{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T23:58:43Z","timestamp":1762300723018,"version":"build-2065373602"},"reference-count":62,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2024,7,23]],"date-time":"2024-07-23T00:00:00Z","timestamp":1721692800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"China NSFC projects","award":["12226004","62076196","62272375"],"award-info":[{"award-number":["12226004","62076196","62272375"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Model-based hyperspectral image (HSI) denoising methods have attracted continuous attention in the past decades, due to their effectiveness and interpretability. In this work, we aim at advancing model-based HSI denoising, through sophisticated investigation for both the fidelity and regularization terms, or correspondingly noise and prior, by virtue of several recently developed techniques. Specifically, we formulate a novel unified probabilistic model for the HSI denoising task, within which the noise is assumed as pixel-wise non-independent and identically distributed (non-i.i.d) Gaussian predicted by a pre-trained neural network, and the prior for the HSI image is designed by incorporating the deep image prior (DIP) with total variation (TV) and spatio-spectral TV. To solve the resulted maximum a posteriori (MAP) estimation problem, we design a Monte Carlo Expectation\u2013Maximization (MCEM) algorithm, in which the stochastic gradient Langevin dynamics (SGLD) method is used for computing the E-step, and the alternative direction method of multipliers (ADMM) is adopted for solving the optimization in the M-step. Experiments on both synthetic and real noisy HSI datasets have been conducted to verify the effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/rs16152694","type":"journal-article","created":{"date-parts":[[2024,7,23]],"date-time":"2024-07-23T14:26:50Z","timestamp":1721744810000},"page":"2694","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Hyperspectral Image Denoising by Pixel-Wise Noise Modeling and TV-Oriented Deep Image Prior"],"prefix":"10.3390","volume":"16","author":[{"given":"Lixuan","family":"Yi","sequence":"first","affiliation":[{"name":"The School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9956-0064","authenticated-orcid":false,"given":"Qian","family":"Zhao","sequence":"additional","affiliation":[{"name":"The School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}]},{"given":"Zongben","family":"Xu","sequence":"additional","affiliation":[{"name":"The School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"14118","DOI":"10.1109\/ACCESS.2018.2812999","article-title":"Modern trends in hyperspectral image analysis: A review","volume":"6","author":"Khan","year":"2018","journal-title":"IEEE Access"},{"doi-asserted-by":"crossref","unstructured":"Stuart, M.B., McGonigle, A.J., and Willmott, J.R. (2019). Hyperspectral imaging in environmental monitoring: A review of recent developments and technological advances in compact field deployable systems. Sensors, 19.","key":"ref_2","DOI":"10.3390\/s19143071"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1109\/MGRS.2019.2902525","article-title":"Hypersectral imaging for military and security applications: Combining myriad processing and sensing techniques","volume":"7","author":"Shimoni","year":"2019","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"doi-asserted-by":"crossref","unstructured":"Okada, N., Maekawa, Y., Owada, N., Haga, K., Shibayama, A., and Kawamura, Y. (2020). Automated identification of mineral types and grain size using hyperspectral imaging and deep learning for mineral processing. Minerals, 10.","key":"ref_4","DOI":"10.3390\/min10090809"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"79534","DOI":"10.1109\/ACCESS.2021.3068392","article-title":"Trends in deep learning for medical hyperspectral image analysis","volume":"9","author":"Khan","year":"2021","journal-title":"IEEE Access"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1205","DOI":"10.1109\/TGRS.2018.2865197","article-title":"Hyperspectral image denoising employing a spatial\u2013spectral deep residual convolutional neural network","volume":"57","author":"Yuan","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1109\/TGRS.2018.2859203","article-title":"HSI-DeNet: Hyperspectral image restoration via convolutional neural network","volume":"57","author":"Chang","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1109\/TCI.2019.2911881","article-title":"Deep spatial\u2013spectral representation learning for hyperspectral image denoising","volume":"5","author":"Dong","year":"2019","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4702","DOI":"10.1109\/TNNLS.2021.3112577","article-title":"FastHyMix: Fast and