A hyperspectral image (HSI) is always modeled as a three-dimensional tensor, with the first two dimensions indicating\r\nthe spatial domain and the third dimension indicating the spectral domain. The classical matrix-based denoising\r\nmethods require to rearrange the tensor into a matrix, then filter noise in the column space, and finally rebuild the\r\ntensor. To avoid the rearranging and rebuilding steps, the tensor-based denoising methods can be used to process\r\nthe HSI directly by employing multilinear algebra. This paper presents a survey on three newly proposed HSI\r\ndenoising methods and shows their performances in reducing noise. The first method is the Multiway Wiener Filter\r\n(MWF), which is an extension of the Wiener filter to data tensors, based on the TUCKER3 decomposition. The second\r\none is the PARAFAC filter, which removes noise by truncating the lower rank K of the PARAFAC decomposition. And\r\nthe third one is the combination of multidimensional wavelet packet transform (MWPT) and MWF (MWPT-MWF),\r\nwhich models each coefficient set as a tensor and then filters each tensor by applying MWF. MWPT-MWF has been\r\nproposed to preserve rare signals in the denoising process, which cannot be preserved well by using the MWF or\r\nPARAFAC filters. A real-world HYDICE HSI data is used in the experiments to assess these three tensor-based denoising\r\nmethods, and the performances of each method are analyzed in two aspects: signal-to-noise ratio and improvement\r\nof subsequent target detection results.
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