{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T06:21:39Z","timestamp":1769840499066,"version":"3.49.0"},"reference-count":51,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2023,10,1]],"date-time":"2023-10-01T00:00:00Z","timestamp":1696118400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62176247"],"award-info":[{"award-number":["62176247"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2020-JCJQ-ZD-057-00"],"award-info":[{"award-number":["2020-JCJQ-ZD-057-00"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Research Funds for the Central Universities","award":["62176247"],"award-info":[{"award-number":["62176247"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["2020-JCJQ-ZD-057-00"],"award-info":[{"award-number":["2020-JCJQ-ZD-057-00"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Polarimetric synthetic aperture radar (PolSAR) image classification has been an important area of research due to its wide range of applications. Traditional machine learning methods were insufficient in achieving satisfactory results before the advent of deep learning. Results have significantly improved with the widespread use of deep learning in PolSAR image classification. However, the challenge of reconciling the complex-valued inputs of PolSAR images with the real-valued models of deep learning remains unsolved. Current complex-valued deep learning models treat complex numbers as two distinct real numbers, providing limited assistance in PolSAR image classification results. This paper proposes a novel, complex-valued deep learning approach for PolSAR image classification to address this issue. The approach includes amplitude-based max pooling, complex-valued nonlinear activation, and a cross-entropy loss function based on complex-valued probability. Amplitude-based max pooling reduces computational effort while preserving the most valuable complex-valued features. Complex-valued nonlinear activation maps feature into a high-dimensional complex-domain space, producing the most discriminative features. The complex-valued cross-entropy loss function computes the classification loss using the complex-valued model output and dataset labels, resulting in more accurate and robust classification results. The proposed method was applied to a shallow CNN, deep CNN, FCN, and SegNet, and its effectiveness was verified on three public datasets. The results showed that the method achieved optimal classification results on any model and dataset.<\/jats:p>","DOI":"10.3390\/rs15194801","type":"journal-article","created":{"date-parts":[[2023,10,2]],"date-time":"2023-10-02T04:28:08Z","timestamp":1696220888000},"page":"4801","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["A New Architecture of a Complex-Valued Convolutional Neural Network for PolSAR Image Classification"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1966-8727","authenticated-orcid":false,"given":"Yihui","family":"Ren","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing 101400, China"}]},{"given":"Wen","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, North China University of Technology, Beijing 100144, China"}]},{"given":"Ying","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing 101400, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,1]]},"reference":[{"key":"ref_1","unstructured":"Lee, J.S., and Pottier, E. (2011). Polarimetric Radar Imaging: From Basic to Application, CRC Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.isprsjprs.2017.11.022","article-title":"Skipping the real world: Classification of PolSAR images without explicit feature extraction","volume":"140","author":"Hellwich","year":"2018","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2299","DOI":"10.1080\/01431169408954244","article-title":"Classification of multi-look polarimetric SAR imagery based on the complex Wishart distribution","volume":"15","author":"Lee","year":"1994","journal-title":"Int. J. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"722","DOI":"10.1109\/TGRS.2003.819883","article-title":"Unsupervised terrain classification preserving polarimetric scattering characteristics","volume":"42","author":"Lee","year":"2004","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4200","DOI":"10.1109\/TGRS.2012.2227755","article-title":"An unsupervised classification approach for polarimetric SAR data based on the Chernoff distance for the complex Wishart distribution","volume":"51","author":"Dabboor","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"668","DOI":"10.1109\/LGRS.2008.2002263","article-title":"Region-based classification of polarimetric SAR images using Wishart MRF","volume":"5","author":"Wu","year":"2008","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"905","DOI":"10.1109\/TGRS.2017.2756621","article-title":"Mixture WG\u0393-MRF model for PolSAR image classification","volume":"56","author":"Song","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1104","DOI":"10.1109\/TGRS.2010.2076285","article-title":"Adaptive model-based decomposition of polarimetric SAR covariance matrices","volume":"49","author":"Arii","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1109\/36.551935","article-title":"An entropy based classification scheme for land applications of polarimetric SAR","volume":"35","author":"Clound","year":"1997","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1109\/36.485127","article-title":"A