{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:52:59Z","timestamp":1760241179606,"version":"build-2065373602"},"reference-count":52,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T00:00:00Z","timestamp":1575244800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61801018"],"award-info":[{"award-number":["61801018"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Advance Research Program","award":["6140452010101"],"award-info":[{"award-number":["6140452010101"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The scattering transform, which applies multiple convolutions using known filters targeting different scales of time or frequency, has a strong similarity to the structure of convolution neural networks (CNNs), without requiring training to learn the convolution filters, and has been used for hyperspectral image classification in recent research. This paper investigates the application of the scattering transform framework to hyperspectral unmixing (STFHU). While state-of-the-art research on unmixing hyperspectral data utilizing scattering transforms is limited, the proposed end-to-end method applies pixel-based scattering transforms and preliminary three-dimensional (3D) scattering transforms to hyperspectral images in the remote sensing scenario to extract feature vectors, which are then trained by employing the regression model based on the k-nearest neighbor (k-NN) to estimate the abundance of maps of endmembers. Experiments compare performances of the proposed algorithm with a series of existing methods in quantitative terms based on both synthetic data and real-world hyperspectral datasets. Results indicate that the proposed approach is more robust to additive noise, which is suppressed by utilizing the rich information in both high-frequency and low-frequency components represented by the scattering transform. Furthermore, the proposed method achieves higher accuracy for unmixing using the same amount of training data with all comparative approaches, while achieving equivalent performance to the best performing CNN method but using much less training data.<\/jats:p>","DOI":"10.3390\/rs11232868","type":"journal-article","created":{"date-parts":[[2019,12,3]],"date-time":"2019-12-03T04:58:39Z","timestamp":1575349119000},"page":"2868","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Scattering Transform Framework for Unmixing of Hyperspectral Data"],"prefix":"10.3390","volume":"11","author":[{"given":"Yiliang","family":"Zeng","sequence":"first","affiliation":[{"name":"Department of Instrument Science and Technology, School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China"},{"name":"Beijing Engineering Research Center of Industrial Spectrum Imaging, Beijing 100083, China"},{"name":"School of Electrical, Computer and Telecommunication Engineering, University of Wollongong, Wollongong 2500, Australia"}]},{"given":"Christian","family":"Ritz","sequence":"additional","affiliation":[{"name":"School of Electrical, Computer and Telecommunication Engineering, University of Wollongong, Wollongong 2500, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4243-2277","authenticated-orcid":false,"given":"Jiahong","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Electrical, Computer and Telecommunication Engineering, University of Wollongong, Wollongong 2500, Australia"}]},{"given":"Jinhui","family":"Lan","sequence":"additional","affiliation":[{"name":"Department of Instrument Science and Technology, School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China"},{"name":"Beijing Engineering Research Center of Industrial Spectrum Imaging, Beijing 100083, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1109\/MGRS.2013.2244672","article-title":"Hyperspectral remote sensing data analysis and future challenge","volume":"1","author":"Plaza","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1844","DOI":"10.1109\/JSTARS.2014.2320576","article-title":"A review of nonlinear hyperspectral unmixing methods","volume":"7","author":"Heylen","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"5987","DOI":"10.1109\/TIP.2016.2618002","article-title":"A spatial compositional model for linear unmixing and endmember uncertainty estimation","volume":"25","author":"Zhou","year":"2016","journal-title":"IEEE Trans. Image Process."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Wang, S., Huang, T.-Z., Zhao, X.-L., Liu, G., and Cheng, Y. (2018). Double Reweighted Sparse Regression and Graph Regularization for Hyperspectral Unmixing. Remote Sens., 10.","DOI":"10.3390\/rs10071046"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1109\/TGRS.2018.2861992","article-title":"Hyperspectral Image Classification in the Presence of Noisy Labels","volume":"57","author":"Jiang","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1232","DOI":"10.1109\/TAES.2003.1261124","article-title":"Automatic spectral target recognition in hyperspectral imagery","volume":"39","author":"Ren","year":"2003","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1109\/TGRS.2003.822750","article-title":"Wavelet-based feature extraction for improved endmember abundance estimation in linear unmixing of hyperspectral signals","volume":"42","author":"Li","year":"2004","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Ghaffari, O., Zoej, M.J.V., and Mokhtarzade, M. (2017). Reducing the effect of the endmembers\u2019 spectral variability by selecting the optimal spectral bands. Remote Sens., 9.","DOI":"10.3390\/rs9090884"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Zou, J., Lan, J., and Shao, Y. (2018). A Hierarchical Sparsity Unmixing Method to Address Endmember Variability in Hyperspectral Image. Remote Sens., 10.","DOI":"10.3390\/rs10050738"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4267","DOI":"10.1109\/JSTARS.2016.2519498","article-title":"Sparsity-Regularized Robust Non-Negative Matrix Factorization for Hyperspectral Unmixing","volume":"9","author":"He","year":"2016","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Bioucas-Dias, J.M., and Figueiredo, M.A. (2010, January 14\u201316). Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing. Proceedings of the 2nd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, Reykjavik, Iceland.","DOI":"10.1109\/WHISPERS.2010.5594963"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/79.974727","article-title":"Spectral unmixing","volume":"19","author":"Keshava","year":"2002","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3890","DOI":"10.1109\/TIP.2016.2579259","article-title":"Blind hyperspectral unmixing using an extended linear mixing model to address spectral variability","volume":"25","author":"Drumetz","year":"2016","journal-title":"IEEE Trans. Image Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/j.rse.2006.01.006","article-title":"Estimation of yellow starthistle abundance through CASI-2 hyperspectral imagery using linear spectral mixture models","volume":"101","author":"Miao","year":"2006","journal-title":"Remote Sens. Environ."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1403","DOI":"10.1109\/TIP.2010.2042993","article-title":"Bayesian estimation of linear mixtures using the normal compositional model. Application to hyperspectral imagery","volume":"19","author":"Eches","year":"2010","journal-title":"IEEE Trans. Image Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1109\/36.911111","article-title":"Fully constrained least squares linear mixture analysis for material quantificationin in hyperspectral imagery","volume":"39","author":"Heinz","year":"2001","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"5067","DOI":"10.1109\/TGRS.2015.2417162","article-title":"Minimum volume simplex analysis: A fast algorithm for linear hyperspectral unmixing","volume":"53","author":"Li","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3558","DOI":"10.1109\/TGRS.2012.2225841","article-title":"Geometric method of fully constrained least squares linear spectral mixture analysis","volume":"51","author":"Wang","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Yang, B., Wang, B., and Wu, Z. (2018). Unsupervised Nonlinear Hyperspectral Unmixing Based on Bilinear Mixture Models via Geometric Projection and Constrained Nonnegative Matrix Factorization. Remote Sens., 10.","DOI":"10.3390\/rs10050801"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1109\/MSP.2013.2279274","article-title":"Nonlinear unmixing of hyperspectral images: Models and algorithms","volume":"31","author":"Dobigeon","year":"2014","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Shao, Y., Lan, J., Zhang, Y., and Zou, J. (2018). Spectral Unmixing of Hyperspectral Remote Sensing Imagery via Preserving the Intrinsic Structure Invariant. Sensors, 18.","DOI":"10.3390\/s18103528"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4153","DOI":"10.1109\/TGRS.2010.2098414","article-title":"Nonlinear unmixing of hyperspectral images using a generalized bilinear model","volume":"49","author":"Halimi","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Zou, J., and Lan, J. (2019). A Multiscale Hierarchical Model for Sparse Hyperspectral Unmixing. Remote Sens., 11.","DOI":"10.3390\/rs11050500"},{"key":"ref_24","first-page":"491","article-title":"Relating the land-cover composition of mixed pixels to artificial neural network classification output","volume":"5","author":"Foody","year":"1996","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4163","DOI":"10.1109\/TGRS.2011.2160950","article-title":"Pixel unmixing in hyperspectral data by means of neural networks","volume":"49","author":"Licciardi","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Guo, R., Wang, W., and Qi, H. (2015, January 2\u20135). Hyperspectral image unmixing using autoencoder cascade. Proceedings of the 7th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, (WHISPERS), Tokyo, Japan.","DOI":"10.1109\/WHISPERS.2015.8075378"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"25646","DOI":"10.1109\/ACCESS.2018.2818280","article-title":"Hyperspectral unmixing using a neural network autoencoder","volume":"6","author":"Palsson","year":"2018","journal-title":"IEEE Access"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1427","DOI":"10.1109\/LGRS.2018.2841400","article-title":"Stacked nonnegative sparse autoencoders for robust hyperspectral unmixing","volume":"15","author":"Su","year":"2018","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1755","DOI":"10.1109\/LGRS.2018.2857804","article-title":"Hyperspectral unmixing via deep convolutional neural networks","volume":"15","author":"Zhang","year":"2018","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.neucom.2018.05.051","article-title":"CNN based sub-pixel mapping for hyperspectral images","volume":"311","author":"Arun","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_31","unstructured":"Bouvrie, J., Rosasco, L., and Poggio, T. (2009). On invariance in hierarchical models. Advances in Neural Information Processing Systems, MIT Press."