DE MORAIS GOULART , José Henrique

Pre-print available at https://arxiv.org/abs/1712.05742

The Candecomp/PARAFAC decomposition (CPD) is an important mathematical tool used in several fields of application. Yet, its computation is usually performed with iterative methods which are subject to reaching local minima and to exhibiting slow convergence. In some practical contexts, the data tensors of interest admit decompositions...

Low-rank tensor recovery (LRTR), i.e., the recovery of tensors having low-rank properties from underdetermined linear measurements, is a very important problem for numerous application areas, like medical/hyperspectral imaging, intelligent transport systems and computer network engineering, among others. This problem can be viewed as an...

Iterative hard thresholding (IHT) is a simple and effective approach to parsimonious data recovery. Its multilinear rank (mrank)-based application to low-rank tensor recovery (LRTR) is especially valuable given the difficulties involved in this problem. In this paper, we propose a novel IHT algorithm for LRTR, choosing sequential per-mode SVD...

Recovering low-rank tensors from undercomplete linear measurements is a computationally challenging problem of great practical importance. Most existing approaches circumvent the intractability of the tensor rank by considering instead the multilinear rank. Among them, the recently proposed tensor iterative hard thresholding (TIHT) algorithm is...

Computing low-rank approximations is one of the most important and well-studied problems involving tensors. In particular, approximations of low multilinear rank (mrank) have long been investigated by virtue of their usefulness for subspace analysis and dimensionality reduction purposes. The first part of this paper introduces a novel algorithm...

Tensors and tensor decompositions are very useful mathematical tools for representing and analyzing multidimensional data. The problem of estimating missing data in a tensor of measurements, named tensor completion, plays an important role in numerous applications. In this paper, to solve this problem, we propose a general iterative imputation...

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In this paper we present a modification of alternating least squares (ALS) for tensor canonical polyadic approximation that takes into account mutual coherence constraints. The proposed algorithm can be used to ensure well-posedness of the tensor approximation problem during ALS iterates and so is an alternative to existing approaches. We...

Super-resolution techniques for fluorescence microscopy areinvaluable tools for studying phenomena that take place atsub-cellular scales, thanks to their capability of overcominglight diffraction. Yet, achieving sufficient temporal resolutionfor imaging live-cell processes remains a challenging prob-lem. Exploiting the temporal...

The computation of a structured canonical polyadic decomposition (CPD) is useful to address several important modeling problems in real-world applications. In this paper, we consider the identification of a nonlinear system by means of a Wiener-Hammerstein model, assuming a high-order Volterra kernel of that system has been previously...

The canonical polyadic decomposition (CPD) of high-order tensors, also known as Candecomp/Parafac, is very useful for representing and analyzing multidimensional data. This paper considers a CPD model having structured matrix factors, as e.g. Toeplitz, Hankel or circulant matrices, and studies its associated estimation problem. This model...

In some applications, blind source separation can be performed by computing an approximate block-term tensor decomposition (BTD), under much milder constraints than matrix-based techniques. However, choosing the BTD model structure (i.e., the number of blocks and their ranks) is a difficult problem, and the standard least-squares formulation...