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...