LOCUS: A REGULARIZED BLIND SOURCE SEPARATION METHOD WITH LOW-RANK STRUCTURE FOR INVESTIGATING BRAIN CONNECTIVITY.

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Sparse and low-rank methods in structural system identification and monitoring

The most standard blind source separation (BSS) methods address the situation when a set of signals are available, e.g. from measurements, and all of them are linear memoryless combinations, with unknown coefficient values, of the same limited set of unknown source signals. BSS methods aim at estimating these unknown source signals and/or coefficients. This generic problem is e.g. faced in the field of Earth observation (where it is also called “unsupervised unmixing”), when considering the commonly used (over)simplified model of hyperspectral images. Each pixel of such an image has an associated reflectance spectrum derived from measurements, which is defined by the fraction of sunlight power reflected by the corresponding Earth surface at each wavelength. Each source signal is then the single reflectance spectrum associated with one of the classes of pure materials which are present in the region of Earth corresponding to the overall considered hyperspectral image. Besides, the associated coefficients define the surfaces on Earth covered with each of these pure materials in each sub-region corresponding to one pixel of the considered image. However, real hyperspectral data e.g. obtained in urban areas have a much more complex structure than the above basic model: each class of pure materials (e.g. roof tiles, trees or asphalt) has so-called spectral or intra-class variability, i.e. it yields a somewhat different spectral component in each pixel of the image. In this complex framework, this chapter shows that Principal Component Analysis (PCA) and its proposed extension are of high interest at three stages of our investigation. First, PCA allows us to analyze the above-mentioned spectral variability of real high-dimensional hyperspectral data and to propose an extended data model which is suited to these complex data. We then develop a versatile extension of BSS methods based on Nonnegative Matrix Factorization, which adds the capability to handle arbitrary forms of intra-class variability by transposing PCA concepts to this original version of the BSS tramework. Finally, PCA again proves to be very well suited to analyzing the high-dimensional data obtained as the result of the proposed BSS method.

This paper presents a convex geometry (CG)-based method for blind separation of nonnegative sources. First, the unaccessible source matrix is normalized to be column-sum-to-one by mapping the available observation matrix. Then, its zero-samples are found by searching the facets of the convex hull spanned by the mapped observations. Considering these zero-samples, a quadratic cost function with respect to each row of the unmixing matrix, together with a linear constraint in relation to the involved variables, is proposed. Upon which, an algorithm is presented to estimate the unmixing matrix by solving a classical convex optimization problem. Unlike the traditional blind source separation (BSS) methods, the CG-based method does not require the independence assumption, nor the uncorrelation assumption. Compared with the BSS methods that are specifically designed to distinguish between nonnegative sources, the proposed method requires a weaker sparsity condition. Provided simulation results illustrate the performance of our method.

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The acquisition of channel state information (CSI) is essential in millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems. The mmWave channel exhibits sparse scattering characteristics and a meaningful low-rank structure, which can be simultaneously employed to reduce the complexity of channel estimation. Most existing works recover the low-rank structure of channels using nuclear norm theory. However, solving the nuclear norm-based convex problem often leads to a suboptimal solution of the rank minimization problem, thus degrading the accuracy of channel estimation. Previous contributions recover the channel using over-complete dictionary with the assumption that the mmWave channel can be sparsely represented under some dictionary. While over-complete dictionary may increase the computational complexity. To address these problems, we propose a channel estimation framework based on non-convex low-rank approximation and dictionary learning by exploring the joint low-rank and sparse representations of wireless channels. We surrogate the widely used nuclear norm theory with non-convex low-rank approximation method and design a dictionary learning algorithm based on channel feature classification employing deep neural network (DNN). Our simulation results reveal the proposed scheme outperform the conventional dictionary learning algorithm, Bayesian framework algorithm, and compressed sensing-based algorithms.

The methods that can be done for the estimation of the number of source signals and separation of source signals using time‐frequency information are proposed as a method of blind source separation. In these methods, some independent conditions are assumed in a time‐frequency domain, and observed signals are expanded to time‐frequency domain using wavelet analysis. However, these methods are not considered phase differences (difference of distance) between source signals and observed signals. A new method is proposed. The method can be done not only for the source separation but also the specification of the locations of source signals considering phase differences. In this method, it is necessary to assume a rather stronger independent condition than former methods. But, on account of this assumption, a function that becomes a real value only when phase differences are coincidence in time‐frequency domain is determined. Using this function, first of all, the number of source signals is calculated, then the locations of source signals and source signals are calculated. The effectiveness of the method is shown using actual synthetic signals.

Chapter 1 - Introduction

In the recent past, blind source separation (BSS) algorithms using multivariate statistical data analysis technique have been successfully used for source identification and separation in the field of biomedical and statistical signal processing. Recently numbers of different BSS techniques have been developed. With BSS methods being the feasible method for source separation and decomposition of biosignals, it is important to compare the different techniques and determine the most suitable method for the applications. This paper presents the performance of five BSS algorithms (SOBI, TDSEP, FastICA, JADE and Infomax) for decomposition of sEMG to identify subtle finger movements. It is observed that BSS algorithms based on second-order statistics (SOBI and TDSEP) gives better performance compared to algorithms based on higher-order statistics (FastICA, JADE and infomax).

Upgrading Sparse NMF algorithm for blind source separation through Adaptive Parameterized Hybrid Kernel based approach

Blind source separation and feature extraction in concurrent control charts pattern recognition: Novel analyses and a comparison of different methods

Brain Connectivity: A Journal of Clinical Neurology, Neuroscience, and Neuroimaging Advancing the Field of Neurology.

MultiXplore: Visual exploration platform for multimodal neuroimaging data

We study a relative optimization framework for quasi-maximum likeli- hood blind source separation and relative Newton method as its particular instance. The structure of the Hessian allows its fast approximate inversion. In the second part we present Smoothing Method of Multipliers (SMOM) for minimization of sum of pairwise maxima of smooth functions, in particular sum of absolute value terms. Incorporating Lagrange multiplier into a smooth approximation of max-type func- tion, we obtain an extended notion of non-quadratic augmented Lagrangian. Our approach does not require artiflcial variables, and preserves the sparse structure of Hessian. Convergence of the method is further accelerated by the Frozen Hessian strategy. We demonstrate e-ciency of this approach on an example of blind sep- aration of sparse sources. The non-linearity in this case is based on the absolute value function, which provides super-e-cient source separation.

The human brain operates as a complex network, and understanding its functional connectivity is a core challenge in neuroscience. Functional near-infrared spectroscopy (fNIRS) offers a non-invasive, portable method for studying brain activity and connectivity, providing valuable insights into the brain's network dynamics. In this study, we used fNIRS to examine the functional connectivity of the human brain during the Dual n-back task, a cognitive challenge that varies in memory load (0-back, 1-back, and 2-back). Data were collected from 24 channels in the frontal cortex and pre-processed with discrete wavelet transform. Functional connectivity matrices for each task level were calculated using correlation analysis, and graph theory metrics such as clustering coefficient and local and global efficiency were assessed. Statistical comparisons (t-tests and ANOVA) revealed significant differences in these metrics across memory load levels, with higher memory loads leading to altered brain connectivity patterns (p < 0.05 for clustering coefficient and local efficiency, p < 0.04 for global efficiency). These findings suggest that as cognitive demand increases, the functional connectivity of the brain's frontal network changes, reflecting the dynamic nature of brain activity during complex tasks. This research highlights the potential of fNIRS for exploring brain network functions and has broader implications for understanding cognitive processes and developing neurocognitive diagnostics and interventions.