":["61890541"],"award-info":[{"award-number":["61890541"]}]},{"name":"Natural Science","award":["61931021"],"award-info":[{"award-number":["61931021"]}]},{"name":"Natural Science","award":["BK20211571"],"award-info":[{"award-number":["BK20211571"]}]},{"name":"Natural Science","award":["30921011207"],"award-info":[{"award-number":["30921011207"]}]},{"DOI":"10.13039\/501100004608","name":"Jiangsu Province Natural Science Foundation","doi-asserted-by":"publisher","award":["62071231"],"award-info":[{"award-number":["62071231"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Jiangsu Province Natural Science Foundation","doi-asserted-by":"publisher","award":["61890541"],"award-info":[{"award-number":["61890541"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Jiangsu Province Natural Science Foundation","doi-asserted-by":"publisher","award":["61931021"],"award-info":[{"award-number":["61931021"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Jiangsu Province Natural Science Foundation","doi-asserted-by":"publisher","award":["BK20211571"],"award-info":[{"award-number":["BK20211571"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Jiangsu Province Natural Science Foundation","doi-asserted-by":"publisher","award":["30921011207"],"award-info":[{"award-number":["30921011207"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Research Funds for the Central Universities","award":["62071231"],"award-info":[{"award-number":["62071231"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["61890541"],"award-info":[{"award-number":["61890541"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["61931021"],"award-info":[{"award-number":["61931021"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["BK20211571"],"award-info":[{"award-number":["BK20211571"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["30921011207"],"award-info":[{"award-number":["30921011207"]}]},{"name":"Laboratory of Pinghu (Beijing Institute of infinite electric Measurement)","award":["62071231"],"award-info":[{"award-number":["62071231"]}]},{"name":"Laboratory of Pinghu (Beijing Institute of infinite electric Measurement)","award":["61890541"],"award-info":[{"award-number":["61890541"]}]},{"name":"Laboratory of Pinghu (Beijing Institute of infinite electric Measurement)","award":["61931021"],"award-info":[{"award-number":["61931021"]}]},{"name":"Laboratory of Pinghu (Beijing Institute of infinite electric Measurement)","award":["BK20211571"],"award-info":[{"award-number":["BK20211571"]}]},{"name":"Laboratory of Pinghu (Beijing Institute of infinite electric Measurement)","award":["30921011207"],"award-info":[{"award-number":["30921011207"]}]},{"name":"Science and Technology on Electromagnetic Scattering Laboratory","award":["62071231"],"award-info":[{"award-number":["62071231"]}]},{"name":"Science and Technology on Electromagnetic Scattering Laboratory","award":["61890541"],"award-info":[{"award-number":["61890541"]}]},{"name":"Science and Technology on Electromagnetic Scattering Laboratory","award":["61931021"],"award-info":[{"award-number":["61931021"]}]},{"name":"Science and Technology on Electromagnetic Scattering Laboratory","award":["BK20211571"],"award-info":[{"award-number":["BK20211571"]}]},{"name":"Science and Technology on Electromagnetic Scattering Laboratory","award":["30921011207"],"award-info":[{"award-number":["30921011207"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>A novel multi-parameter inversion method is proposed for the Advanced Integral Equation Model (AIEM) by using bi-directional deep neural network. There is a very complex nonlinear relationship between the surface parameters (dielectric constant and roughness) and radar backscattering coefficient. The traditional inverse neural network, which is constructed by using the backscattering coefficients as the input and the surface parameters as the output, leads to bad convergence and wrong results. This is because many sets of surface parameters can get the same backscattering coefficient. Therefore, the proposed bi-directional deep neural network starts with building an AIEM-based forward deep neural network (AIEM-FDNN), whose inputs are the surface parameters and outputs are the backscattering coefficients. In this way, the weights and biases of the forward deep neural network can be optimized and predicted, which can be used for the backward deep neural network (AIEM-BDNN). Then, the multi-parameters are updated by minimizing the loss between the output backscattering coefficients with the measured ones. By inserting a sigmoid function between the input and the first hidden layer, the input multi-parameters can be efficiently approximated and continuously updated. As a result, both the forward and backward deep neural networks can be built