DENOISING OF HYPERSPECTRAL IMAGES BY BEST MULTILINEAR RANK APPROXIMATION OF A TENSOR

摘要

The hyperspectral image cube can be modeled as a three dimensional array. Tensors and the tools of multilinear algebraprovide a natural framework to deal with this type of mathematical object. Singular value decomposition (SVD) and itsvariants have been used by the HSI community for denoising of hyperspectral imagery. Denoising of HSI using SVD isachieved by finding a low rank approximation of a matrix representation of the hyperspectral image cube. This paperinvestigates similar concepts in hyperspectral denoising by using a low multilinear rank approximation the given HSItensor representation. The Best Multilinear Rank Approximation (BMRA) of a given tensor A. is to find a lower multilinear rank tensor B that is as close as possible to A in the Frobenius norm. Different numerical methods tocompute the BMRA using Alternating Least Square (ALS) method and Newton's Methods over product of Grassmannmanifolds are presented. The effect of the multilinear rank, the numerical method used to compute the BMRA, anddifferent parameter choices in those methods are studied. Results show that comparable results are achievable with bothALS and Newton type methods. Also, classification results using the filtered tensor are better than those obtained eitherwith denoising using SVD or MNF.