Nonorthogonal Tensor Matricization for Hyperspectral Image Filtering

Letexier, Damien; Bourennane, Salah; Talon, J.B.

doi:10.1109/lgrs.2007.905117

Cited by 51 publications

(12 citation statements)

References 18 publications

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“…Unfolding [9], also known as matricization [22], [23] or flattening [24], consists in rearranging a tensor (multiway array) into a matrix. To transform a third-order tensor X ∈ R I 1 ×I 2 ×I 3 into a matrix, the three-mode fibers must be arranged as the columns of the resulting matrix, i.e., a matrix X n (n = 1, 2, 3) with size I n × M n where…”

Section: B Unfolding Tensormentioning

confidence: 99%

Denoising of Hyperspectral Images Using the PARAFAC Model and Statistical Performance Analysis

Liu

Bourennane

Fossati

2012

IEEE Trans. Geosci. Remote Sensing

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254

136

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Denoising is an important preprocessing step to further analyze a hyperspectral image (HSI). The common denoising methods, such as 2-D (two dimensions) filter, actually rearrange data from 3-D to 2-D and ignore the spectral relationships among different bands of the image. Tensor decomposition method has been adapted to denoise HSIs, for instance Tucker3 (three-mode factor analysis) model. However, this model has problems in uniqueness of decomposition and in estimation of multiple ranks. In this paper, to overcome these problems, we exploit a powerful multilinear algebra model, named parallel factor analysis (PARAFAC), and the number of estimated rank is reduced to one. Assumed that HSI is disturbed by white Gaussian noise, the optimal rank of PARAFAC is estimated according to that the covariance matrix of the n-mode unfolding matrix of the removed noise should be approach to a scalar matrix. Then, the denoising results by PARAFAC decomposition are presented and compared with those obtained by Tucker3 model and 2-D filters. To further verify the denoising performance of PARAFAC decomposition, Cramer-Rao lower bound (CRLB) of denoising is deduced theoretically for the first time, and the experiment results show that the PARAFAC model is a preferable denoising method since the variance of the HSI denoised by it is closer to the CRLB than by other considered methods.Index Terms-Classification, Cramer-Rao lower bound (CRLB), denoising, hyperspectral image (HSI), parallel factor analysis (PARAFAC), Tucker3.

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Section: B Unfolding Tensormentioning

confidence: 99%

Denoising of Hyperspectral Images Using the PARAFAC Model and Statistical Performance Analysis

Liu

Bourennane

Fossati

2012

IEEE Trans. Geosci. Remote Sensing

Self Cite

254

136

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“…However, The method cannot be used directly for tensors. Some improved methods, which are combined with unfolding, are proposed [10,11]. The main idea of unfolding is converting tensors into matrices so that original tensors can be replaced by the matrices which reserve the original values of every element.…”

Section: Introductionmentioning

confidence: 99%

Short-Term Load Forecasting with Tensor Partial Least Squares-Neural Network

Feng

Meng

2019

Energies

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Short-term load forecasting is very important for power systems. The load is related to many factors which compose tensors. However, tensors cannot be input directly into most traditional forecasting models. This paper proposes a tensor partial least squares-neural network model (TPN) to forecast the power load. The model contains a tensor decomposition outer model and a nonlinear inner model. The outer model extracts common latent variables of tensor input and vector output and makes the residuals less than the threshold by iteration. The inner model determines the relationship between the latent variable matrix and the output by using a neural network. This model structure can preserve the information of tensors and the nonlinear features of the system. Three classical models, partial least squares (PLS), least squares support vector machine (LSSVM) and neural network (NN), are selected to compare the forecasting results. The results show that the proposed model is efficient for short-term load and daily load peak forecasting. Compared to PLS, LSSVM and NN, the TPN has the best forecasting accuracy.

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“…We address the problem of estimating simultaneously the ranges and the bearings of the objects in presence of phase errors due to the distortions of the array and to the perturbations of the impinging wavefronts. The idea is to associate the Spline Interpolation algorithm to DIRECT algorithm for accelerating the computation times [3,4]. To estimate the coherent signal subspace, a novel focusing operator is proposed.…”

Section: Introductionmentioning

confidence: 99%

Characterization of buried objects using wideband signals

Fossati

Han

Bourennane

2011

International Workshop on Systems, Signal Processing and Their Applications, WOSSPA

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This paper deals with buried object localization using a towed flexible array of sensors. We consider a new model by taking into account both the reflection and the refraction of wave at water-sediment interface. A new directional vector containing the bearings and the ranges of objects is proposed instead of classical plane wave used in MUSIC algorithm. To decorrelate the received signals and to estimate the coherent signal subspace a fast focusing operator is proposed. The robust DIRECT (DIviding RECTangles) method accelerated by spline interpolation is applied to estimate simultaneously the bearings and the ranges in the presence of phase errors. The performance of the developed methods is investigated on experimental data recorded during underwater acoustics experiments.

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Nonorthogonal Tensor Matricization for Hyperspectral Image Filtering

Cited by 51 publications

References 18 publications

Denoising of Hyperspectral Images Using the PARAFAC Model and Statistical Performance Analysis

Denoising of Hyperspectral Images Using the PARAFAC Model and Statistical Performance Analysis

Short-Term Load Forecasting with Tensor Partial Least Squares-Neural Network

Characterization of buried objects using wideband signals

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