Low-rank tensor decomposition based dynamic network tracking

Infrared small target detection is widely used for early warning, aircraft monitoring, ship monitoring, and so on, which requires the small target and its background to be represented and modeled effectively to achieve their complete separation. Low-rank sparse decomposition based on the structural features of infrared images has attracted much attention among many algorithms because of its good interpretability. Based on our study, we found some shortcomings in existing baseline methods, such as redundancy of constructing tensors and fixed compromising factors. A self-adaptive low-rank sparse tensor decomposition model for infrared dim small target detection is proposed in this paper. In this model, the entropy of image block is used for fast matching of non-local similar blocks to construct a better sparse tensor for small targets. An adaptive strategy of low-rank sparse tensor decomposition is proposed for different background environments, which adaptively determines the weight coefficient to achieve effective separation of background and small targets in different background environments. Tensor robust principal component analysis (TRPCA) was applied to achieve low-rank sparse tensor decomposition to reconstruct small targets and their backgrounds separately. Sufficient experiments on the various types data sets show that the proposed method is competitive.

Reconfigurations of dynamic functional network connectivity after 1HZ repetitive transcranial magnetic stimulation in insomnia disorder.

Background/foreground separation is one of the most fundamental tasks in computer vision, especially for video data. Robust PCA (RPCA) and its tensor extension, namely, Robust Tensor PCA (RTPCA), provide an effective framework for background/foreground separation by decomposing the data into low-rank and sparse components, which contain the background and the foreground (moving objects), respectively. However, in real-world applications, the video data is contaminated with noise. For example, in metal additive manufacturing (AM), the processed X-ray video to study melt pool dynamics is very noisy. RPCA and RTPCA are not able to separate the background, foreground, and noise simultaneously. As a result, the noise will contaminate the background or the foreground or both. There is a need to remove the noise from the background and foreground. To achieve the three components decomposition, a smooth sparse Robust Tensor Decomposition (SS-RTD) model is proposed to decompose the data into static background, smooth foreground, and noise, respectively. Specifically, the static background is modeled by the low-rank tucker decomposition, the smooth foreground (moving objects) is modeled by the spatio-temporal continuity, which is enforced by the total variation regularization, and the noise is modeled by the sparsity, which is enforced by the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> norm. An efficient algorithm based on alternating direction method of multipliers (ADMM) is implemented to solve the proposed model. Extensive experiments on both simulated and real data demonstrate that the proposed method significantly outperforms the state-of-the-art approaches for background/foreground separation in noisy cases. Note to Practitioners—This work is motivated by melt pool detection in metal additive manufacturing where the processed X-ray video from the monitoring system is very noisy. The objective is to recover the background with porosity defects and the foreground with melt pool in the presence of noise. Existing methods fail to separate the noise from the background and foreground since RPCA and RTPCA have only two components, which cannot explain the three components in the data. This paper puts forward a smooth sparse Robust Tensor Decomposition by decomposing the tensor data into low-rank, smooth, and sparse components, respectively. It is a highly effective method for background/foreground separation in noisy case. In the case studies on simulated video and X-ray data, the proposed method can handle non-additive noise, and even the case of high noise-ratio. In the proposed algorithm, there is only one tuning parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula> . Based on the case studies, our method achieves satisfying performance by taking any <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda \in [{0.2,1}]$ </tex-math></inline-formula> with anisotropic total variation regularization. With this observation, practitioners can apply the proposed method without extensive parameter tuning work. Furthermore, the proposed method is also applicable to other popular industrial applications. Practitioners can use the proposed SS-RTD for degradation processes monitoring, where the degradation image contains the static background, anomaly, and random disturbance, respectively.

In this paper, we propose a novel multi-dimensional reconstruction method based on the low-rank plus sparse tensor (L+S) decomposition model to reconstruct dynamic magnetic resonance imaging (dMRI). The multi-dimensional reconstruction method is formulated using a non-convex alternating direction method of multipliers (ADMM), where the weighted tensor nuclear norm (WTNN) and l1-norm are used to enforce the low-rank in L and the sparsity in S, respectively. In particular, the weights used in the WTNN are sorted in a non-descending order, and we obtain a closed-form optimal solution of the WTNN minimization problem. The theoretical properties provided guarantee the weak convergence of our reconstruction method. In addition, a fast inexact reconstruction method is proposed to increase imaging speed and efficiency. Experimental results demonstrate that both of our reconstruction methods can achieve higher reconstruction quality than the state-of-the-art reconstruction methods.

