Abstract
Noise effect as an unwanted and troubler component was investigated in this study. It generally exists more or less in the remote sensing data because of the device errors and natural effects. Therefore, its correct estimation will lead to better analysis. This paper aims to examine the noise effect on selecting the spectral mixing model. A set of synthetic data was first designed based on one linear and five nonlinear models. Then, the noise was added to the data at different signal-to-noise (SNR) levels. After designing the models, to evaluate the noise intensity, it was determined using the noise estimation methods (multiple linear regression (MLR) based method and L1HyMixDe), assuming that each synthetic dataset stayed on the linear model. A comparison was made between the obtained noise values from the linear and each of the nonlinear models using one-way Analysis of Variance (ANOVA) and Wilcoxon statistical tests. According to the significant difference between the noise values of linear and nonlinear data in different SNR levels, an SNR limit was determined for each model and below this value, the noise overcomes the nonlinear portion of the data. As a result, Polynomial Post Nonlinear Mixing Model (PPNMM) shows the best performance in the nonlinear unmixing of data in the presence of noise. This study was tested on real Hyperion data and the obtained results agreed with our assessments.
Similar content being viewed by others
References
Altmann Y, Dobigeon N, Tourneret J-Y (2012a) Nonlinearity detection in hyperspectral images using a polynomial post-nonlinear mixing model. IEEE Trans Image Process 22(4):1267–1276
Altmann Y, Halimi A, Dobigeon N, Tourneret J-Y (2012b) Supervised nonlinear spectral unmixing using a postnonlinear mixing model for hyperspectral imagery. IEEE Trans Image Process 21(6):3017–3025
Ben-Dor E, Notesco G (2016) A simple indicator for estimating the noise level of a hyperspectral data cube for earth observation missions. Acta Astronaut 128:304–312
Bioucas-Dias JM, Nascimento JMP (2008) Hyperspectral subspace identification. IEEE Trans Geosci Remote Sens 46(8):2435–2445
Bioucas-Dias JM, Plaza A, Dobigeon N, Parente M, Du Q, Gader P, Chanussot J (2012) Hyperspectral unmixing overview: geometrical, statistical, and sparse regression-based approaches. IEEE J Sel Top Appl Earth Observ Remote Sens 5(2):354–379. https://doi.org/10.1109/JSTARS.2012.2194696
Canditiis D (2019) Statistical inference techniques. In: Ranganathan S, Gribskov M, Nakai K, Schönbach C (eds) Encyclopedia of bioinformatics and computational biology. Academic Press, Oxford, pp 698–705
Chakravortty S, Shah E (2013) Application of non-linear spectral unmixing on hyperspectral data for species level classification of mangroves. In: Paper presented at the Communications and Signal Processing (ICCSP), 2013 International Conference on Communication and Signal Processing
Chen SY, Ouyang YC, Lin C, Chen HM, Gao C, Chang CI (2015) Progressive endmember finding by fully constrained least-squares method. In: Paper presented at the 2015 7th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS)
Dobigeon N, Altmann Y, Brun N, Moussaoui S (2016) "Linear and nonlinear unmixing in hyperspectral imaging. Data handling in science and technology: resolving spectral mixtures. Elsevier, Amsterdam, p 41
Fan W, Baoxin Hu, Miller J, Li M (2009) Comparative study between a new nonlinear model and common linear model for analysing laboratory simulated-forest hyperspectral data. Int J Remote Sens 30(11):2951–2962
Gao L, Qian D, Wei Y, Bing Z (2012) A comparative study on noise estimation for hyperspectral imagery. In: Paper presented at the 2012 4th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS)
Gersman R, Ben-Dor E, Beyth M, Avigad D, Abraha M, Kibreab A (2008) Mapping of hydrothermally altered rocks by the EO-1 Hyperion sensor, Northern Danakil Depression, Eritrea. Int J Remote Sens 29(13):3911–3936
Halimi A, Altmann Y, Dobigeon N, Tourneret J-Y (2011) Nonlinear unmixing of hyperspectral images using a generalized bilinear model. IEEE Trans Geosci Remote Sens 49(11):4153–4162
Hapke B (1981) Bidirectional reflectance spectroscopy: 1. Theory. J Geophys Res 86(B4):3039–3054
Hesamian G (2016) One-way ANOVA based on interval information. Int J Syst Sci 47(11):2682–2690
Heylen R, Gader P (2014) Nonlinear spectral unmixing with a linear mixture of intimate mixtures model. IEEE Geosci Remote Sens Lett 11(7):1195–1199
Heylen R, Scheunders P (2016) A multilinear mixing model for nonlinear spectral unmixing. IEEE Trans Geosci Remote Sens 54(1):240–251
Heylen R, Parente M, Gader P (2014) A review of nonlinear hyperspectral unmixing methods. IEEE J Sel Top Appl Earth Observ Remote Sens 7(6):1844–1868
Hill SA (2006) Chapter 18 - Statistics. In: Hemmings HC, Hopkins PM (eds) Foundations of anesthesia, 2nd edn. Mosby, Edinburgh, pp 207–217
Imbiriba TCO (2016) Nonlinear hyperspectral unmixing: strategies for nonlinear mixture detection, endmember estimation, and band-selection.
