Reconstruction of Multiway Arrays from Incomplete Information Using the Tucker Tensor Decomposition

Tensor decomposition models for multidimensional datasets (multiway arrays) have a long history in Mathematics and applied sciences. While these models have recently been applied to multidimensional signal processing, they were developed independently of the theory of sparse representations and Compressed Sensing (CS). We discuss and illustrate recent results revealing connections among tensor decompositions models, recovery of low-rank multidimensional signals and CS theory. It is shown that, if a multidimensional signal has a good low rank or sparse multilinear representation, in the sense of the Tucker decomposition model, then it can be reconstructed from incomplete measurements. We discuss reconstructions methods for the cases where only a subset of fibers (mode-n vectors) in each dimension of the signal are available (Fiber Sampling Tensor Decomposition - FSTD), or when only the values of a limited set of entries are known (Tensor completion or multidimensional inpainting problem) or when measurements are given in a compressed multilinear format (Kronecker CS). We illustrate these methods by computer simulations taken on real world multidimensional signals including Magnetic Resonance Imaging (MRI) datasets and Hyperspectral images of natural scenes.Fil: Caiafa, César Federico. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; ArgentinaNew Trends in Applied Harmonic Analysis Sparse Representations, Compressed Sensing and Multifractal Analysis (CIMPA 2013)Mar del PlataArgentinaUniversidad de Buneos Aire

Tópico en Procesamiento de Señales: Separación Ciega de Fuentes y Aplicaciones

En este artículo presentamos el problema de la Separación Ciega de Fuentes ("Blind Source Separation - BSS"), un tópico de gran interés en el área del Procesamiento de Señales con aplicaciones al procesamiento de imágenes satelitales y a la separación de fuentes de radiación en Radioastronomía entre otras.Los algoritmos de BSS (?Blind Source Separation - BSS") han sido desarrollados ampliamente durante los últimos 15 años y han sido aplicados con éxito a problemas prácticos en diversas áreas científicas y tecnológicas, a saber: separación de señales acústicas (audio), análisis de señales neuronales en Neurociencias, etc. (Comon & Jutten, 2010). Además, BSS también representa una herramienta muy útil para el procesamiento de imágenes satelitales y en Radioastronomía, dos aplicaciones que abordamos en este artículo.Fil: Caiafa, César Federico. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; Argentin

A sparse coding approach to inverse problems with application to microwave tomography

Inverse imaging problems that are ill-posed can be encountered across multiple domains of science and technology, ranging from medical diagnosis to astronomical studies. To reconstruct images from incomplete and distorted data, it is necessary to create algorithms that can take into account both, the physical mechanisms responsible for generating these measurements and the intrinsic characteristics of the images being analyzed. In this work, the sparse representation of images is reviewed, which is a realistic, compact and effective generative model for natural images inspired by the visual system of mammals. It enables us to address ill-posed linear inverse problems by training the model on a vast collection of images. Moreover, we extend the application of sparse coding to solve the non-linear and ill-posed problem in micrFil: Caiafa, César Federico. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; ArgentinaFil: Irastorza, Ramiro Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaIAR 60th Anniversary: Prospects for Low Frequency Radio Astronomy in South AmericaBuenos AiresArgentinaInstituto Argentino de Astronomí

Using generic order moments for separation of dependent sources with linear conditional expectations

In this work, we approach the blind separation of dependent sources based only on a set of their linear mixtures. We prove that, when the sources have a pairwise dependence characterized by the linear conditional expectation (LCE) law, we are able to separate them by maximizing or minimizing a Generic Order Moment (GOM) of their mixture. This general measure includes the higher order as well as the fractional moment cases. Our results, not only confirm some of the existing results for the independent sources case but also they allow us to explore new objective functions for Dependent Component Analysis. A set of examples illustrating the consequences of our theory is presented. Also, a comparison of our GOM based algorithm, the classical FASTICA and a very recently proposed algorithm for dependent sources, the Bounded Component Analysis (BCA) algorithm, is shown.Fil: Caiafa, César Federico. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; ArgentinaFil: Kuruoglu, Ercan E.. Istituto di Scienza e Tecnologie dell’Informazione; Italia. Consiglio Nazionale delle Ricerche; Italia21ª European Signal Processing ConferenceMarrakechMarruecosEuropean Signal Processing Society (EURASIP