Existing methods of the small target detection from infrared videos are not effective with the complex background. It is mainly caused by: 1) the interference of strong edges and the similarity with other nontarget objects and 2) the lack of the context information of both the background and the target in a spatio-temporal domain. By considering these two points, we propose to slide a window in a single frame and form a spatio-temporal cube with the current frame patch and other frame patches in the spatio-temporal domain. Then, we establish a spatio-temporal tensor model based on these patches. According to the sparse prior of the target and the local correlation of the background, the separation of the target and the background can be cast as a low rank and sparse tensor decomposition problem. The target is obtained from the sparse tensor by the tensor decomposition. The experiments show that our method gains better detection performance in infrared videos with the complex background by making full use of the spatio-temporal context information.

Cross-bispectral analysis identifies higher-order neural interactions, but the resulting high-dimensional tensors are difficult to interpret at the source level. Standard dimensionality reduction often lacks a physical link to the underlying neural generators. We introduce a low-rank tensor decomposition framework explicitly grounded in the physics of EEG signal generation. The method represents the cross-bispectrum using a single spatial mixing matrix and a compact source-interaction tensor, yielding a structured and physically interpretable model. This formulation enables a direct source-space interpretation and supports subsequent spatial demixing using MOCA to recover distinct source maps. Through extensive simulations, we show that the method robustly captures the dominant bispectral structure across a range of conditions, including varying signal-to-noise ratio, dipole orientation, amplitude balance, and source complexity. Applied to resting-state EEG, the approach identifies anatomically plausible parietal generators associated with prominent alpha-band bispectral interactions. In contrast to standard tensor decompositions such as Tucker and PARAFAC, which rely on unconstrained cores or rank-one assumptions, the proposed framework enforces a compact and interpretable source-interaction structure. This structure significantly improves interpretability and spatial localization while suppressing spurious high-dimensional variability. The proposed low-rank decomposition offers a principled and computationally efficient approach for reducing and interpreting cross-bispectral EEG data. By bridging tensor decomposition with biophysical source models, it enables insights into complex neural coupling that are inaccessible with standard matrix or tensor techniques.

Low back pain (LBP) is a prevalent pain condition whose persistence can lead to changes in the brain regions responsible for sensory, cognitive, attentional, and emotional processing. Previous neuroimaging studies have identified various structural and functional abnormalities in patients with LBP; however, how the static and dynamic large-scale functional network connectivity (FNC) of the brain is affected in these patients remains unclear. Forty-one patients with chronic low back pain (cLBP) and 42 healthy controls underwent resting-state functional MRI scanning. The independent component analysis method was employed to extract the resting-state networks. Subsequently, we calculate and compare between groups for static intra- and inter-network functional connectivity. In addition, we investigated the differences between dynamic functional network connectivity and dynamic temporal metrics between cLBP patients and healthy controls. Finally, we tried to distinguish cLBP patients from healthy controls by support vector machine method. The results showed that significant reductions in functional connectivity within the network were found within the DMN,DAN, and ECN in cLBP patients. Significant between-group differences were also found in static FNC and in each state of dynamic FNC. In addition, in terms of dynamic temporal metrics, fraction time and mean dwell time were significantly altered in cLBP patients. In conclusion, our study suggests the existence of static and dynamic large-scale brain network alterations in patients with cLBP. The findings provide insights into the neural mechanisms underlying various brain function abnormalities and altered pain experiences in patients with cLBP.

Dynamic functional network connectivity associated with post-traumatic stress symptoms in COVID-19 survivors

