Denoising of Hyperspectral Images Using the PARAFAC Model and Statistical Performance Analysis

Denoising is an important preprocessing step to further analyze a hyperspectral image (HSI). The common denoising methods, such as 2-D (two dimensions) filter, actually rearrange data from 3-D to 2-D and ignore the spectral relationships among different bands of the image. Tensor decomposition metho...

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Bibliographic Details
Published in:IEEE transactions on geoscience and remote sensing 2012-10, Vol.50 (10), p.3717-3724
Main Authors: Xuefeng Liu, Bourennane, S., Fossati, C.
Format: Article
Language:English
Subjects:
Applied geophysics
Argon
Classification
Covariance matrix
Cramer-Rao lower bound (CRLB)
denoising
Earth sciences
Earth, ocean, space
Engineering Sciences
Exact sciences and technology
hyperspectral image (HSI)
Internal geophysics
Matrix decomposition
Noise
Noise reduction
parallel factor analysis (PARAFAC)
Signal and Image processing
Tensile stress
Tucker3
Vectors
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Summary:Denoising is an important preprocessing step to further analyze a hyperspectral image (HSI). The common denoising methods, such as 2-D (two dimensions) filter, actually rearrange data from 3-D to 2-D and ignore the spectral relationships among different bands of the image. Tensor decomposition method has been adapted to denoise HSIs, for instance Tucker3 (three-mode factor analysis) model. However, this model has problems in uniqueness of decomposition and in estimation of multiple ranks. In this paper, to overcome these problems, we exploit a powerful multilinear algebra model, named parallel factor analysis (PARAFAC), and the number of estimated rank is reduced to one. Assumed that HSI is disturbed by white Gaussian noise, the optimal rank of PARAFAC is estimated according to that the covariance matrix of the n -mode unfolding matrix of the removed noise should be approach to a scalar matrix. Then, the denoising results by PARAFAC decomposition are presented and compared with those obtained by Tucker3 model and 2-D filters. To further verify the denoising performance of PARAFAC decomposition, Cramer-Rao lower bound (CRLB) of denoising is deduced theoretically for the first time, and the experiment results show that the PARAFAC model is a preferable denoising method since the variance of the HSI denoised by it is closer to the CRLB than by other considered methods.
ISSN:0196-2892
1558-0644
DOI:10.1109/TGRS.2012.2187063