Ensemble tractography

Fiber tractography uses diffusion MRI to estimate the trajectory and cortical projection zones of white matter fascicles in the living human brain. There are many different tractography algorithms and each requires the user to set several parameters, such as curvature threshold. Choosing a single algorithm with a specific parameters sets poses two challenges. First, different algorithms and parameter values produce different results. Second, the optimal choice of algorithm and parameter value may differ between different white matter regions or different fascicles, subjects, and acquisition parameters. We propose using ensemble methods to reduce algorithm and parameter dependencies. To do so we separate the processes of fascicle generation and evaluation. Specifically, we analyze the value of creating optimized connectomes by systematically combining candidate fascicles from an ensemble of algorithms (deterministic and probabilistic) and sweeping through key parameters (curvature and stopping criterion). The ensemble approach leads to optimized connectomes that provide better cross-validatedprediction error of the diffusion MRI data than optimized connectomes generated using the singlealgorithms or parameter set. Furthermore, the ensemble approach produces connectomes that contain both short- and long-range fascicles, whereas single-parameter connectomes are biased towards one or the other. In summary, a systematic ensemble tractography approach can produce connectomes that are superior to standard single parameter estimates both for predicting the diffusion measurements and estimating white matter fascicles.Fil: Takemura, Hiromasa. University of Stanford; Estados Unidos. Osaka University; JapónFil: Caiafa, César Federico. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; ArgentinaFil: Wandell, Brian A.. University of Stanford; Estados UnidosFil: Pestilli, Franco. Indiana University; Estados Unido

A Sparse Tensor Decomposition with Multi-Dictionary Learning Applied to Diffusion Brain Imaging

We use a multidimensional signal representation that integrates diffusion Magnetic Resonance Imaging (dMRI) and tractography (brain connections) using sparse tensor decomposition. The representation encodes brain connections (fibers) into a very-large, but sparse, core tensor and allows to predict dMRI measurements based on a dictionary of diffusion signals. We propose an algorithm to learn the constituent parts of the model from a dataset. The algorithm assumes a tractography model (support of core tensor) and iteratively minimizes the Frobenius norm of the error as a function of the dictionary atoms, the values of nonzero entries in the sparse core tensor and the fiber weights. We use a nonparametric dictionary learning (DL) approach to estimate signal atoms. Moreover, the algorithm is able to learn multiple dictionaries associated to different brain locations (voxels) allowing for mapping distinctive tissue types. We illustrate the algorithm through results obtained on a large in-vivo high-resolution dataset.Fil: Caiafa, César Federico. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; Argentina. Indiana University; Estados UnidosFil: Cichocki, Andrzej. Labsp. Riken; JapónFil: Pestilli, Franco. Indiana University; Estados UnidosSignal Processing with Adaptive Sparse Structured Representations workshopLisboaPortugalUniversity of Lisbo

Unified representation of tractography and diffusion-weighted MRI data using sparse multidimensional arrays

Recently, linear formulations and convex optimization methods have been proposed to predict diffusion-weighted Magnetic Resonance Imaging (dMRI) data given estimates of brain connections generated using tractography algorithms. The size of the linear models comprising such methods grows with both dMRI data and connectome resolution, and can become very large when applied to modern data. In this paper, we introduce a method to encode dMRI signals and large connectomes, i.e., those that range from hundreds of thousands to millions of fascicles (bundles of neuronal axons), by using a sparse tensor decomposition. We show that this tensor decomposition accurately approximates the Linear Fascicle Evaluation (LiFE) model, one of the recently developed linear models. We provide a theoretical analysis of the accuracy of the sparse decomposed model, LiFE_SD, and demonstrate that it can reduce the size of the model significantly. Also, we develop algorithms to implement the optimization solver using the tensor representation in an efficient way.Fil: Caiafa, César Federico. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; Argentina. Indiana University; Estados UnidosFil: Sporns, Olaf. Indiana University; Estados UnidosFil: Saykin, Andy. Indiana University; Estados UnidosFil: Pestilli, Franco. Indiana University; Estados Unidos31st Conference on Neural Information Processing SystemsLong BeachEstados UnidosNational Science Foundatio

Learning from Incomplete Features by Simultaneous Training of Neural Networks and Sparse Coding

