{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T00:37:20Z","timestamp":1777336640783,"version":"3.51.4"},"reference-count":34,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,8,21]],"date-time":"2018-08-21T00:00:00Z","timestamp":1534809600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>With the current state-of-the-art computer aided manufacturing tools, the spatial resolution of hyperspectral sensors is becoming increasingly higher thus making it easy to obtain much more detailed information of the scene captured. However, the improvement of the spatial resolution also brings new challenging problems to address with signal dependent photon noise being one of them. Unlike the signal independent thermal noise, the variance of photon noise is dependent on the signal, therefore many denoising methods developed for the stationary noise cannot be applied directly to the photon noise. To make things worse, both photon and thermal noise coexist in the captured hyperspectral image (HSI), thus making it more difficult to whiten noise. In this paper, we propose a new denoising framework to cope with signal dependent nonwhite noise (SDNW), Pre-estimate\u2014Whitening\u2014Post-estimate (PWP) loop, to reduce both photon and thermal noise in HSI. Previously, we proposed a method based on multidimensional wavelet packet transform and multi-way Wiener filter which performs both white noise and spectral dimensionality reduction, referred to as MWPT-MWF, which was restricted to white noise. We get inspired from this MWPT-MWF to develop a new iterative method for reducing photon and thermal noise. Firstly, the hyperspectral noise parameters estimation (HYNPE) algorithm is used to estimate the noise parameters, the SD noise is converted to an additive white Gaussian noise by pre-whitening procedure and then the whitened HSI is denoised by the proposed method SDNW-MWPT-MWF. As comparative experiments, the Multiple Linear Regression (MLR) based denoising method and tensor-based Multiway Wiener Filter (MWF) are also used in the denoising framework. An HSI captured by Reflective Optics System Imaging Spectrometer (ROSIS) is used in the experiments and the denoising performances are assessed from various aspects: the noise whitening performance, the Signal-to-Noise Ratio (SNR), and the classification performance. The results on the real-world airborne hyperspectral image HYDICE (Hyperspectral Digital Imagery Collection Experiment) are also presented and analyzed. These experiments show that it is worth taking into account noise signal-dependency hypothesis for processing HYDICE and ROSIS HSIs.<\/jats:p>","DOI":"10.3390\/rs10091330","type":"journal-article","created":{"date-parts":[[2018,8,21]],"date-time":"2018-08-21T11:12:42Z","timestamp":1534849962000},"page":"1330","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Noise Removal Based on Tensor Modelling for Hyperspectral Image Classification"],"prefix":"10.3390","volume":"10","author":[{"given":"Salah","family":"Bourennane","sequence":"first","affiliation":[{"name":"Centrale Marseille, Institut Fresnel, Aix Marseille Universit\u00e9, CNRS, 13013 Marseille, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Caroline","family":"Fossati","sequence":"additional","affiliation":[{"name":"Centrale Marseille, Institut Fresnel, Aix Marseille Universit\u00e9, CNRS, 13013 Marseille, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Lin","sequence":"additional","affiliation":[{"name":"Centrale Marseille, Institut Fresnel, Aix Marseille Universit\u00e9, CNRS, 13013 Marseille, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2957","DOI":"10.1109\/TGRS.2011.2110657","article-title":"Signal-dependent noise modeling and model parameter estimation in hyperspectral images","volume":"8","author":"Acito","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1844","DOI":"10.1109\/TGRS.2007.895841","article-title":"Stripe noise reduction in modis data by combining histogram matching with facet filter","volume":"45","author":"Rakwatin","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1109\/JSTSP.2010.2104312","article-title":"Local signal-dependent noise variance estimation from hyperspectral textural images","volume":"3","author":"Uss","year":"2011","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2719","DOI":"10.1080\/01431169608949102","article-title":"Principal components transform with simple, automatic noise ajustment","volume":"17","author":"Roger","year":"1996","journal-title":"INT J. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2387","DOI":"10.1109\/36.789637","article-title":"Interference and noise adjusted principal components analysis","volume":"37","author":"Chang","year":"1999","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","unstructured":"Rhodes, H., Agranov, G., Hong, C., Boettiger, U., Mauritzson, R., Ladd, J., Karasev, I., McKee, J., Jenkins, E., and Quinlin, W. (2004, January 16). Cmos imager technology shrinks and image performance. Proceedings of the 2004 IEEE Workshop on Microelectronics and Electron Devices, Boise, ID, USA."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Alparone, L., Selva, M., Aiazzi, B., Baronti, S., Butera, F., and Chiarantini, L. (2009, January 26\u201328). Signal-dependent noise modelling and estimation of new-generation imaging spectrometers. Proceedings of the Workshop on Hyperspectral Image and Signal Processing (WHISPERS), Grenoble, France.","DOI":"10.1109\/WHISPERS.2009.5289080"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3717","DOI":"10.1109\/TGRS.2012.2187063","article-title":"Denoising of hyperspectral images using the parafac model and statistical performance analysis","volume":"50","author":"Liu","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Gao, L., Yao, D., Li, Q., Zhuang, L., Zhang, B., and Bioucas-Dias, J.M. (2017). A New Low-Rank Representation based hyperspectral image denoising method for mineral mapping. Remote Sens., 9.","DOI":"10.3390\/rs9111145"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Fan, Y.R., Huang, T.Z., Zhao, X.L., Deng, L.J., and Fan, S. (2018). Multispectral Image Denoising via Nonlocal Multitask Sparse Learning. Remote Sens., 10.","DOI":"10.3390\/rs10010116"},{"key":"ref_11","unstructured":"Atkinson, I., Kamalabadi, F., Mohan, S., and Jones, D. (2003, January 14\u201317). Wavelet-based 2D multichannel signal estimation. Proceedings of the IEEE International Conference on Image Processing, Barcelona, Spain."