Survey of hyperspectral image denoising methods based on tensor decompositions

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.