Stable, Robust and Super Fast Reconstruction of Tensors Using Multi-Way Projections

In the framework of multidimensional Compressed Sensing (CS), we introduce an analytical reconstruction formula that allows one to recover an $N$th-order $(I_1\times I_2\times \cdots \times I_N)$ data tensor $\underline{\mathbf{X}}$ from a reduced set of multi-way compressive measurements by exploiting its low multilinear-rank structure. Moreover, we show that, an interesting property of multi-way measurements allows us to build the reconstruction based on compressive linear measurements taken only in two selected modes, independently of the tensor order $N$. In addition, it is proved that, in the matrix case and in a particular case with $3$rd-order tensors where the same 2D sensor operator is applied to all mode-3 slices, the proposed reconstruction $\underline{\mathbf{X}}_\tau$ is stable in the sense that the approximation error is comparable to the one provided by the best low-multilinear-rank approximation, where $\tau$ is a threshold parameter that controls the approximation error. Through the analysis of the upper bound of the approximation error we show that, in the 2D case, an optimal value for the threshold parameter $\tau=\tau_0 > 0$ exists, which is confirmed by our simulation results. On the other hand, our experiments on 3D datasets show that very good reconstructions are obtained using $\tau=0$, which means that this parameter does not need to be tuned. Our extensive simulation results demonstrate the stability and robustness of the method when it is applied to real-world 2D and 3D signals. A comparison with state-of-the-arts sparsity based CS methods specialized for multidimensional signals is also included. A very attractive characteristic of the proposed method is that it provides a direct computation, i.e. it is non-iterative in contrast to all existing sparsity based CS algorithms, thus providing super fast computations, even for large datasets.Comment: Submitted to IEEE Transactions on Signal Processin

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

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 microwave tomography imaging, which could lead to a significant improvement of the state-of-the-arts algorithms.Comment: submitted to RevMexAA (conference series

A copula-based method for synthetic microarray data generation

In this work, we propose a copula-based method to generate synthetic gene expression data that account for marginal and joint probability distributions features captured from real data. Our method allows us to implant significant genes in the synthetic dataset in a controlled manner, giving the possibility of testing new detection algorithms under more realistic environments

Improving Pre-movement Pattern Detection with Filter Bank Selection

Pre-movement decoding plays an important role in movement detection and is able to detect movement onset with low-frequency electroencephalogram (EEG) signals before the limb moves. In related studies, pre-movement decoding with standard task-related component analysis (STRCA) has been demonstrated to be efficient for classification between movement state and resting state. However, the accuracies of STRCA differ among subbands in the frequency domain. Due to individual differences, the best subband differs among subjects and is difficult to be determined. This study aims to improve the performance of the STRCA method by a feature selection on multiple subbands and avoid the selection of best subbands. This study first compares three frequency range settings ($M_1$: subbands with equally spaced bandwidths; $M_2$: subbands whose high cut-off frequencies are twice the low cut-off frequencies; $M_3$: subbands that start at some specific fixed frequencies and end at the frequencies in an arithmetic sequence.). Then, we develop a mutual information based technique to select the features in these subbands. A binary support vector machine classifier is used to classify the selected essential features. The results show that $M_3$ is a better setting than the other two settings. With the filter banks in $M_3$, the classification accuracy of the proposed FBTRCA achieves 0.8700$\pm$0.1022, which means a significantly improved performance compared to STRCA (0.8287$\pm$0.1101) as well as to the cross validation and testing method (0.8431$\pm$0.1078)

A new catalog of HI supershell candidates in the outer part of the Galaxy

Aims. The main goal of this work is to a have a new neutral hydrogen (H i) supershell candidate catalog to analyze their spatial distribution in the Galaxy and to carry out a statistical study of their main properties. Methods. This catalog was carried out making use of the Leiden-Argentine-Bonn (LAB) survey. The supershell candidates were identified using a combination of two techniques: a visual inspection plus an automatic searching algorithm. Our automatic algorithm is able to detect both closed and open structures. Results. A total of 566 supershell candidates were identified. Most of them (347) are located in the second Galactic quadrant, while 219 were found in the third one. About 98% of a subset of 190 structures (used to derive the statistical properties of the supershell candidates) are elliptical with a mean weighted eccentricity of 0.8 ± 0.1, and ∼70% have their major axes parallel to the Galactic plane. The weighted mean value of the effective radius of the structures is ∼160 pc. Owing to the ability of our automatic algorithm to detect open structures, we have also identified some “galactic chimney” candidates. We find an asymmetry between the second and third Galactic quadrants in the sense that in the second one we detect structures as far as 32 kpc, while for the 3rd one the farthest structure is detected at 17 kpc. The supershell surface density in the solar neighborhood is ∼8 kpc−2, and decreases as we move farther away form the Galactic center. We have also compared our catalog with those by other authorsInstituto Argentino de RadioastronomíaFacultad de Ciencias Astronómicas y Geofísica