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"654","DOI":"10.1109\/TIP.2005.863698","article-title":"Estimating the probability of the presence of a signal of interest in multiresolution single-and multiband image denoising","volume":"3","author":"Pizurica","year":"2006","journal-title":"IEEE Trans. Image Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2061","DOI":"10.1109\/TGRS.2008.916641","article-title":"Noise removal from hyperspectral images by multidimensional filtering","volume":"7","author":"Letexier","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2407","DOI":"10.1109\/TGRS.2008.918419","article-title":"Improvement of target detection methods by multiway filtering","volume":"8","author":"Renard","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","first-page":"1","article-title":"Noise modelling and estimation of hyperspectral data from airborne imaging spectrometers","volume":"1","author":"Aiazzi","year":"2006","journal-title":"Ann. Geophys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1109\/LGRS.2007.909927","article-title":"A new operational method for estimating noise in hyperspectral images","volume":"1","author":"Gao","year":"2008","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Aiazzi, B., Alparone, L., and Baronti, S. (1997, January 2\u20134). A robust method for parameter estimation of signal-dependent noise models in digital images. Proceedings of the IEEE International Conference on Digital Signal Processin, Santorini, Greece.","DOI":"10.1109\/ICDSP.1997.628421"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2531","DOI":"10.1109\/TGRS.2003.818813","article-title":"Coherence estimation from multilook incoherent sar imagery","volume":"11","author":"Aiazzi","year":"2003","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2056","DOI":"10.1016\/j.sigpro.2005.10.014","article-title":"Mmse filtering of generalised signal-dependent noise in spatial and shift-invariant wavelet domains","volume":"8","author":"Argenti","year":"2006","journal-title":"Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1737","DOI":"10.1109\/TIP.2008.2001399","article-title":"Practical poissonian-Gaussian noise modeling and fitting for single-image raw-data","volume":"10","author":"Foi","year":"2008","journal-title":"IEEE Trans. Image Process."},{"key":"ref_21","first-page":"1","article-title":"Exploring Hierarchical Convolutional Features for Hyperspectral Image Classification","volume":"99","author":"Cheng","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3529","DOI":"10.1109\/TGRS.2012.2225065","article-title":"Hyperspectral image processing by jointly filtering wavelet component tensor","volume":"6","author":"Lin","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","unstructured":"Lin, T., and Bourennane, S. (2013, January 10\u201312). Hyperspectral image denoising with rare signal preserving by jointly filtering image component. Proceedings of the 2013 4th European Workshop on Visual Information Processing (EUVIP), Paris, France."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2676","DOI":"10.1109\/TIP.2006.877363","article-title":"CCD noise removal in digital images","volume":"9","author":"Faraji","year":"2006","journal-title":"IEEE Trans. Image Process."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Aiazzi, B., Alparone, L., Baronti, S., Butera, F., Chiarantini, L., and Selva, M. (2011, January 6\u20139). Benefits of signal-dependent noise reduction for spectral analysis of data from advanced imaging spectrometers. Proceedings of the Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS), Lisbon, Portugal.","DOI":"10.1109\/WHISPERS.2011.6080866"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1109\/TGRS.2005.860982","article-title":"Noise reduction of hyperspectral imagery using hybrid spatial-spectral derivative-domain wavelet shrinkage","volume":"2","author":"Othman","year":"2006","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1109\/TGRS.2010.2075937","article-title":"Denoising of hyperspectral imagery using principal component analysis and wavelet shrinkage","volume":"3","author":"Chen","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1137\/07070111X","article-title":"Tensor decompositions and applications","volume":"3","author":"Kolda","year":"2009","journal-title":"SIAM Rev."},{"key":"ref_29","first-page":"1253","article-title":"A multilinear singular value decomposition","volume":"4","author":"Vandewalle","year":"2000","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"ref_30","first-page":"1324","article-title":"On the best rank-1 and rank-(r1, r2, ..., rn) approximation of higher-order tensors","volume":"4","author":"Vandewalle","year":"2000","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Cichocki, A., Zdunek, R., Phan, A., and Amari, S. (2009). Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-Way Data Analysis and Blind Source Separation, Wiley.","DOI":"10.1002\/9780470747278"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1109\/34.192463","article-title":"A theory for multiresolution signal decomposition: The wavelet representation","volume":"7","author":"Mallat","year":"1989","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2338","DOI":"10.1016\/j.sigpro.2004.11.029","article-title":"Multidimensional filtering based on a tensor approach","volume":"12","author":"Muti","year":"2005","journal-title":"Signal Process."},{"key":"ref_34","first-page":"1317","article-title":"Ideal denoising in an orthonormal basis chosen from a library of bases","volume":"12","author":"Donoho","year":"1994","journal-title":"Comptes Rendus de l\u2019Academie des Sciences-Serie I-Mathematique"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/9\/1330\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:20:09Z","timestamp":1760196009000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/9\/1330"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,21]]},"references-count":34,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2018,9]]}},"alternative-id":["rs10091330"],"URL":"https:\/\/doi.org\/10.3390\/rs10091330","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,21]]}}}