Genetic associations with macroscopic brain networks can provide insights into healthy and aberrant cortical connectivity in disease. However, associations specific to dynamic functional connectivity in Alzheimer's disease are still largely unexplored. Understanding the association between gene expression in the brain and functional networks may provide useful information about the molecular processes underlying variations in impaired brain function. Given the potential of dynamic functional connectivity to uncover brain states associated with Alzheimer's disease, it is interesting to ask: How does gene expression associated with Alzheimer's disease map onto the dynamic functional brain connectivity? If genetic variants associated with neurodegenerative processes involved in Alzheimer's disease are to be correlated with brain function, it is essential to generate such a map. Here, we investigate how the relation between gene expression in the brain and dynamic functional connectivity arises from nodal interactions, quantified by their role in network centrality (i.e. the drivers of the metastability), and the principal component of genetic co-expression across the brain. Our analyses include genetic variations associated with Alzheimer's disease and also genetic variants expressed within the cholinergic brain pathways. Our findings show that contrasts in metastability of functional networks between Alzheimer's and healthy individuals can in part be explained by the two combinations of genetic co-variations in the brain with the confidence interval between 72% and 92%. The highly central nodes, driving the brain aberrant metastable dynamics in Alzheimer's disease, highly correlate with the magnitude of variations from two combinations of genes expressed in the brain. These nodes include mainly the white matter, parietal and occipital brain regions, each of which (or their combinations) are involved in impaired cognitive function in Alzheimer's disease. In addition, our results provide evidence of the role of genetic associations across brain regions in asymmetric changes in ageing. We validated our findings on the same cohort using alternative brain parcellation methods. This work demonstrates how genetic variations underpin aberrant dynamic functional connectivity in Alzheimer's disease.

Tensor representation plays a very important role in high-dimensional problems, like in the emerging big data applications. The numerical treatment of high-dimensional problems is difficult because of the curse of dimensionality, i.e., the number of elements and the computational complexity increase exponentially with the data dimension. To break the curse of dimensionality, finding a low-dimensional representations of the original data is always important in practical applications, especially in big data applications. Tensor representation and decomposition are emerging and promising tools for big data analysis and data mining. In this paper, we exploit the technique of tensor train decomposition which is one of the most effective and stable representations of high dimensional tensors to learn a low-dimensional representation of original data. By combining tensor train decomposition with the support vector machine, we proposed a support vector machine based on low-rank tensor decomposition for big data applications. The proposed method possesses high classification performance and has significantly reduced computational complexity.

Background/Objectives: Young adulthood is a critical developmental period during which lifestyle behaviors may shape intrinsic brain network dynamics that support cognition. This pilot longitudinal intervention study examined whether variability in physical activity and sedentary behavior during an 8-week exercise and/or cognitive intervention protocol was associated with changes in intrinsic brain dynamics and cognitive and mood outcomes in undergraduate young adults. Methods: Participants (n = 32) completed resting-state functional magnetic resonance imaging (rs-fMRI) at baseline (T1) and post-intervention (T2). Dynamic functional network connectivity (dFNC) was estimated from 53 intrinsic connectivity networks derived using spatially constrained independent component analysis (ICA). Ten recurring dynamic connectivity states were identified and individualized using constrained dynamic double functional independent primitives (c-ddFIPs). State occupancy and dynamic convergence and divergence metrics were computed to characterize network flexibility. Results: Greater moderate-to-vigorous physical activity was modestly but consistently associated with increased occupancy of integrative higher-order states, particularly States 6 and 7, and reduced occupancy of more segregated configurations. More physically active individuals also demonstrated greater divergence between integrative and low-engagement states, whereas greater sedentary time corresponded to increased similarity among segregated configurations. Working memory performance showed parallel associations with more integrative and better-differentiated dynamic patterns. Conclusions: These findings suggest that dynamic functional network reconfiguration may represent a neurobiological mechanism linking lifestyle behaviors and cognitive health in young adulthood. Furthermore, they highlight the translational promise of engagement-driven, low-burden programs for college-aged young adults, showing that even modest variability in habitual physical activity corresponds to greater engagement and differentiation of integrative connectivity states linked to executive and broader cognitive functions.

Optical remote sensing images are often partially obscured by clouds due to the inability of visible light to penetrate cloud cover, which significantly limits their subsequent applications. Most existing cloud removal methods formulate the problem using low-rank and sparse priors within a discrete representation framework. However, these approaches typically rely on manually designed regularization terms, which fail to accurately capture the complex geostructural patterns in remote sensing imagery. In response to this issue, we develop a continuous blind cloud removal model. Specifically, the cloud-free component is represented using a continuous tensor function that integrates implicit neural representations with low-rank tensor decomposition. This representation enables the model to capture both global correlations and local smoothness. Furthermore, a band-wise sparsity constraint is employed to represent the cloud component. To preserve the information in regions not covered by clouds during reconstruction, a box constraint is incorporated. In this constraint, cloud detection is performed using an adaptive thresholding strategy, and a morphological erosion function is employed to ensure accurate detection of cloud boundaries. To efficiently handle the developed model, we formulate an alternating minimization algorithm that decouples the optimization into three interpretable subproblems: cloud-free reconstruction, cloud component estimation, and cloud detection. Our extensive evaluations on both synthetic and real-world data reveal that the proposed method performs competitively against state-of-the-art cloud removal methods.

