Nonnegative tensor CP decomposition of hyperspectral data

International audienceNew hyperspectral missions will collect huge amounts of hyperspectral data. Besides, it is possible now to acquire time series and multiangular hyperspectral images. The process and analysis of these big data collections will require common hyperspectral techniques to be adapted or reformulated. The tensor decomposition, \textit{a.k.a.} multiway analysis, is a technique to decompose multiway arrays, that is, hypermatrices with more than two dimensions (ways). Hyperspectral time series and multiangular acquisitions can be represented as a 3-way tensor. Here, we apply Canonical Polyadic tensor decomposition techniques to the blind analysis of hyperspectral big data. In order to do so, we use a novel compression-based nonnegative CP decomposition. We show that the proposed methodology can be interpreted as multilinear blind spectral unmixing, a higher order extension of the widely known spectral unmixing. In the proposed approach, the big hyperspectral tensor is decomposed in three sets of factors which can be interpreted as spectral signatures, their spatial distribution and temporal/angular changes. We provide experimental validation using a study case of the snow coverage of the French Alps during the snow season

Dictionary-based Tensor Canonical Polyadic Decomposition

To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images

An Optimal HSI Image Compression using DWT and CP

The compression of hyperspectral images (HSIs) has recently become a very attractive issue for remote sensing applications because of their volumetric data. An efficient method for hyperspectral image compression is presented. The proposed algorithm, based on Discrete Wavelet Transform and CANDECOM/PARAFAC (DWT-CP), exploits both the spectral and the spatial information in the images. The core idea behind our proposed technique is to apply CP on the DWT coefficients of spectral bands of HSIs. We use DWT to effectively separate HSIs into different sub-images and CP to efficiently compact the energy of sub-images. We evaluate the effect of the proposed method on real HSIs and also compare the results with the well-known compression methods. The obtained results show a better performance when comparing with the existing method PCA with JPEG 2000 and 3D SPECK.DOI:http://dx.doi.org/10.11591/ijece.v4i3.6326

Hyperspectral Super-Resolution with Coupled Tucker Approximation: Recoverability and SVD-based algorithms

We propose a novel approach for hyperspectral super-resolution, that is based on low-rank tensor approximation for a coupled low-rank multilinear (Tucker) model. We show that the correct recovery holds for a wide range of multilinear ranks. For coupled tensor approximation, we propose two SVD-based algorithms that are simple and fast, but with a performance comparable to the state-of-the-art methods. The approach is applicable to the case of unknown spatial degradation and to the pansharpening problem.Comment: IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, in Pres

Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis

The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that higher-order tensors (i.e., multiway arrays) enable such a fundamental paradigm shift towards models that are essentially polynomial and whose uniqueness, unlike the matrix methods, is guaranteed under verymild and natural conditions. Benefiting fromthe power ofmultilinear algebra as theirmathematical backbone, data analysis techniques using tensor decompositions are shown to have great flexibility in the choice of constraints that match data properties, and to find more general latent components in the data than matrix-based methods. A comprehensive introduction to tensor decompositions is provided from a signal processing perspective, starting from the algebraic foundations, via basic Canonical Polyadic and Tucker models, through to advanced cause-effect and multi-view data analysis schemes. We show that tensor decompositions enable natural generalizations of some commonly used signal processing paradigms, such as canonical correlation and subspace techniques, signal separation, linear regression, feature extraction and classification. We also cover computational aspects, and point out how ideas from compressed sensing and scientific computing may be used for addressing the otherwise unmanageable storage and manipulation problems associated with big datasets. The concepts are supported by illustrative real world case studies illuminating the benefits of the tensor framework, as efficient and promising tools for modern signal processing, data analysis and machine learning applications; these benefits also extend to vector/matrix data through tensorization. Keywords: ICA, NMF, CPD, Tucker decomposition, HOSVD, tensor networks, Tensor Train