Search

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)

In this paper, we extend the Discrete Empirical Interpolation Method (DEIM) to the third-order tensor case based on the t-product and use it to select important/ significant lateral and horizontal slices/features. The proposed Tubal DEIM (TDEIM) is investigated both theoretically and numerically. The experimental results show that the TDEIM can provide more accurate approximations than the existing methods. An application of the proposed method to the supervised classification task is also presented.

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~\cite{li2022permutation} 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 new algorithm that updates each structure-related variable alternately by local enumeration, \emph{greatly} reducing the number of evaluations compared to TNLS. We theoretically investigate the descent steps for TNLS and TnALE, proving that both algorithms can achieve linear convergence up to a constant if a sufficient reduction of the objective is \emph{reached} in each neighborhood. We also compare the evaluation efficiency of TNLS and TnALE, revealing that $\Omega(2^N)$ evaluations are typically required in TNLS for \emph{reaching} the objective reduction in the neighborhood, while ideally $O(N^2R)$ evaluations are sufficient in TnALE, where $N$ denotes the tensor order and $R$ reflects the \emph{``low-rankness''} of the neighborhood. Experimental results verify that TnALE can find practically good TN-ranks and permutations with vastly fewer evaluations than the state-of-the-art algorithms., Comment: Accepted by ICML2023, pre-printed version

In non-invasive brain-computer interface systems, pre-movement decoding plays an important role in the detection of movement before limbs actually move. Movement-related cortical potential is a kind of brain activity associated with pre-movement decoding. In current studies, patterns decoded from movement are mainly applied to the binary classification between movement state and resting state, such as elbow flexion and rest. The classifications between two movement states and among multiple movement states are still challenging. This study proposes a new method, the star-arrangement spectral filtering (SASF), to solve the multi-class pre-movement classification problem. We first design a referenced task-related component analysis (RTRCA) framework that consists of two modules. This first module is the classification between movement state and resting state; the second module is the classification of multiple movement states. SASF is developed by optimizing the features in RTRCA. In SASF, feature selection on filter banks is used on the first module of RTRCA, and feature selection on time windows is used on the second module of RTRCA. A linear discriminant analysis classifier is used to classify the optimized features. In the binary classification between two motions, the classification accuracy of SASF achieves 0.9670$\pm$0.0522, which is significantly higher than the result provided by the deep convolutional neural network (0.6247$\pm$0.0680) and the discriminative spatial pattern method (0.4400$\pm$0.0700). In the multi-class classification of 7 states, the classification accuracy of SASF is 0.9491$\pm$0.0372. The proposed SASF greatly improves the classification between two motions and enables the classification among multiple motions. The result shows that the movement can be decoded from EEG signals before the actual limb movement.

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).

Empirical mode decomposition (EMD) has developed into a prominent tool for adaptive, scale-based signal analysis in various fields like robotics, security and biomedical engineering. Since the dramatic increase in amount of data puts forward higher requirements for the capability of real-time signal analysis, it is difficult for existing EMD and its variants to trade off the growth of data dimension and the speed of signal analysis. In order to decompose multi-dimensional signals at a faster speed, we present a novel signal-serialization method (serial-EMD), which concatenates multi-variate or multi-dimensional signals into a one-dimensional signal and uses various one-dimensional EMD algorithms to decompose it. To verify the effects of the proposed method, synthetic multi-variate time series, artificial 2D images with various textures and real-world facial images are tested. Compared with existing multi-EMD algorithms, the decomposition time becomes significantly reduced. In addition, the results of facial recognition with Intrinsic Mode Functions (IMFs) extracted using our method can achieve a higher accuracy than those obtained by existing multi-EMD algorithms, which demonstrates the superior performance of our method in terms of the quality of IMFs. Furthermore, this method can provide a new perspective to optimize the existing EMD algorithms, that is, transforming the structure of the input signal rather than being constrained by developing envelope computation techniques or signal decomposition methods. In summary, the study suggests that the serial-EMD technique is a highly competitive and fast alternative for multi-dimensional signal analysis., Comment: 19 pages, 17 figures

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., Comment: 11 pages, 7 figures, paper accepted for presentation at L2ID Workshop at CVPR 2021 (19-25 June, 2021)

