Survey of hyperspectral image denoising methods based on tensor decompositions

Abstract

A hyperspectral image (HSI) is always modeled as a three-dimensional tensor, with the first two dimensions indicating the spatial domain and the third dimension indicating the spectral domain. The classical matrix-based denoising methods require to rearrange the tensor into a matrix, then filter noise in the column space, and finally rebuild the tensor. To avoid the rearranging and rebuilding steps, the tensor-based denoising methods can be used to process the HSI directly by employing multilinear algebra. This paper presents a survey on three newly proposed HSI denoising methods and shows their performances in reducing noise. The first method is the Multiway Wiener Filter (MWF), which is an extension of the Wiener filter to data tensors, based on the TUCKER3 decomposition. The second one is the PARAFAC filter, which removes noise by truncating the lower rank K of the PARAFAC decomposition. And the third one is the combination of multidimensional wavelet packet transform (MWPT) and MWF (MWPT-MWF), which models each coefficient set as a tensor and then filters each tensor by applying MWF. MWPT-MWF has been proposed to preserve rare signals in the denoising process, which cannot be preserved well by using the MWF or PARAFAC filters. A real-world HYDICE HSI data is used in the experiments to assess these three tensor-based denoising methods, and the performances of each method are analyzed in two aspects: signal-to-noise ratio and improvement of subsequent target detection results. Review IntroductionHyperspectral images (HSI) attract more and more interest in recent years in different domains, such as geography, agriculture, and military [1][2][3]. They use the HSI to do the target detection [4] or classification [5] to find objects or materials of interest on the ground. Unfortunately, in the capturing procedure, the HSI is usually impaired by several types of noise, such as thermal noise [6], photonic noise [7], and strip noise [8]. Therefore, denoising methods [9-13] have become a critical step for improving the subsequent target detection and classification in remote sensing imaging applications [14].In HSI processing, images are modeled as a threedimensional tensor, i.e., two spatial dimensions and one spectral dimension. The classical denoising methods [15][16][17][18] rearrange the HSI into a matrix whose columns contain the spectral signatures of all the pixels, then estimate the signal subspace by methods based on the analysis *Correspondence: salah.bourennane@fresnel.fr Institut Fresnel/CNRS-UMR 7249 Ecole Centrale Marseille, Aix-Marseille Université, Marseille 13013, France of second-order statistics, and finally rebuild the original HSI structure after processing.Since matrix-based techniques cannot take advantage of spectra in hyperspectral images, therefore, in order to treat the HSI as a whole entity, some new techniques were developed. For example, an HSI was treated as a hypercube in order to take into account the correlation among different bands [19,20], tensor-algebra was brought to joi...

Discriminant Tensor Spectral–Spatial Feature Extraction for Hyperspectral Image Classification

“…Bourennane et al [15] have proposed multidimensional Wiener filtering to jointly achieve denoising and dimension reduction. Lin and Bourennane [16] have surveyed two tensor-based denoising methods and proposed a novel combination to preserve rare signals during the denoising procedure. Velasco-Forero and Angulo [17] have integrated morphological decomposition and tensor PC analysis to improve hyperspectral pixel-wise classification.…”

Spectral–Spatial Adaptive Sparse Representation for Hyperspectral Image Denoising

“…In addition, there are some more advanced multidimensional methods, including the genetic kernel Tucker decomposition [16] and adaptive 3-D filtering [17]. Since all the abundant signals (containing a large number of relative pixels) and the rare signals (containing only a few relative pixels) are processed together, these multidimensional methods easily lead the rare signals to be unexpectedly removed [19].…”

Hyperspectral image denoising using the robust low-rank tensor recovery

“…Therefore, in order to treat the HSI as a whole entity, spatial and spectral information should be taken into consideration jointly to remove the noise efficiently [1]. In recent years, tensor-algebra methods have been used to denoise the 3D HSI, which utilize the multilinear algebra to analyze the HSI tensor directly [15]. There are two main models, the TUCKER3 model and the PARAFAC model [16].…”

“…The PARAFAC-model-based denoising methods include the parallel factor analysis (PARAFAC) [20] and the rank-1 tensor decomposition [8]. In addition, multidimensional wavelet packet transform (MWPT)-based methods have been used for the denoising of the 3D HSI [15,21,22]. Under the limitation of the prior knowledge, the above-mentioned tensoralgebra methods are implicitly developed for the additive white Gaussian noise.…”