The low-rank approximation of big data matrices and tensors plays a pivotal role in many modern applications. Recently, the randomized subspace iteration has shown to be a powerful tool in approximating large matrices. In this paper we present a rank-revealing, two-sided variant of the randomized subspace iteration. Novelty of our work lies in the utilization of the unpivoted QR factorization, rather than the singular value decomposition (SVD), for factorizing the compressed matrix. We provide bounds on the rank-revealingness of our algorithm as well as bounds on the error of the low-rank approximations, in both 2- and Frobenius norm. In addition, we employ the proposed algorithm to efficiently compute the low rank tensor decomposition using the truncated higher-order SVD. We conduct tests on (i) two classes of matrices, and (ii) synthetic data tensor and real dataset to demonstrate the efficacy of the proposed algorithms.

Schizophrenia is currently thought as a disorder with dysfunctional communication within and between sensory and cognitive processes. It has been hypothesized that these deficits mediate heterogeneous and comprehensive schizophrenia symptomatology. In this study, we investigated as to how the abnormal dynamic functional architecture of sensory and cognitive networks may contribute to these symptoms in schizophrenia. We calculated a sliding-window-based dynamic functional connectivity strength (FCS) and amplitude of low-frequency fluctuation (ALFF) maps. Then, using group-independent component analysis, we characterized spatial organization of dynamic functional network (sDFN) across various time windows. The spatial architectures of FCS/ALFF-sDFN were similar with traditional resting-state functional networks and cannot be accounted by length of the sliding window. Moreover, schizophrenic subjects demonstrated reduced dynamic functional connectivity (dFC) within sensory and perceptual sDFNs, as well as decreased connectivity between these sDFNs and high-order frontal sDFNs. The severity of patients' positive and total symptoms was related to these abnormal dFCs. Our findings revealed that the sDFN during rest might form the intrinsic functional architecture and functional changes associated with psychotic symptom deficit. Our results support the hypothesis that the dynamic functional network may influence the aberrant sensory and cognitive function in schizophrenia, further highlighting that targeting perceptual deficits could extend our understanding of the pathophysiology of schizophrenia.

Background Autism spectrum disorder (ASD) is characterized by aberrant functional brain connectivity and deficits in network dynamics. Transcranial direct current stimulation (tDCS) has emerged as a promising intervention with potential therapeutic effects; however, its effects on both static and dynamic functional brain network organization remained insufficiently understood. Methods A total of 42 children with ASD aged 4–6 years were enrolled and randomly assigned to either active tDCS or sham stimulation groups. Resting-state electroencephalography (EEG) data were acquired before and after the intervention. Low-order functional connectivity (LOFC) and high-order functional connectivity (HOFC) networks were constructed, followed by graph-theoretical analyses to assess clustering coefficient, characteristic path length, global efficiency, and local efficiency. Furthermore, state entropy was employed to evaluate dynamic network transitions between integrated and segregated states. Results Active tDCS was associated with increased LOFC strength in the delta, alpha, and beta bands, and more widespread increases in HOFC across all examined frequency bands. Changes in network topology were primarily observed in HOFC, with reductions in characteristic path length and increases in global and local efficiency, particularly in the delta and theta bands. Dynamic network analysis indicated that tDCS modulated state entropy at specific time scales in both LOFC and HOFC networks. These findings suggest shifts in functional coordination and temporal variability among the recorded regions. Behavioral measures exhibited a trend toward improvement in the active group; however, these changes were not the focus of the present analysis, and their relationship to neural modulation remains to be clarified in future work. Conclusions tDCS modulated functional interaction patterns and dynamic state characteristics among the recorded brain regions in children with ASD. These results provide preliminary neurophysiological evidence regarding the influence of tDCS on both static and dynamic network organization and highlight potential network-based markers to guide future individualized neuromodulation research. Further studies with larger samples and longitudinal follow-ups are needed to clarify the functional and clinical significance of these network-level changes.