The Milky Way, when viewed in the neutral hydrogen line emission, presents large structures called Galactic supershells (GSs). The origin of these structures is still a subject of debate. The most common scenario invoked is the combined action of strong winds from massive stars and their subsequent explosion as supernova. The aim of this work is to determine the origin of 490 GSs that belong to the Catalog of HI supershell candidates in the outer part of the Galaxy. To know the physical processes that took place to create these expanding structures, it is necessary to determine their kinetic energies. To obtain all the GS masses, we developed and used an automatic algorithm, which was tested on 95 GSs whose masses were also estimated by hand. The estimated kinetic energies of the GSs vary from $1\times10^{47}$ to $3.4\times10^{51}$ erg. Considering an efficiency of 20% for the conversion of mechanical stellar wind energy into the kinetic energy of the GSs, the estimated values of the GS energies could be reached by stellar OB associations. For the GSs located at high Galactic latitudes, the possible mechanism for their creation could be attributed to collision with high velocity clouds (HVC). We have also analysed the distribution of GSs in the Galaxy, showing that at low Galactic latitudes, $|b|<2^\circ$, most of the structures in the third Galactic quadrant seem to be projected onto the Perseus Arm. The detection of GSs at very high distances from the Galactic centre may be attributed to diffuse gas associated with the circumgalactic medium of M31 and to intra-group gas in the Local Group filament., Comment: Accepted for publication in Astronomy and Astrophysics

One interesting question in love relationships is: finally, what and when is the end of this love relationship? Using a prey-predator Verhulst-Lotka-Volterra (VLV) model we imply cooperation and competition tendency between people in order to describe a "love dilemma game". We select the most simple but immediately most complex case for studying the set of nonlinear differential equations, i.e. that implying three persons, being at the same time prey and predator. We describe four different scenarios in such a love game containing either a one-way love or a love triangle. Our results show that it is hard to love more than one person simultaneously. Moreover, to love several people simultaneously is an unstable state. We find some condition in which persons tend to have a friendly relationship and love someone in spite of their antagonistic interaction. We demonstrate the dynamics by displaying flow diagrams., Comment: 23 pages, 16 references, 4 tables, 23 figures

One of the current issues in Brain-Computer Interface is how to deal with noisy Electroencephalography measurements organized as multidimensional datasets. On the other hand, recently, significant advances have been made in multidimensional signal completion algorithms that exploit tensor decomposition models to capture the intricate relationship among entries in a multidimensional signal. We propose to use tensor completion applied to EEG data for improving the classification performance in a motor imagery BCI system with corrupted measurements. Noisy measurements are considered as unknowns that are inferred from a tensor decomposition model. We evaluate the performance of four recently proposed tensor completion algorithms plus a simple interpolation strategy, first with random missing entries and then with missing samples constrained to have a specific structure (random missing channels), which is a more realistic assumption in BCI Applications. We measured the ability of these algorithms to reconstruct the tensor from observed data. Then, we tested the classification accuracy of imagined movement in a BCI experiment with missing samples. We show that for random missing entries, all tensor completion algorithms can recover missing samples increasing the classification performance compared to a simple interpolation approach. For the random missing channels case, we show that tensor completion algorithms help to reconstruct missing channels, significantly improving the accuracy in the classification of motor imagery, however, not at the same level as clean data. Tensor completion algorithms are useful in real BCI applications. The proposed strategy could allow using motor imagery BCI systems even when EEG data is highly affected by missing channels and/or samples, avoiding the need of new acquisitions in the calibration stage., Comment: 21 pages, 3 tables, 4 figures

A multiagent based model for a system of cooperative agents aiming at growth is proposed. This is based on a set of generalized Verhulst-Lotka-Volterra differential equations. In this study, strong cooperation is allowed among agents having similar sizes, and weak cooperation if agent have markedly different "sizes", thus establishing a peer-to-peer modulated interaction scheme. A rigorous analysis of the stable configurations is presented first examining the fixed points of the system, next determining their stability as a function of the model parameters. It is found that the agents are self-organizing into clusters. Furthermore, it is demonstrated that, depending on parameter values, multiple stable configurations can coexist. It occurs that only one of them always emerges with probability close to one, because its associated attractor dominates over the rest. This is shown through numerical integrations and simulations,after analytic developments. In contrast to the competitive case, agents are able to increase their capacity beyond the no-interaction case limit. In other words, when some collaborative partnership among a relatively small number of partners takes place, all agents act in good faith prioritizing the common good, whence receiving a mutual benefit allowing them to surpass their capacity., Comment: 14 pages, 31 refs., 6 figures, 1 table; quasi final version for Phys. Rev. E