parameter-free hyperspectral image mixed noise removal","volume":"34","author":"Zhuang","year":"2021","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"9435","DOI":"10.1109\/JSTARS.2021.3111404","article-title":"Hyperspectral mixed noise removal via spatial-spectral constrained unsupervised deep image prior","volume":"14","author":"Luo","year":"2021","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4729","DOI":"10.1109\/TGRS.2013.2284280","article-title":"Hyperspectral image restoration using low-rank matrix recovery","volume":"52","author":"Zhang","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3050","DOI":"10.1109\/JSTARS.2015.2398433","article-title":"Hyperspectral image denoising via noise-adjusted iterative low-rank matrix approximation","volume":"8","author":"He","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1109\/TGRS.2015.2452812","article-title":"Total-variation-regularized low-rank matrix factorization for hyperspectral image restoration","volume":"54","author":"He","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.1109\/JSTARS.2017.2779539","article-title":"Hyperspectral image restoration via total variation regularized low-rank tensor decomposition","volume":"11","author":"Wang","year":"2017","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"6916","DOI":"10.1109\/TNNLS.2021.3083931","article-title":"Multilayer Sparsity-Based Tensor Decomposition for Low-Rank Tensor Completion","volume":"33","author":"Xue","year":"2022","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"13887","DOI":"10.1109\/TCYB.2021.3140148","article-title":"When Laplacian Scale Mixture Meets Three-Layer Transform: A Parametric Tensor Sparsity for Tensor Completion","volume":"52","author":"Xue","year":"2022","journal-title":"IEEE Trans. Cybern."},{"key":"ref_17","first-page":"442","article-title":"Hyperspectral image denoising using spatio-spectral total variation","volume":"13","author":"Aggarwal","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1080\/01431161.2017.1382742","article-title":"Joint weighted nuclear norm and total variation regularization for hyperspectral image denoising","volume":"39","author":"Du","year":"2018","journal-title":"Int. J. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/TIP.2019.2926736","article-title":"Hyperspectral images denoising via nonconvex regularized low-rank and sparse matrix decomposition","volume":"29","author":"Xie","year":"2019","journal-title":"IEEE Trans. Image Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.1109\/JSTARS.2020.2979801","article-title":"Hyperspectral mixed noise removal by \u21131-norm-based subspace representation","volume":"13","author":"Zhuang","year":"2020","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1054","DOI":"10.1109\/TCYB.2017.2677944","article-title":"Denoising hyperspectral image with non-iid noise structure","volume":"48","author":"Chen","year":"2017","journal-title":"IEEE Trans. Cybern."},{"doi-asserted-by":"crossref","unstructured":"Yue, Z., Meng, D., Sun, Y., and Zhao, Q. (2018). Hyperspectral image restoration under complex multi-band noises. Remote Sens., 10.","key":"ref_22","DOI":"10.3390\/rs10101631"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1628","DOI":"10.1109\/JSTARS.2020.3046488","article-title":"Hyperspectral image restoration combining intrinsic image characterization with robust noise modeling","volume":"14","author":"Ma","year":"2020","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_24","first-page":"1","article-title":"Fast noise removal in hyperspectral images via representative coefficient total variation","volume":"60","author":"Peng","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"doi-asserted-by":"crossref","unstructured":"Rui, X., Cao, X., Xie, Q., Yue, Z., Zhao, Q., and Meng, D. (2021, January 20\u201325). Learning an explicit weighting scheme for adapting complex HSI noise. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Nashville, TN, USA.","key":"ref_25","DOI":"10.1109\/CVPR46437.2021.00667"},{"doi-asserted-by":"crossref","unstructured":"He, S., Zhou, H., Wang, Y., Cao, W., and Han, Z. (2016, January 10\u201315). Super-resolution reconstruction of hyperspectral images via low rank tensor modeling and total variation regularization. Proceedings of the 2016 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Beijing, China.","key":"ref_26","DOI":"10.1109\/IGARSS.2016.7730816"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"7889","DOI":"10.1109\/TIP.2020.3007840","article-title":"Enhanced 3DTV Regularization and Its Applications on HSI Denoising and Compressed Sensing","volume":"29","author":"Peng","year":"2020","journal-title":"IEEE Trans. Image Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/j.neucom.2020.01.103","article-title":"Spatial-spectral weighted nuclear norm minimization for hyperspectral image denoising","volume":"399","author":"Huang","year":"2020","journal-title":"Neurocomputing"},{"unstructured":"Ulyanov, D., Vedaldi, A., and Lempitsky, V. (2018, January 18\u201323). Deep image prior. