<p>Sensors are being used in many industrial applications for equipment health mon-itoring and anomaly detection. However, sometimes operation and maintenanceof these sensors are costly. Thus companies are interested in reducing the num-ber of required sensors as much as possible. The straightforward solution is tocheck the prediction power of sensors and eliminate those sensors with limitedprediction capabilities. However, this is not an optimal solution because if we dis-card the identified sensors. Their historical data also will not be utilized anymore.However, typically such historical data can help improve the remaining sensors’signal power, and abolishing them does not seem the right solution. Therefore, wepropose the first data-driven approach based on tensor completion for re-utilizingdata of removed sensors, in addition to remaining sensors to create virtual sensors.We applied the proposed method on vibration sensors of high-speed separators,operating with five sensors. The producer company was interested in reducing thesensors to two. But with the aid of tensor completion-based virtual sensors, weshow that we can safely keep only one sensor and use four virtual sensors thatgive almost equal detection power compared to when we keep only two physicalsensors.</p>

How to handle large multi-dimensional datasets such as hyperspectral images and video information both efficiently and effectively plays an important role in big-data processing. The characteristics of tensor low-rank decomposition in recent years demonstrate the importance of capturing the tensor structure adequately which usually yields efficacious approaches. In this dissertation, we first aim to explore the tensor singular value decomposition (t-SVD) with the nonconvex regularization on the multi-view subspace clustering (MSC) problem, then develop two new tensor decomposition models with the Bayesian inference framework on the tensor completion and tensor robust principal component analysis (TRPCA) and tensor completion (TC) problems. Specifically, the following developments for multi-dimensional datasets under the mathematical tensor framework will be addressed. (1) By utilizing the t-SVD proposed by Kilmer et al. \cite{kilmer2013third}, we unify the Hyper-Laplacian (HL) and exclusive $\ell_{2,1}$ (L21) regularization with Tensor Log-Determinant Rank Minimization (TLD) to identify data clusters from the multiple views' inherent information. Whereby the HL regularization maintains the local geometrical structure that makes the estimation prune to nonlinearities, and the mixed $\ell_{2,1}$ and $\ell_{1,2}$ regularization provides the joint sparsity within-cluster as well as the exclusive sparsity between-cluster. Furthermore, a log-determinant function is used as a tighter tensor rank approximation to discriminate the dimension of features. (2) By considering a tube as an atom of a third-order tensor and constructing a data-driven learning dictionary from the observed noisy data along the tubes of a tensor, we develop a Bayesian dictionary learning model with tensor tubal transformed factorization to identify the underlying low-tubal-rank structure of the tensor substantially with the data-adaptive dictionary for the TRPCA problem. With the defined page-wise operators, an efficient variational Bayesian dictionary learning algorithm is established for TPRCA that enables to update of the posterior distributions along the third dimension simultaneously. (3) With the defined matrix outer product into the tensor decomposition process, we present a new decomposition model for a third-order tensor. The fundamental idea is to decompose tensors mathematically in a compact manner as much as possible. By incorporating the framework of Bayesian probabilistic inference, the new tensor decomposition model on the subtle matrix outer product (BPMOP) is developed for the TC and TRPCA problems. Extensive experiments on synthetic data and real-world datasets are conducted for the multi-view clustering, TC, and TRPCA problems to demonstrate the desirable effectiveness of the proposed approaches, by detailed comparison with currently available results in the literature.

Modern robotics and automation systems require high-level reasoning capability in representing, identifying, and interpreting the three-dimensional data of the real world. Understanding the world's geometric structure by visual data is known as 3D perception. The necessity of analyzing irregular and complex 3D data has led to the development of high-dimensional frameworks for data learning. Here, we design several sparse learning-based approaches for high-dimensional data that effectively tackle multiple perception problems, including data filtering, data recovery, and data retrieval. The frameworks offer generative solutions for analyzing complex and irregular data structures without prior knowledge of data. The first part of the dissertation proposes a novel method that simultaneously filters point cloud noise and outliers as well as completing missing data by utilizing a unified framework consisting of a novel tensor data representation, an adaptive feature encoder, and a generative Bayesian network. In the next section, a novel multi-level generative chaotic Recurrent Neural Network (RNN) has been proposed using a sparse tensor structure for image restoration. In the last part of the dissertation, we discuss the detection followed by localization, where we discuss extracting features from sparse tensors for data retrieval. / Doctor of Philosophy / The development of automation systems and robotics brought the modern world unrivaled affluence and convenience. However, the current automated tasks are mainly simple repetitive motions. Tasks that require more artificial capability with advanced visual cognition are still an unsolved problem for automation. Many of the high-level cognition-based tasks require the accurate visual perception of the environment and dynamic objects from the data received from the optical sensor. The capability to represent, identify and interpret complex visual data for understanding the geometric structure of the world is 3D perception. To better tackle the existing 3D perception challenges, this dissertation proposed a set of generative learning-based frameworks on sparse tensor data for various high-dimensional robotics perception applications: underwater point cloud filtering, image restoration, deformation detection, and localization. Underwater point cloud data is relevant for many applications such as environmental monitoring or geological exploration. The data collected with sonar sensors are however subjected to different types of noise, including holes, noise measurements, and outliers. In the first chapter, we propose a generative model for point cloud data recovery using Variational Bayesian (VB) based sparse tensor factorization methods to tackle these three defects simultaneously. In the second part of the dissertation, we propose an image restoration technique to tackle missing data, which is essential for many perception applications. An efficient generative chaotic RNN framework has been introduced for recovering the sparse tensor from a single corrupted image for various types of missing data. In the last chapter, a multi-level CNN for high-dimension tensor feature extraction for underwater vehicle localization has been proposed.