Jutten C, Karhunen J (2003) Advances in nonlinear blind source separation. In: Paper presented at the Proceedings of the 4th International Symposium on Independent Component Analysis and Blind Signal Separation (ICA2003)
Karami A, Rob H, Paul S (2014) Hyperspectral image noise reduction and its effect on spectral unmixing. In: Paper presented at the 2014 6th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS)
Kim TK (2015) T test as a parametric statistic. Korean J Anesthesiol 68(6):540
Kruse FA, Lefkoff AB, Boardman JW, Heidebrecht KB, Shapiro AT, Barloon PJ, Goetz AFH (1993) The spectral image processing system (SIPS)—interactive visualization and analysis of imaging spectrometer data. Remote Sens Environ 44(2–3):145–163
Kruse FA, Boardman JW, Huntington JF (2003) Comparison of airborne hyperspectral data and EO-1 Hyperion for mineral mapping. IEEE Trans Geosci Remote Sens 41(6):1388–1400
Luo W, Gao L, Zhang R, Marinoni A, Zhang B (2019) Bilinear normal mixing model for spectral unmixing. IET Image Process 13(2):344–354
Mahmood A, Sears M (2021) Estimation of correlated signal-dependent noise statistics in hyperspectral images. Remote Sens Lett 12(10):961–969
Mishra P, Karami A, Nordon A, Rutledge DN, Roger J-M (2019) Automatic de-noising of close-range hyperspectral images with a wavelength-specific shearlet-based image noise reduction method. Sens Actuators B 281:1034–1044
Moghadam HJ, Oskouei MM, Nouri T (2020) Unmixing of hyperspectral data for mineral detection using a hybrid method, Sar Chah-e Shur, Iran. Arab J Geosci 13(19):1041. https://doi.org/10.1007/s12517-020-06070-7
Montgomery DC, Runger GC (2010) Applied statistics and probability for engineers. John Wiley & Sons, London
Nascimento JMP, Bioucas-Dias JM (2009) Nonlinear mixture model for hyperspectral unmixing. Proc SPIE Image Signal Process Remote Sens XV 7477(1):74770
Nascimento JMP, Bioucas-Dias JM (2010) Unmixing hyperspectral intimate mixtures. In: Paper presented at the Image and Signal Processing for Remote Sensing XVI
Nascimento JMP, Dias JMB (2005) Vertex component analysis: a fast algorithm to unmix hyperspectral data. IEEE Trans Geosci Remote Sens 43(4):898–910
Nouri T, Oskouei MM, Alizadeh B, Gamba P, Marinoni A (2019) Improvement of the MVC-NMF problem using particle swarm optimization for mineralogical unmixing of noisy hyperspectral data. J Indian Soc Remote Sens 47(4):541–550
Rasti B, Scheunders P, Ghamisi P, Licciardi G, Chanussot J (2018) Noise reduction in hyperspectral imagery: overview and application. Remote Sensing 10(3):482
Smalheiser NR (2017) Chapter 12: nonparametric tests. In: Neil RS (ed) Data literacy. Academic Press, London, pp 157–167
Türkmenoğlu M, Orhan Ş, Erdem D (2013) SNR calculation method for remote sensing satellite imaging systems. Gazi Üniv Mühendis Mimarlık Fakültesi Dergisi 28(2):217–222
Van Der Meer F (2004) Analysis of spectral absorption features in hyperspectral imagery. Int J Appl Earth Obs Geoinf 5(1):55–68
Wendisch M, Brenguier J-L (2013) Airborne measurements for environmental research: methods and instruments. John Wiley & Sons, London
Xu D, Sun L, Luo J (2013) Noise estimation of hyperspectral remote sensing image based on multiple linear regression and wavelet transform. Boletim De Ciências Geodésicas 19(4):639–652
Yang B, Wang B, Zongmin Wu (2017) Nonlinear hyperspectral unmixing based on geometric characteristics of bilinear mixture models. IEEE Trans Geosci Remote Sens 56(2):694–714
Zhang Q, Yuan Q, Li J, Liu X, Shen H, Zhang L (2019) Hybrid noise removal in hyperspectral imagery with a spatial-spectral gradient network. IEEE Trans Geosci Remote Sens 57(10):7317–7329
Zhuang L, Bioucas-Dias JM (2018) Fast hyperspectral image denoising and inpainting based on low-rank and sparse representations. IEEE J Sel Top Appl Earth Observ Remote Sens 11(3):730–742
Zhuang L, Ng MK (2020) Hyperspectral mixed noise removal by $\ell _1 $-norm-based subspace representation. IEEE J Sel Top Appl Earth Observ Remote Sens 13:1143–1157
Funding
This study had no financial support or fund.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of Interest
The authors declare that they have no conflict of interest.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Jamshid Moghadam, H., Mohammady Oskouei, M. & Nouri, T. The Influence of Noise Intensity in the Nonlinear Spectral Unmixing of Hyperspectral Data. PFG 91, 29–42 (2023). https://doi.org/10.1007/s41064-022-00223-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41064-022-00223-x