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","key":"ref_29"},{"unstructured":"Sidorov, O., and Yngve Hardeberg, J. (November, January 27). Deep hyperspectral prior: Single-image denoising, inpainting, super-resolution. Proceedings of the IEEE\/CVF International Conference on Computer Vision Workshops, Seoul, Republic of Korea.","key":"ref_30"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"5967","DOI":"10.1109\/JSTARS.2022.3187722","article-title":"Unsupervised hyperspectral denoising based on deep image prior and least favorable distribution","volume":"15","author":"Niresi","year":"2022","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"unstructured":"Welling, M., and Teh, Y.W. (July, January 28). Bayesian learning via stochastic gradient Langevin dynamics. Proceedings of the 28th International Conference on Machine Learning (ICML-11), Bellevue, WA, USA.","key":"ref_32"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/2200000016","article-title":"Distributed optimization and statistical learning via the alternating direction method of multipliers","volume":"3","author":"Boyd","year":"2011","journal-title":"Found. Trends Mach. Learn."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4457","DOI":"10.1109\/TGRS.2019.2891288","article-title":"A novel rank approximation method for mixture noise removal of hyperspectral images","volume":"57","author":"Ye","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1109\/TIP.2012.2210725","article-title":"Nonlocal transform-domain filter for volumetric data denoising and reconstruction","volume":"22","author":"Maggioni","year":"2012","journal-title":"IEEE Trans. Image Process."},{"doi-asserted-by":"crossref","unstructured":"Xie, Q., Zhao, Q., Meng, D., Xu, Z., Gu, S., Zuo, W., and Zhang, L. (2016, January 27\u201330). Multispectral images denoising by intrinsic tensor sparsity regularization. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA.","key":"ref_36","DOI":"10.1109\/CVPR.2016.187"},{"doi-asserted-by":"crossref","unstructured":"Peng, Y., Meng, D., Xu, Z., Gao, C., Yang, Y., and Zhang, B. (2014, January 23\u201328). Decomposable nonlocal tensor dictionary learning for multispectral image denoising. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Columbus, OH, USA.","key":"ref_37","DOI":"10.1109\/CVPR.2014.377"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"95","DOI":"10.5194\/isprsannals-I-7-95-2012","article-title":"Hyperspectral image denoising with cubic total variation model","volume":"1","author":"Zhang","year":"2012","journal-title":"ISPRS Ann. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_39","first-page":"5511413","article-title":"Adaptive Hyperspectral Mixed Noise Removal","volume":"60","author":"Jiang","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"5701","DOI":"10.1109\/TGRS.2019.2901737","article-title":"A 3-D atrous convolution neural network for hyperspectral image denoising","volume":"57","author":"Liu","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1109\/TNNLS.2020.2978756","article-title":"3-D quasi-recurrent neural network for hyperspectral image denoising","volume":"32","author":"Wei","year":"2020","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_42","first-page":"5504714","article-title":"Deep spatial-spectral global reasoning network for hyperspectral image denoising","volume":"60","author":"Cao","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"10348","DOI":"10.1109\/TGRS.2020.3045273","article-title":"Hyperspectral image denoising using a 3-D attention denoising network","volume":"59","author":"Shi","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"8797","DOI":"10.1109\/TNNLS.2022.3215751","article-title":"Hider: A hyperspectral image denoising transformer with spatial\u2013spectral constraints for hybrid noise removal","volume":"35","author":"Chen","year":"2022","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"unstructured":"Li, M., Fu, Y., and Zhang, Y. (2023, January 7\u201314). Spatial-spectral transformer for hyperspectral image denoising. Proceedings of the AAAI Conference on Artificial Intelligence, Washington, DC, USA.","key":"ref_45"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"4677","DOI":"10.1109\/TIP.2016.2593343","article-title":"Robust low-rank matrix factorization under general mixture noise distributions","volume":"25","author":"Cao","year":"2016","journal-title":"IEEE Trans. Image Process."