with these weights and biases. By sharing the weights and biases of the forward network, the training of the inverse network is avoided. The bi-directional deep neural network can not only predict the backscattering coefficient but can also inverse the surface parameters. Numerical results are given to demonstrate that the RMSE of the backscattering coefficients calculated by the proposed bi-directional neural network can be reduced to 0.1%. The accuracy of the inversion parameters, including the real and imaginary parts of the dielectric constant, the root mean square height and the correlation length, can be improved to 97.56%, 91.14%, 99.04% and 98.45%, respectively. At the same time, the bi-directional neural network also has good accuracy for the inversion of the POLARSCAT measured data.<\/jats:p>","DOI":"10.3390\/rs14143302","type":"journal-article","created":{"date-parts":[[2022,7,11]],"date-time":"2022-07-11T00:06:21Z","timestamp":1657497981000},"page":"3302","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Multi-Parameter Inversion of AIEM by Using Bi-Directional Deep Neural Network"],"prefix":"10.3390","volume":"14","author":[{"given":"Yu","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Communication Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zi","family":"He","sequence":"additional","affiliation":[{"name":"Department of Communication Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ying","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Communication Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dazhi","family":"Ding","sequence":"additional","affiliation":[{"name":"Department of Communication Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fan","family":"Ding","sequence":"additional","affiliation":[{"name":"China Ship Development and Design Centre, Wuhan 430064, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xun-Wang","family":"Dang","sequence":"additional","affiliation":[{"name":"Science and Technology on Electromagnetic Scattering Laboratory, Beijing 100089, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3106","DOI":"10.1016\/j.asr.2021.01.058","article-title":"Substitution of satellite-based land surface temperature defective data using GSP method","volume":"67","author":"Mohammad","year":"2021","journal-title":"Adv. Space Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4069","DOI":"10.1080\/01431161.2013.772309","article-title":"Monitoring soybean growth using L-, C- and X-band scatterometer data","volume":"34","author":"Kim","year":"2013","journal-title":"Int. J. Remote Sens."},{"key":"ref_3","first-page":"451","article-title":"Polarimetric SAR surface parameters inversion based on network","volume":"6","author":"Yang","year":"2002","journal-title":"J. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3931","DOI":"10.1109\/TGRS.2012.2228209","article-title":"Bare surface soil moisture estimation using double-angle and dual-polarization L-band radar data","volume":"51","author":"Shen","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2004113","DOI":"10.1109\/TGRS.2021.3139669","article-title":"Computation of backscattered fields in polarimetric SAR imaging simulation of complex targets","volume":"60","author":"Chiang","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"078002","DOI":"10.1117\/1.2752180","article-title":"Modified Beckmann-Kirchhoff scattering model for rough surface with large incident and scattering angles","volume":"46","author":"Sancer","year":"2007","journal-title":"Opt. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1121\/1.398342","article-title":"The validity of the perturbation approximation for rough surface scattering using a Gaussian roughness spectrum","volume":"86","author":"Thorsos","year":"1989","journal-title":"Acoust. Soc. Am."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1364\/JOSAA.7.001185","article-title":"Scattering from slightly rough random surfaces: A detailed study on the validity of the small perturbation method","volume":"7","author":"VesPerinas","year":"1990","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1088\/0959-7174\/13\/2\/306","article-title":"A study of the higher-order small-slope approximation for scattering from a Gaussian rough surface","volume":"13","author":"Gilbert","year":"2003","journal-title":"Waves Random Media"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"131","DOI":"10.2528\/PIER07030806","article-title":"The small-slope approximation method applied to a three-dimensional slab with rough boundaries","volume":"73","author":"Berginc","year":"2007","journal-title":"Prog. Electromagn. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3219","DOI":"10.1109\/TGRS.2006.879544","article-title":"Imaging simulation of po-larimetric SAR for a comprehensive terrain scene using the mapping and projection algorithm","volume":"44","author":"Xu","year":"2006","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1696","DOI":"10.1109\/TGRS.2016.2629759","article-title":"A comprehensive analysis of rough soil surface scattering and emission predicted by AIEM with comparison to numerical simulations and experimental measurements","volume":"55","author":"Zeng","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1109\/TGRS.2002.807587","article-title":"Emission of rough surfaces calculated by the integral equation method with comparison to three-dimensional moment method simulations","volume":"41","author":"Chen","year":"2003","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1223","DOI":"10.1080\/01431169008955090","article-title":"Michigan microwave canopy scattering model","volume":"11","author":"Ulaby","year":"1990","journal-title":"Int. J. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1109\/36.406677","article-title":"Measuring soil moisture with imaging radars","volume":"33","author":"Dubois","year":"1995","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1109\/TGRS.2003.821065","article-title":"Quantitative retrieval of soil moisture content and surface roughness from multipolarized radar observations of bere soil surfaces","volume":"42","author":"Oh","year":"2004","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","first-page":"77","article-title":"Inverse calculation of hydrogeological parameters in Henan based on improved genetic algorithm","volume":"41","author":"Zhao","year":"2019","journal-title":"Ground Water"},{"key":"ref_18","first-page":"577","article-title":"Parameter inversion of rough surface optimization based on multiple algorithms for SVM","volume":"36","author":"Wang","year":"2019","journal-title":"Chin. J. Comput. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"eaar4206","DOI":"10.1126\/sciadv.aar4206","article-title":"Nanophotonic particle simulation and inverse design using artificial neural networks","volume":"4","author":"Peurifoy","year":"2018","journal-title":"Sci. Adv."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1905467","DOI":"10.1002\/adma.201905467","article-title":"A bidirectional deep neural network for accurate silicon color design","volume":"31","author":"Li","year":"2019","journal-title":"Adv. Mater."},{"key":"ref_21","first-page":"136","article-title":"Deep learning as applied in SAR target recognition and terrain classification","volume":"6","author":"Xu","year":"2017","journal-title":"J. Radars"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1007\/s12524-018-0891-y","article-title":"Ship classification in SAR images using a new hybrid CNN-MLP classifier","volume":"47","author":"Sharifzadeh","year":"2019","journal-title":"J. Indian Soc. Remote Sens."},{"key":"ref_23","first-page":"364","article-title":"Convolutional Neural Network with Data Augmentation for SAR Target Recognition","volume":"13","author":"Ding","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4901","DOI":"10.1109\/TGRS.2020.2968493","article-title":"Parameter extraction based on deep neural network for SAR target simulation","volume":"58","author":"Niu","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1109\/36.134086","article-title":"An empirical model and inversion technique for radar scattering from bare soil surfaces","volume":"30","author":"Oh","year":"1992","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Yang, Y., Chen, K.S., and Shang, G.F. (2019). Surface parameters retrieval from fully bistatic radar scattering data. Remote Sens., 11.","DOI":"10.3390\/rs11050596"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Chen, K.S. (2021). Radar Scattering and Imaging of Rough Surfaces, CRC Press. [1st ed.].","DOI":"10.1201\/9781351011570"},{"key":"ref_28","first-page":"4740","article-title":"Depolarized backscattering of rough surface by AIEM model","volume":"10","author":"Yang","year":"2017","journal-title":"IEEE J. Sel. Top. Appl. Earth Sci. Remote Sens."},{"key":"ref_29","first-page":"79","article-title":"The effective permittivity and roughness parameters inversion by the land backscattering measured data","volume":"31","author":"Zhang","year":"2016","journal-title":"Chin. J. Radio Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1515\/nanoph-2019-0474","article-title":"Deep learning enable inverse design in nanophotonics","volume":"9","author":"So","year":"2020","journal-title":"Nanophotonics"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2521","DOI":"10.1364\/OE.413079","article-title":"Neural network enabled metasurface design for phase manipulation","volume":"29","author":"Li","year":"2021","journal-title":"Opt. 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