In this paper, the problem of training a classifier on a dataset with incomplete features is addressed. We assume that different subsets of features (random or structured) are available at each data instance. This situation typically occurs in the applications when not all the features are collected for every data sample. A new supervised learning method is developed to train a general classifier, such as a logistic regression or a deep neural network, using only a subset of features per sample, while assuming sparse representations of data vectors on an unknown dictionary. Sufficient conditions are identified, such that, if it is possible to train a classifier on incomplete observations so that their reconstructions are well separated by a hyperplane, then the same classifier also correctly separates the original (unobserved) data samples. Extensive simulation results on synthetic and well-known datasets are presented that validate our theoretical findings and demonstrate the effectiveness of the proposed method compared to traditional data imputation approaches and one state-of-the-art algorithm.Fil: Caiafa, César Federico. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; ArgentinaFil: Wang, Ziyao. South East University; ChinaFil: Sole Casals, Jordi. University of Vic; EspañaFil: Zhao, Qibin. Center for Advanced Intelligence Project; JapónIEEE Computer Society Conference on Computer Vision and Pattern Recognition 2021New YorkEstados UnidosIEE

¿Qué es la Inteligencia Artificial?

Muy probablemente, el lector haya descubierto el término Inteligencia Artificial (IA) a través de la literatura fantástica o producciones cinematográficas que, frecuentemente, aluden a un futuro dominado por la tecnología y plagado de robots humanoides. Sin duda, esas obras de ciencia ficción estuvieron inspiradas en discusiones científicas iniciadas a partir de mediados del siglo XX con la aparición de las primeras computadoras y con la idea de que éstas pudieran imitar, y hasta superar, las habilidades intelectuales de los humanos. No es casual que Isaac Asimov, autor del libro de ciencia ficción pionero en IA publicado en 1950: ?Yo, Robot? (Asimov, 2001), fuera profesor de la Universidad de Boston, doctorado en Química, cuyo desempeño en la academia le permitió estar al tanto de los avances en las por entonces florecientes ciencias de la computación. Si bien en el pasado reciente la IA pertenecía casi exclusivamente al mundo de la ciencia ficción o era materia de estudio de un puñado de científicos, durante los últimos años hemos comenzado a familiarizarnos con este término que ya forma parte de nuestra vida cada día. Nuestros teléfonos celulares están dotados de IA, nos sugieren itinerarios óptimos, nos recomiendan artículos para comprar y nos identifican en una fotografía tomada por un contacto en una red social, entre otras acciones cotidianas. La IA, ha dejado de ser una idea futurística para formar parte de nuestras vidas, además de tener un rol relevante en el desarrollo de la ciencia moderna. Nos permite descubrir inteligentemente nuevas drogas para tratamientos de enfermedades, ayuda a los médicos a diagnosticar enfermedades a partir de imágenes, asiste a los astrónomos en el análisis de grandes volúmenes de datos para validar nuevas teorías científicas, entre otras aplicaciones a la ciencia. Pero ¿de qué hablamos exactamente cuando nos referimos a la IA? En este breve artículo, se cuenta brevemente la historia de esta tecnología con una introducción a sus principios fundamentales y utilidades.Fil: Caiafa, César Federico. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; ArgentinaFil: Lew, Sergio Eduardo. Universidad de Buenos Aires. Facultad de Ingeniería; Argentin

Alternating Local Enumeration (TnALE): solving tensor network structure search with fewer evaluations

Tensor network (TN) is a powerful framework in machine learning, but selecting a good TN model, known as TN structure search (TN-SS), is a challenging and computationally intensive task. The recent approach TNLS (Li et al., 2022) showed promising results for this task. However, its computational efficiency is still unaffordable, requiring too many evaluations of the objective function. We propose TnALE, a surprisingly simple algorithm that updates each structure-related variable alternately by local enumeration, greatly reducing the number of evaluations compared to TNLS. We theoretically investigate the descent steps for TNLS and TnALE, proving that both the algorithms can achieve linear convergence up to a constant if a sufficient reduction of the objective is reached in each neighborhood. We further compare the evaluation efficiency of TNLS and TnALE, revealing that Ω(2K) evaluations are typically required in TNLS for reaching the objective reduction, while ideally O(KR) evaluations are sufficient in TnALE, where K denotes the dimension of search space and R reflects the “low-rankness” of the neighborhood. Experimental results verify that TnALE can find practically good TN structures with vastly fewer evaluations than the state-of-the-art algorithms.Fil: Li, Chao. Riken Aip; JapónFil: Zeng, Junhua. Riken Aip; Japón. Guangdong University of Technology; ChinaFil: Li, Chunmei. Riken Aip; Japón. Harbin Engineering University; ChinaFil: Caiafa, César Federico. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; ArgentinaFil: Zhao, Qibin. Riken Aip; Japón40th International Conference on Machine LearningHonoluluEstados UnidosInternational Council for Machinery Lubricatio