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1150","DOI":"10.1137\/060662617","article-title":"Total variation regularization for image denoising, I. Geometric theory","volume":"39","author":"Allard","year":"2008","journal-title":"SIAM J. Math. Anal."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1852","DOI":"10.1109\/TIP.2015.2404782","article-title":"Anisotropic spectral-spatial total variation model for multispectral remote sensing image destriping","volume":"24","author":"Chang","year":"2015","journal-title":"IEEE Trans. Image Process."},{"doi-asserted-by":"crossref","unstructured":"Yue, Z., Zhao, Q., Xie, J., Zhang, L., Meng, D., and Wong, K.Y.K. (2022, January 28\u201324). Blind image super-resolution with elaborate degradation modeling on noise and kernel. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, New Orleans, LA, USA.","key":"ref_49","DOI":"10.1109\/CVPR52688.2022.00217"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1111\/j.1467-9868.2005.00499.x","article-title":"Ascent-based Monte Carlo expectation\u2013maximization","volume":"67","author":"Caffo","year":"2005","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"unstructured":"Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., and Antiga, L. (2019, January 8\u201314). Pytorch: An imperative style, high-performance deep learning library. Proceedings of the Annual Conference on Neural Information Processing Systems 2019, NeurIPS 2019, Vancouver, BC, Canada.","key":"ref_51"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1080\/01621459.1990.10474930","article-title":"A Monte Carlo implementation of the EM algorithm and the poor man\u2019s data augmentation algorithms","volume":"85","author":"Wei","year":"1990","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1080\/00949659608811772","article-title":"Stochastic versions of the EM algorithm: An experimental study in the mixture case","volume":"55","author":"Celeux","year":"1996","journal-title":"J. Stat. Comput. Simul."},{"unstructured":"Kingma, D.P., and Ba, J. (2014). Adam: A method for stochastic optimization. arXiv.","key":"ref_54"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"2241","DOI":"10.1109\/TIP.2010.2046811","article-title":"Generalized assorted pixel camera: Postcapture control of resolution, dynamic range, and spectrum","volume":"19","author":"Yasuma","year":"2010","journal-title":"IEEE Trans. Image Process."},{"doi-asserted-by":"crossref","unstructured":"Arad, B., and Ben-Shahar, O. (2016, January 11\u201314). Sparse recovery of hyperspectral signal from natural RGB images. Proceedings of the Computer Vision\u2013ECCV 2016: 14th European Conference, Amsterdam, The Netherlands. Proceedings, Part VII 14.","key":"ref_56","DOI":"10.1007\/978-3-319-46478-7_2"},{"doi-asserted-by":"crossref","unstructured":"Zhuang, L., Ng, M.K., and Fu, X. (2021). Hyperspectral image mixed noise removal using subspace representation and deep CNN image prior. Remote Sens., 13.","key":"ref_57","DOI":"10.3390\/rs13204098"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"2378","DOI":"10.1109\/TIP.2011.2109730","article-title":"FSIM: A Feature Similarity Index for Image Quality Assessment","volume":"20","author":"Zhang","year":"2011","journal-title":"IEEE Trans. Image Process."},{"unstructured":"Wald, L. (2002). Data Fusion: Definitions and Architectures: Fusion of Images of Different Spatial Resolutions, Presses des Mines.","key":"ref_59"},{"unstructured":"Yuhas, R.H., Goetz, A.F., and Boardman, J.W. (1992, January 1\u20135). Discrimination among semi-arid landscape endmembers using the spectral angle mapper (SAM) algorithm. Proceedings of the JPL, Summaries of the Third Annual JPL Airborne Geoscience Workshop, Pasadena, CA, USA.","key":"ref_60"},{"unstructured":"Ghahramani, Z., Welling, M., Cortes, C., Lawrence, N., and Weinberger, K. (2014, January 8\u201313). Generative Adversarial Nets. Proceedings of the Twenty-Eighth Annual Conference on Neural Information Processing Systems, Montr\u00e9al, QC, Canada.","key":"ref_61"},{"unstructured":"Larochelle, H., Ranzato, M., Hadsell, R., Balcan, M., and Lin, H. (2020, January 6\u201312). Denoising Diffusion Probabilistic Models. Proceedings of the Thirty-Fourth Annual Conference on Neural Information Processing Systems, Virtual.","key":"ref_62"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/15\/2694\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:21:41Z","timestamp":1760109701000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/15\/2694"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,23]]},"references-count":62,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2024,8]]}},"alternative-id":["rs16152694"],"URL":"https:\/\/doi.org\/10.3390\/rs16152694","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2024,7,23]]}}}