review of target decomposition theorems in radar polarimetry","volume":"34","author":"Cloude","year":"1996","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2732","DOI":"10.1109\/TGRS.2010.2041242","article-title":"Three-Component Model-Based Decomposition for Polarimetric SAR Data","volume":"48","author":"An","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4576","DOI":"10.1109\/TGRS.2012.2236338","article-title":"Texture Classification of PolSAR Data Based on Sparse Coding of Wavelet Polarization Textons","volume":"51","author":"He","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4143","DOI":"10.1109\/TGRS.2009.2023908","article-title":"Support vector machine for multifrequency SAR polarimetric data classification","volume":"47","author":"Lardeux","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1109\/36.823921","article-title":"An explicit fuzzy supervised classification method for multispectral remote sensing images","volume":"38","author":"Melgani","year":"2000","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1080\/10106049009354274","article-title":"Radar polaritnetry for geoscience applications","volume":"5","author":"Ulaby","year":"1990","journal-title":"Geocarto Int."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1109\/36.673687","article-title":"A three-component scattering model for polarimetric SAR data","volume":"36","author":"Freeman","year":"1998","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","unstructured":"Huynen, J.R. (2022, April 14). Phenomenological Theory of Radar Targets. Available online: http:\/\/resolver.tudelft.nl\/uuid:e4a140a0-c175-45a7-ad41-29b28361b426."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1109\/JSTARS.2017.2752282","article-title":"A Novel Technique Based on Deep Learning and a Synthetic Target Database for Classification of Urban Areas in PolSAR Data","volume":"11","author":"De","year":"2018","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1935","DOI":"10.1109\/LGRS.2016.2618840","article-title":"Polarimetric SAR image classification using deep convolutional neural networks","volume":"13","author":"Zhou","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2116","DOI":"10.1109\/TGRS.2018.2871504","article-title":"A Graph-Based Semisupervised Deep Learning Model for PolSAR Image Classification","volume":"57","author":"Bin","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Li, Y., Chen, Y., Liu, G., and Jiao, L. (2018). A novel deep fully convolutional network for PolSAR image classification. Remote Sens., 10.","DOI":"10.3390\/rs10121984"},{"key":"ref_22","unstructured":"Pham, M., and Lefevre, S. (April, January 29). Very high resolution Airborne PolSAR Image Classification using Convolutional Neural Networks. Proceedings of the 13th European Conference on Synthetic Aperture Radar (EUSAR 2021), Online."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1580","DOI":"10.1109\/LGRS.2020.3005076","article-title":"Active Ensemble Deep Learning for Polarimetric Synthetic Aperture Radar Image Classification","volume":"18","author":"Liu","year":"2021","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_24","first-page":"1","article-title":"PolSAR Image Classification with Multiscale Superpixel-Based Graph Convolutional Network","volume":"60","author":"Cheng","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"100794","DOI":"10.1016\/j.swevo.2020.100794","article-title":"Multiobjective evolutionary algorithm assisted stacked autoencoder for PolSAR image classification","volume":"60","author":"Liu","year":"2021","journal-title":"Swarm Evol. Comput."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"10716","DOI":"10.1109\/JSTARS.2021.3116062","article-title":"PSRN: Polarimetric Space Reconstruction Network for PolSAR Image Semantic Segmentation","volume":"14","author":"Jing","year":"2021","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_27","first-page":"1","article-title":"A Deep Reinforcement Learning-Based Framework for PolSAR Imagery Classification","volume":"60","author":"Nie","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_28","first-page":"1","article-title":"N-Cluster Loss and Hard Sample Generative Deep Metric Learning for PolSAR Image Classification","volume":"60","author":"Yang","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"9224","DOI":"10.1109\/TGRS.2020.3048967","article-title":"A Mutual Information-Based Self-Supervised Learning Model for PolSAR Land Cover Classification","volume":"59","author":"Ren","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1109\/36.312890","article-title":"Intensity and phase statistics of multilook polarimetric and interferometric SAR imagery","volume":"32","author":"Lee","year":"1994","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"464","DOI":"10.1016\/j.isprsjprs.2008.12.008","article-title":"Classification comparisons between dual-pol, compact polarimetric and quad-pol SAR imagery","volume":"64","author":"Ainsworth","year":"2009","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"936","DOI":"10.1109\/JSTARS.2012.2192915","article-title":"Classification accuracy of multi-frequency and multi-polarization SAR images for various land covers","volume":"5","author":"Turkar","year":"2012","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1109\/82.142037","article-title":"Complex domain backpropagation","volume":"39","author":"Georgiou","year":"1992","journal-title":"IEEE Trans. Circuits Syst. II Analog Digital Signal Process."