The number of neuroimaging data sets publicly available is growing at fast rate. The increase in availability and resolution of neuroimaging data requires modern approaches to signal processing for data analysis and results validation. We introduce the application of sparse multiway decomposition methods (Caiafa and Cichocki, 2012) to linearized neuroimaging models. We show that decomposed models are more compact but as accurate as full models and can be successfully used for fast data analysis. We focus as example on a recent model for the evaluation of white matter connectomes (Pestilli et al, 2014). We show that the multiway decomposed model achieves accuracy comparable to the full model, while requiring only a small fraction of the memory and compute time. The approach has implications for a majority of neuroimaging methods using linear approximations to measured signals., Comment: 19 pages, 1 table, 9 figures

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 Processing

The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that higher-order tensors (i.e., multiway arrays) enable such a fundamental paradigm shift towards models that are essentially polynomial and whose uniqueness, unlike the matrix methods, is guaranteed under verymild and natural conditions. Benefiting fromthe power ofmultilinear algebra as theirmathematical backbone, data analysis techniques using tensor decompositions are shown to have great flexibility in the choice of constraints that match data properties, and to find more general latent components in the data than matrix-based methods. A comprehensive introduction to tensor decompositions is provided from a signal processing perspective, starting from the algebraic foundations, via basic Canonical Polyadic and Tucker models, through to advanced cause-effect and multi-view data analysis schemes. We show that tensor decompositions enable natural generalizations of some commonly used signal processing paradigms, such as canonical correlation and subspace techniques, signal separation, linear regression, feature extraction and classification. We also cover computational aspects, and point out how ideas from compressed sensing and scientific computing may be used for addressing the otherwise unmanageable storage and manipulation problems associated with big datasets. The concepts are supported by illustrative real world case studies illuminating the benefits of the tensor framework, as efficient and promising tools for modern signal processing, data analysis and machine learning applications; these benefits also extend to vector/matrix data through tensorization. Keywords: ICA, NMF, CPD, Tucker decomposition, HOSVD, tensor networks, Tensor Train.

The main goal of this work is to a have a new neutral hydrogen HI supershell candidates catalog to analyze their spatial distribution in the Galaxy and to carry out a statistical study of their main properties.}{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. 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 $0.8 \pm 0.1$, and $\sim 70 \,\%$ have their major axes parallel to the Galactic plane. The weighted mean value of the effective radius of the structures is $\sim$ 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 $\sim$ 8 kpc$^{-2}$, and decreases as we move farther away form the Galactic center. We have also compared our catalog with those by other authors., Comment: 14 pages, 12 figures

A new generalized multilinear regression model, termed the Higher-Order Partial Least Squares (HOPLS), is introduced with the aim to predict a tensor (multiway array) $\tensor{Y}$ from a tensor $\tensor{X}$ through projecting the data onto the latent space and performing regression on the corresponding latent variables. HOPLS differs substantially from other regression models in that it explains the data by a sum of orthogonal Tucker tensors, while the number of orthogonal loadings serves as a parameter to control model complexity and prevent overfitting. The low dimensional latent space is optimized sequentially via a deflation operation, yielding the best joint subspace approximation for both $\tensor{X}$ and $\tensor{Y}$. Instead of decomposing $\tensor{X}$ and $\tensor{Y}$ individually, higher order singular value decomposition on a newly defined generalized cross-covariance tensor is employed to optimize the orthogonal loadings. A systematic comparison on both synthetic data and real-world decoding of 3D movement trajectories from electrocorticogram (ECoG) signals demonstrate the advantages of HOPLS over the existing methods in terms of better predictive ability, suitability to handle small sample sizes, and robustness to noise.