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Bruna, J., and Mallat, S. (2011, January 20\u201325). Classification with scattering operators. Proceedings of the CVPR 2011, Providence, RI, USA.","DOI":"10.1109\/CVPR.2011.5995635"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Oyallon, E., Belilovsky, E., and Zagoruyko, S. (2017, January 22\u201329). Scaling the scattering transform: Deep hybrid networks. Proceedings of the IEEE International Conference on Computer Vision (ICCV), Venice, Italy.","DOI":"10.1109\/ICCV.2017.599"},{"key":"ref_34","unstructured":"Pontus, W. (2019, August 25). Wavelets, Scattering Transforms and Convolutional Neural Networks, Tools for Image Processing. Available online: https:\/\/pdfs.semanticscholar.org\/c354\/c467d126e05f63c43b5ab2af9d0c652dfe3e.pdf."},{"key":"ref_35","unstructured":"And\u00e9n, J., and Mallat, S. (2011, January 24\u201328). Multiscale Scattering for Audio Classification. Proceedings of the ISMIR 2011, Miami, FL, USA."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1331","DOI":"10.1002\/cpa.21413","article-title":"Group invariant scattering","volume":"65","author":"Mallat","year":"2012","journal-title":"Commun. Pure Appl. Math."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"20150203","DOI":"10.1098\/rsta.2015.0203","article-title":"Understanding deep convolutional networks","volume":"374","author":"Mallat","year":"2016","journal-title":"Philos. Trans. R. Soc."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Czaja, W., Kavalerov, I., and Li, W. (2018). Scattering Transforms and Classification of Hyperspectral Images. Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XXIV, International Society for Optics and Photonics.","DOI":"10.1117\/12.2305152"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2467","DOI":"10.1109\/TGRS.2014.2360672","article-title":"Hyperspectral image classification based on three-dimensional scattering wavelet transform","volume":"53","author":"Tang","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_40","unstructured":"Ilya, K., Li, W., Czaja, W., and Chellappa, R. (2019, September 12). Three Dimensional Scattering Transform and Classification of Hyperspectral Images. Available online: https:\/\/arxiv.org\/pdf\/1906.06804.pdf."},{"key":"ref_41","unstructured":"(2019, August 10). USGS Digital Spectral Library, Available online: http:\/\/speclab.cr.usgs.gov\/spectral-lib.html."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1109\/TGRS.2006.888466","article-title":"Endmember extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization","volume":"45","author":"Miao","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_43","unstructured":"(2019, August 10). Hyperspectral Unmixing Datasets & Ground Truths. Available online: http:\/\/www.escience.cn\/people\/feiyunZHU\/Dataset_GT.html."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.isprsjprs.2013.11.014","article-title":"Structured sparse method for hyperspectral unmixing","volume":"88","author":"Zhu","year":"2014","journal-title":"ISPRS J. Photogram. Remote Sens."},{"key":"ref_45","unstructured":"(2019, July 20). TensorFlow Software. Available online: https:\/\/www.tensorflow.org."},{"key":"ref_46","unstructured":"(2019, July 20). Scikit-Learn Software. Available online: https:\/\/scikit-learn.org."},{"key":"ref_47","unstructured":"(2019, July 20). Keras Software. Available online: https:\/\/keras.io."},{"key":"ref_48","first-page":"13","article-title":"Research progress on unmixing of hyperspectral remote sensing imagery","volume":"22","author":"Lan","year":"2018","journal-title":"J. Remote Sens."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"4114","DOI":"10.1109\/TSP.2014.2326991","article-title":"Deep scattering spectrum","volume":"62","author":"Mallat","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_50","unstructured":"(2019, November 17). CS840a Machine Learning in Computer Vision. Available online: http:\/\/www.csd.uwo.ca\/courses\/CS9840a\/Lecture2_knn.pdf."},{"key":"ref_51","unstructured":"(2019, November 17). Computational Complexity of Least Square Regression Operation. Available online: https:\/\/math.stackexchange.com\/questions\/84495\/computational-complexity-of-least-square-regression-operation."},{"key":"ref_52","unstructured":"(2019, November 17). Computational Complexity of Neural Networks. Available online: https:\/\/kasperfred.com\/series\/computational-complexity\/computational-complexity-of-neural-networks."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/23\/2868\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:39:33Z","timestamp":1760189973000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/23\/2868"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,2]]},"references-count":52,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2019,12]]}},"alternative-id":["rs11232868"],"URL":"https:\/\/doi.org\/10.3390\/rs11232868","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2019,12,2]]}}}