Denoising of hyperspectral images by best multilinear rank approximation of a tensor

Maider Marin-McGee; Miguel Velez-Reyes

doi:10.1117/12.851745

12 May 2010 Denoising of hyperspectral images by best multilinear rank approximation of a tensor

Proceedings Volume 7695, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XVI; 76950J (2010) https://doi.org/10.1117/12.851745
Event: SPIE Defense, Security, and Sensing, 2010, Orlando, Florida, United States

Abstract

The hyperspectral image cube can be modeled as a three dimensional array. Tensors and the tools of multilinear algebra provide a natural framework to deal with this type of mathematical object. Singular value decomposition (SVD) and its variants have been used by the HSI community for denoising of hyperspectral imagery. Denoising of HSI using SVD is achieved by finding a low rank approximation of a matrix representation of the hyperspectral image cube. This paper investigates similar concepts in hyperspectral denoising by using a low multilinear rank approximation the given HSI tensor 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 to compute the BMRA using Alternating Least Square (ALS) method and Newton's Methods over product of Grassmann manifolds are presented. The effect of the multilinear rank, the numerical method used to compute the BMRA, and different parameter choices in those methods are studied. Results show that comparable results are achievable with both ALS and Newton type methods. Also, classification results using the filtered tensor are better than those obtained either with denoising using SVD or MNF.

Citation Download Citation

Maider Marin-McGee and Miguel Velez-Reyes "Denoising of hyperspectral images by best multilinear rank approximation of a tensor", Proc. SPIE 7695, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XVI, 76950J (12 May 2010); https://doi.org/10.1117/12.851745

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KEYWORDS

Denoising

Hyperspectral imaging

RGB color model

Matrices

Image classification

Principal component analysis

Radon

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