Recent Numerical and Conceptual Advances for Tensor Decompositions — A Preview of Tensorlab 4.0

Vervliet, Nico; Vandecappelle, Michiel; Bousse, Martijn; Zink, Rob; Lathauwer, Lieven De

doi:10.1109/dsw.2019.8755590

Cited by 2 publications

(2 citation statements)

References 19 publications

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“…Consequently, the operational time of the algorithms can be substantially reduced, and an enhanced super-resolution accuracy is empirically observed. Detailed description of the initialization techniques are relegated to Appendix D. The CPD part performed in the initialization procedure is computed using Tensorlab [47] with 25 iterations at maximum. In all the simulations, we fix λ = 1.…”

Section: Simulationsmentioning

confidence: 99%

Hyperspectral Super-Resolution: A Coupled Tensor Factorization Approach

Kanatsoulis

Sidiropoulos

et al. 2018

IEEE Trans. Signal Process.

189

220

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Hyperspectral super-resolution refers to the problem of fusing a hyperspectral image (HSI) and a multispectral image (MSI) to produce a super-resolution image (SRI) that has fine spatial and spectral resolution. State-of-the-art methods approach the problem via low-rank matrix approximations to the matricized HSI and MSI. These methods are effective to some extent, but a number of challenges remain. First, HSIs and MSIs are naturally third-order tensors (data "cubes") and thus matricization is prone to loss of structural information-which could degrade performance. Second, it is unclear whether or not these low-rank matrix-based fusion strategies can guarantee identifiability or exact recovery of the SRI. However, identifiability plays a pivotal role in estimation problems and usually has a significant impact on performance in practice. Third, the majority of the existing methods assume that there are known (or easily estimated) degradation operators applied to the SRI to form the corresponding HSI and MSI-which is hardly the case in practice. In this work, we propose to tackle the super-resolution problem from a tensor perspective. Specifically, we utilize the multidimensional structure of the HSI and MSI to propose a coupled tensor factorization framework that can effectively overcome the aforementioned issues. The proposed approach guarantees the identifiability of the SRI under mild and realistic conditions. Furthermore, it works with little knowledge of the degradation operators, which is clearly an advantage over the existing methods. Semi-real numerical experiments are included to show the effectiveness of the proposed approach.

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Section: Simulationsmentioning

confidence: 99%

Hyperspectral Super-Resolution: A Coupled Tensor Factorization Approach

Kanatsoulis

Sidiropoulos

et al. 2018

IEEE Trans. Signal Process.

189

220

View full text Add to dashboard Cite

show abstract

“…There are several ways to handle the above non-convex problem. We choose to employ the tensorlab [62] toolbox, which uses a Gauss Newton approach to solve this nonlinear least squares (NLS) problem. After obtaining the estimates of A, B and C, X can be reconstructed by:…”

Section: Step 3: Coupled Cpdmentioning

confidence: 99%

Tensor Completion From Regular Sub-Nyquist Samples

Kanatsoulis

Sidiropoulos

et al. 2020

IEEE Trans. Signal Process.

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Signal sampling and reconstruction is a fundamental engineering task at the heart of signal processing. The celebrated Shannon-Nyquist theorem guarantees perfect signal reconstruction from uniform samples, obtained at a rate twice the maximum frequency present in the signal. Unfortunately a large number of signals of interest are far from being bandlimited. This motivated research on reconstruction from sub-Nyquist samples, which mainly hinges on the use of random / incoherent sampling procedures. However, uniform or regular sampling is more appealing in practice and from the system design point of view, as it is far simpler to implement, and often necessary due to system constraints. In this work, we study regular sampling and reconstruction of three-or higherdimensional signals (tensors). We show that reconstructing a tensor signal from regular samples is feasible. Under the proposed framework, the sample complexity is determined by the tensor rank-rather than the signal bandwidth. This result offers new perspectives for designing practical regular sampling patterns and systems for signals that are naturally tensors, e.g., images and video. For a concrete application, we show that functional magnetic resonance imaging (fMRI) acceleration is a tensor sampling problem, and design practical sampling schemes and an algorithmic framework to handle it. Numerical results show that our tensor sampling strategy accelerates the fMRI sampling process significantly without sacrificing reconstruction accuracy.

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Recent Numerical and Conceptual Advances for Tensor Decompositions — A Preview of Tensorlab 4.0

Cited by 2 publications

References 19 publications

Hyperspectral Super-Resolution: A Coupled Tensor Factorization Approach

Hyperspectral Super-Resolution: A Coupled Tensor Factorization Approach

Tensor Completion From Regular Sub-Nyquist Samples

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