},{"key":"ref_34","unstructured":"Trabelsi, C., Bilaniuk, O., Zhang, Y., Serdyuk, D., Subramanian, S., Santos, J., Mehri, S., Rostamzadeh, N., Bengio, Y., and Pal, C. (May, January 30). Deep complex networks. Proceedings of the International Conference on Learning Representations (ICLR2018), Vancouver, BC, Canada."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"7177","DOI":"10.1109\/TGRS.2017.2743222","article-title":"Complex-Valued Convolutional Neural Network and Its Application in Polarimetric SAR Image Classification","volume":"55","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"107110","DOI":"10.1016\/j.patcog.2019.107110","article-title":"Complex Contourlet-CNN for polarimetric SAR image classification","volume":"100","author":"Li","year":"2020","journal-title":"Pattern Recognit."},{"key":"ref_37","unstructured":"Xiao, D., Liu, C., Wang, Q., Wang, C., and Zhang, X. (2020). PolSAR Image Classification Based on Dilated Convolution and Pixel-Refining Parallel Mapping network in the Complex Domain. arXiv."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"10116","DOI":"10.1109\/TGRS.2019.2931620","article-title":"Contrastive-Regulated CNN in the Complex Domain: A Method to Learn Physical Scattering Signatures From Flexible PolSAR Images","volume":"57","author":"Zhao","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1022","DOI":"10.1109\/LGRS.2019.2940387","article-title":"Complex-Valued 3-D Convolutional Neural Network for PolSAR Image Classification","volume":"17","author":"Tan","year":"2020","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1713","DOI":"10.1109\/TAES.2021.3050648","article-title":"PolSAR Image Classification Using Hybrid Conditional Random Fields Model Based on Complex-Valued 3-D CNN","volume":"57","author":"Zhang","year":"2021","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Qin, X., Hu, T., Zou, H., Yu, W., and Wang, P. (August, January 28). Polsar Image Classification via Complex-Valued Convolutional Neural Network Combining Measured Data and Artificial Features. Proceedings of the 2019 IEEE International Geoscience and Remote Sensing Symposium (IGARSS2019), Yokohama, Japan.","DOI":"10.1109\/IGARSS.2019.8898978"},{"key":"ref_42","first-page":"1","article-title":"PolSAR Image Classification Based on Complex-Valued Convolutional Long Short-Term Memory Network","volume":"19","author":"Fang","year":"2022","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"10179","DOI":"10.1109\/TGRS.2021.3053013","article-title":"Deep Triplet Complex-Valued Network for PolSAR Image Classification","volume":"59","author":"Tan","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1080\/21642583.2015.1108885","article-title":"The paradigm of complex probability and the Brownian motion","volume":"3","author":"Abdo","year":"2015","journal-title":"Syst. Sci. Control Eng."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1080\/21642583.2016.1185044","article-title":"The paradigm of complex probability and Chebyshev\u2019s inequality","volume":"4","author":"Abdo","year":"2016","journal-title":"Syst. Sci. Control Eng."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1080\/21642583.2017.1367970","article-title":"The paradigm of complex probability and Claude Shannon\u2019s information theory","volume":"5","author":"Abdo","year":"2017","journal-title":"Syst. Sci. Control Eng."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1080\/21642583.2018.1471427","article-title":"The paradigm of complex probability and Ludwig Boltzmann\u2019s entropy","volume":"6","author":"Abdo","year":"2018","journal-title":"Syst. Sci. Control Eng."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1080\/21642583.2019.1691674","article-title":"The paradigm of complex probability and Monte Carlo methods","volume":"7","author":"Abdo","year":"2019","journal-title":"Syst. Sci. Control Eng."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.neucom.2020.01.020","article-title":"PolSAR image classification via a novel semi-supervised recurrent complex-valued convolution neural network","volume":"388","author":"Xie","year":"2020","journal-title":"Neurocomputing"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"108922","DOI":"10.1016\/j.asoc.2022.108922","article-title":"Spatial feature-based convolutional neural network for PolSAR image classification","volume":"123","author":"Shang","year":"2022","journal-title":"Appl. Soft Comput."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/LGRS.2022.3188257","article-title":"Attention-Based Multiscale Sequential Network for PolSAR Image Classification","volume":"19","author":"Hua","year":"2022","journal-title":"IEEE Geosci. Remote Sens. Lett."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/19\/4801\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:03:54Z","timestamp":1760130234000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/19\/4801"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,1]]},"references-count":51,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2023,10]]}},"alternative-id":["rs15194801"],"URL":"https:\/\/doi.org\/10.3390\/rs15194801","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,1]]}}}