Detection of Wind Turbine Failures through Cross-Information between Neighbouring Turbines

In this paper, the time variation of signals from several SCADA systems of geographically closed turbines are analysed and compared. When operating correctly, they show a clear pattern of joint variation. However, the presence of a failure in one of the turbines causes the signals from the faulty turbine to decouple from the pattern. From this information, SCADA data is used to determine, firstly, how to derive reference signals describing this pattern and, secondly, to compare the evolution of different turbines with respect to this joint variation. This makes it possible to determine whether the behaviour of the assembly is correct, because they maintain the well-functioning patterns, or whether they are decoupled. The presented strategy is very effective and can provide important support for decision making in turbine maintenance and, in the near future, to improve the classification of signals for training supervised normality models. In addition to being a very effective system, it is a low computational cost strategy, which can add great value to the SCADA data systems present in wind farms.Peer ReviewedObjectius de Desenvolupament Sostenible::7 - Energia Assequible i No Contaminant::7.a - Per a 2030, augmentar la cooperació internacional per tal de facilitar l’accés a la investigació i a les tecnolo­gies energètiques no contaminants, incloses les fonts d’energia renovables, l’eficiència energètica i les tecnologies de combustibles fòssils avançades i menys contaminants, i promoure la inversió en infraestructures energètiques i tecnologies d’energia no contaminantObjectius de Desenvolupament Sostenible::7 - Energia Assequible i No Contaminant::7.b - Per a 2030, ampliar la infraestructura i millorar la tecnologia per tal d’oferir serveis d’energia moderns i sos­tenibles per a tots els països en desenvolupament, en particular els països menys avançats, els petits estats insulars en desenvolupament i els països en desenvolupament sense litoral, d’acord amb els programes de suport respectiusObjectius de Desenvolupament Sostenible::7 - Energia Assequible i No ContaminantPostprint (published version

Machine Learning Methods with Noisy, Incomplete or Small Datasets

In this article, we present a collection of fifteen novel contributions on machine learning methods with low-quality or imperfect datasets, which were accepted for publication in the special issue “Machine Learning Methods with Noisy, Incomplete or Small Datasets”, Applied Sciences (ISSN 2076-3417). These papers provide a variety of novel approaches to real-world machine learning problems where available datasets suffer from imperfections such as missing values, noise or artefacts. Contributions in applied sciences include medical applications, epidemic management tools, methodological work, and industrial applications, among others. We believe that this special issue will bring new ideas for solving this challenging problem, and will provide clear examples of application in real-world scenarios.Instituto Argentino de Radioastronomí

A Fast Gradient Approximation for Nonlinear Blind Signal Processing

When dealing with nonlinear blind processing algorithms (deconvolution or post-nonlinear source separation), complex mathematical estimations must be done giving as a result very slow algorithms. This is the case, for example, in speech processing, spike signals deconvolution or microarray data analysis. In this paper, we propose a simple method to reduce computational time for the inversion of Wiener systems or the separation of post-nonlinear mixtures, by using a linear approximation in a minimum mutual information algorithm. Simulation results demonstrate that linear spline interpolation is fast and accurate, obtaining very good results (similar to those obtained without approximation) while computational time is dramatically decreased. On the other hand, cubic spline interpolation also obtains similar good results, but due to its intrinsic complexity, the global algorithm is much more slow and hence not useful for our purpose

A Simple Approximation for Fast Nonlinear Deconvolution

When dealing with nonlinear blind deconvolution, complex mathematical estimations must be done giving as a result very slow algorithms. This is the case, for example, in speech processing or in microarray data analysis. In this paper we propose a simple method to reduce computational time for the inversion of Wiener systems by using a linear approximation in a minimum-mutual information algorithm. Experimental results demonstrate that linear spline interpolation is fast and accurate, obtaining very good results (similar to those obtained without approximation) while computational time is dramatically decreased