This thesis considers regularized block multi-convex optimization, where the feasible set and objective function are generally non-convex but convex in each block of variables. I review some of its interesting examples and propose a generalized block coordinate descent (BCD) method. The generalized BCD uses three different block-update schemes. Based on the property of one block subproblem, one can freely choose one of the three schemes to update the corresponding block of variables. Appropriate choices of block-update schemes can often speed up the algorithm and greatly save computing time. Under certain conditions, I show that any limit point satisfies the Nash equilibrium conditions. Furthermore, I establish its global convergence and estimate its asymptotic convergence rate by assuming a property based on the Kurdyka-{\L}ojasiewicz inequality. As a consequence, this thesis gives a global linear convergence result of cyclic block coordinate descent for strongly convex optimization. The proposed algorithms are adapted for factorizing nonnegative matrices and tensors, as well as completing them from their incomplete observations. The algorithms were tested on synthetic data, hyperspectral data, as well as image sets from the CBCL, ORL and Swimmer databases. Compared to the existing state-of-the-art algorithms, the proposed algorithms demonstrate superior performance in both speed and solution quality.

<p>Future wireless applications will require networks to provide high rates, reduced power consumption, reliable communications, and low latencies in a wide range of deployment scenarios. To support the never-ending growth in wireless data traffic, a solution is to operate wireless networks on the wide bandwidth available at higher frequencies, e.g., millimeter wave (mmWave) and sub-terahertz (sub-THz) bands. However, new challenges arise as networks operating at higher frequencies experience harsher propagation characteristics. To compensate for such severe signal attenuation, the directional beamforming via massive multipleinput multiple-output (MIMO) is adopted to provide array gains, but it necessitates accurate MIMO channel state information incurring unacceptably large training overhead. Wireless system engineers will require to develop fast and efficient channel training algorithms for massive MIMO systems. Another new challenge arises in scenarios without a direct link between the source and destination due to serious pathloss, which requires cooperative relay beamforming to enhance the communication coverage. The beamforming weights of the distributed relays and the receive combiner can be jointly optimized to enhance Quality-of-Service in multi-user relay beamforming networks. Our contributions cover three specific topics as follows: First, we develop a learning-based beam alignment approach, which enables the position-aided beam recommendation to support users at new positions, to reduce the training overhead in MIMO systems. Second, we propose a compressed training framework to estimate the time-varying sub-THz MIMO-OFDM channels with dual-wideband effect. Lastly, we propose a joint relay beamforming and receive combiner design, considering an optimization problem formulation that maximizes the minimum of the receiving signal-to-interference-plus-noise ratios among multiple users. In each specific topic, we provide the algorithms and show the numerical results to demonstrate the improved performance over the state-of-the-art techniques.</p>

Dans la première partie de cette thèse, on formule deux méthodes pour le calcul d'une décomposition polyadique canonique avec facteurs matriciels linéairement structurés (tels que des facteurs de Toeplitz ou en bande): un algorithme de moindres carrés alternés contraint (CALS) et une solution algébrique dans le cas où tous les facteurs sont circulants. Des versions exacte et approchée de la première méthode sont étudiées. La deuxième méthode fait appel à la transformée de Fourier multidimensionnelle du tenseur considéré, ce qui conduit à la résolution d'un système d'équations monomiales homogènes. Nos simulations montrent que la combinaison de ces approches fournit un estimateur statistiquement efficace, ce qui reste vrai pour d'autres combinaisons de CALS dans des scénarios impliquant des facteurs non-circulants. La seconde partie de la thèse porte sur la récupération de tenseurs de rang faible et, en particulier, sur le problème de reconstruction tensorielle (TC). On propose un algorithme efficace, noté SeMPIHT, qui emploie des projections séquentiellement optimales par mode comme opérateur de seuillage dur. Une borne de performance est dérivée sous des conditions d'isométrie restreinte habituelles, ce qui fournit des bornes d'échantillonnage sous-optimales. Cependant, nos simulations suggèrent que SeMPIHT obéit à des bornes optimales pour des mesures Gaussiennes. Des heuristiques de sélection du pas et d'augmentation graduelle du rang sont aussi élaborées dans le but d'améliorer sa performance. On propose aussi un schéma d'imputation pour TC basé sur un seuillage doux du coeur du modèle de Tucker et son utilité est illustrée avec des données réelles de trafic routier / In the first part of this thesis, we formulate two methods for computing a canonical polyadic decomposition having linearly structured matrix factors (such as, e.g., Toeplitz or banded factors): a general constrained alternating least squares (CALS) algorithm and an algebraic solution for the case where all factors are circulant. Exact and approximate versions of the former method are studied. The latter method relies on a multidimensional discrete-time Fourier transform of the target tensor, which leads to a system of homogeneous monomial equations whose resolution provides the desired circulant factors. Our simulations show that combining these approaches yields a statistically efficient estimator, which is also true for other combinations of CALS in scenarios involving non-circulant factors. The second part of the thesis concerns low-rank tensor recovery (LRTR) and, in particular, the tensor completion (TC) problem. We propose an efficient algorithm, called SeMPIHT, employing sequentially optimal modal projections as its hard thresholding operator. Then, a performance bound is derived under usual restricted isometry conditions, which however yield suboptimal sampling bounds. Yet, our simulations suggest SeMPIHT obeys optimal sampling bounds for Gaussian measurements. Step size selection and gradual rank increase heuristics are also elaborated in order to improve performance. We also devise an imputation scheme for TC based on soft thresholding of a Tucker model core and illustrate its utility in completing real-world road traffic data acquired by an intelligent transportation