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Multimodal data fusion by coupled low-rank tensor approximations

Abstract : Due to the recent emergence of new modalities, the amount of signals collected daily has been increasing. As a result, it frequently occurs that various signals provide information about the same phenomenon. However, a single signal may only contain partial information about this phenomenon. Multimodal data fusion was proposed to overcome this issue. It is defined as joint processing of datasets acquired from different modalities. The aim of data fusion is to enhance the capabilities of each modality to express their specific information about the phenomenon of interest; it is also expected from data fusion that it brings out additional information that would be ignored by separate processing. However, due to the complex interactions between the modalities, understanding the advantages and limits of data fusion may not be straightforward.In a lot of applications such as biomedical imaging or remote sensing, the observed signals are three-dimensional arrays called tensors, thus tensor-based data fusion can be envisioned. Tensor low-rank modeling preserves the multidimensional structure of the observations and enjoys interesting uniqueness properties arising from tensor decompositions. In this work, we address the problem of recovering a high-resolution tensor from tensor observations with some lower resolutions.In particular, hyperspectral super-resolution (HSR) aims at reconstructing a tensor from two degraded versions. While one is degraded in two (spatial) modes, the second is degraded in the third (spectral) mode. Recently, tensor-based approaches were proposed for solving the problem at hand. These works are based on the assumption that the target tensor admits a given low-rank tensor decomposition. The first work addressing the problem of tensor-based HSR was based on a coupled canonical polyadic (CP) decomposition of the observations. This approach gave rise to numerous following reconstruction methods based on coupled tensor models, including our work.The first part of this thesis is devoted to the design of tensor-based algorithms for solving the HSR problem. In Chapter 2, we propose to formulate the problem as a coupled Tucker decomposition. We introduce two simple but fast algorithms based on the higher-order singular value decomposition of the observations. Our experiments show that our algorithms have a competitive performance with state-of-the-art tensor and matrix methods, with a lower computational time. In Chapter 3, we consider spectral variability between the observations. We formulate the reconstruction problem as a coupled block-term decomposition. We impose non-negativity of the low-rank factors, so that they can be incorporated into a physically-informed mixing model. Thus the proposed approach provides a solution to the joint HSR and unmixing problems.The second part of this thesis adresses the performance analysis of the coupled tensor models. The aim of this part is to assess the efficiency of some algorithms introduced in the first part. In Chapter 4, we consider constrained Cramér-Rao lower bounds (CCRB) for coupled tensor CP models. We provide a closed-form expression for the constrained Fisher information matrix in two scenarios, whether i) we only consider the fully-coupled reconstruction problem or ii) if we are interested in comparing the performance of fully-coupled, partially-coupled and uncoupled approaches. We prove that the existing CP-based algorithms are asymptotically efficient. Chapter 5 addresses a non-standard estimation problem in which the constraints on the deterministic model parameters involve a random parameter. We show that in this case, the standard CCRB is a non-informative bound. As a result, we introduce a new randomly constrained Cramér-Rao bound (RCCRB). The relevance of the RCCRB is illustrated using a coupled block-term decomposition model accounting for random uncertainties.
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Submitted on : Thursday, January 27, 2022 - 3:34:43 PM
Last modification on : Monday, January 31, 2022 - 3:12:35 AM


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Clémence Prévost. Multimodal data fusion by coupled low-rank tensor approximations. Automatic. Université de Lorraine, 2021. English. ⟨NNT : 2021LORR0180⟩. ⟨tel-03545904⟩



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