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Complex-valued shift-invariant canonical polyadic decomposition (CPD) under a spatial phase sparsity constraint (pcsCPD) shows excellent separation performance when applied to band-pass filtered complex-valued multi-subject fMRI data. However, some useful information may also be eliminated when using a band-pass filter to suppress unwanted noise. As such, we propose an alternating rank- R and rank-1 least squares optimization to relax the CPD model. Based upon this optimization method, we present a novel constrained CPD algorithm with temporal shift-invariance and spatial sparsity and orthonormality constraints. More specifically, four steps are conducted until convergence for each iteration of the proposed algorithm: 1) use rank- R least-squares fit under spatial phase sparsity constraint to update shared spatial maps after phase de-ambiguity; 2) use orthonormality constraint to minimize the cross-talk between shared spatial maps; 3) update the aggregating mixing matrix using rank- R least-squares fit; 4) utilize shift-invariant rank-1 least-squares on a series of rank-1 matrices reconstructed by each column of the aggregating mixing matrix to update shared time courses, and subject-specific time delays and intensities. The experimental results of simulated and actual complex-valued fMRI data show that the proposed algorithm improves the estimates for task-related sensorimotor and auditory networks, compared to pcsCPD and tensorial spatial ICA. The proposed alternating rank- R and rank-1 least squares optimization is also flexible to improve CPD-related algorithm using alternating least squares.

Despite the impressive performance of correlation filter-based trackers in terms of robustness and accuracy, the trackers have room for improvement. The majority of existing trackers use a single feature or fixed fusion weights, which makes it possible for tracking to fail in the case of deformation or severe occlusion. In this paper, we propose a multi-feature response map adaptive fusion strategy based on the consistency of individual features and fused feature. It is able to improve the robustness and accuracy by building the better object appearance model. Moreover, since the response map has multiple local peaks when the target is occluded, we propose an anti-occlusion mechanism. Specifically, if the nonmaximal local peak is satisfied with our proposed conditions, we generate a new response map which is obtained by moving the center of the region of interest to the nonmaximal local peak position of the response map and re-extracting features. We then select the response map with the largest response value as the final response map. This proposed anti-occlusion mechanism can effectively cope with the problem of tracking failure caused by occlusion. Finally, by adjusting the learning rate in different scenes, we designed a high-confidence model update strategy to deal with the problem of model pollution. Besides, we conducted experiments on OTB2013, OTB2015, TC128 and UAV123 datasets and compared them with the current state-of-the-art algorithms, and the proposed algorithms have impressive advantages in terms of accuracy and robustness.

Recently, object trackers based on Siamese networks have attracted considerable attentions due to their remarkable tracking performance and widespread application. Especially, the anchor-based methods exploit the region proposal subnetwork to get accurate prediction of a target and make great performance improvement. However, those trackers cannot capture the spatial information very well and the pre-defined anchors will hinder robustness. To solve these problems, we propose a Siamese-based anchor-free object tracking algorithm with multiscale spatial attentions in this paper. Firstly, we take ResNet-50 as the backbone network to generate multiscale features of both template patch and search regions. Secondly, we propose the spatial attention extraction (SAE) block to capture the spatial information among all positions in the template and search region feature maps. Thirdly, we put these features into the SAE block to get the multiscale spatial attentions. Finally, an anchor-free classification and regression subnetwork is used for predicting the location of the target. Unlike anchor-based methods, our tracker directly predicts the target position without predefined parameters. Extensive experiments with state-of-the-art trackers are carried out on four challenging visual object tracking benchmarks: OTB100, UAV123, VOT2016 and GOT-10k. Those experimental results confirm the effectiveness of our proposed tracker.

Tucker decomposition (TKD) has been utilized to identify functional connectivity patterns using processed fMRI data, but seldom focuses on originally acquired fMRI data. This study proposes to decompose multi-subject fMRI data in a natural three-way of voxel × time × subject via TKD. Different from existing tensor decomposition algorithms such as canonical polyadic decomposition (CPD) for extracting shared spatial maps (SMs), we propose to extract both shared and individual SMs by exploring spatial-temporal-subject relationship contained in the core tensor. We test the proposed method using multi-subject resting-state fMRI data with comparison to CPD for evaluating shared SMs and independent vector analysis (IVA) for assessing individual SMs under different model orders. The results show that the proposed method yields better and more robust shared SMs than CPD and more consistent individual SMs than IVA, indicating the potential of TKD in providing group and individual brain networks in a high-dimensional coupling way.

Background Spatial sparsity has been found to be in line with the intrinsic characteristic of brain activation. However, identifying a sparse representation of complex-valued fMRI data is challenging due to high noise within the phase data. New methods We propose to reduce the noise by combining real and imaginary parts of complex-valued fMRI data along spatial and temporal dimensions to form a real-valued spatiotemporal concatenation model. This model not only enables flexible usage of existing real-valued sparse representation algorithms but also allows for the reconstruction of complex-valued spatial and temporal components from their real and imaginary estimates. We propose to select components from both real and imaginary estimates to reconstruct the complex-valued component, using phase denoising to recover weak brain activity from high-amplitude noise. Results The K-SVD algorithm was used to obtain a sparse representation within the spatiotemporal concatenation model. The results from simulated and experimental complex-valued fMRI datasets validated the efficacy of our method. Comparison with existing methods Compared to a magnitude-only approach, the proposed method detected additional voxels manifest within several specific regions expected to be involved but likely missing from the magnitude-only data, e.g., in the anterior cingulate cortex region. Simulation results showed that the additional voxels were accurate and unique information from the phase data. Compared to a complex-valued dictionary learning algorithm, our method exhibited lower noise for both magnitude and phase maps. Conclusions The proposed method is robust to noise and effective for identifying a sparse representation of the natively complex-valued fMRI data.

Convolutional neural networks (CNN) have exhibited great success in image classification. The application of CNN to classification of patients with brain disorders and healthy controls is also promising using functional magnetic resonance imaging (fMRI) data. However, the shortage of the number of subjects is a challenge for training CNN. Spatial maps separated from the fMRI data by independent component analysis (ICA) can provide a solution to this problem within an ICA-CNN framework. As such, we propose three strategies for both prior to and post ICA sample augmentation in the ICA-CNN framework. More precisely, we propose to increase the number of samples by performing spatial smoothing and band-pass filtering on the observed fMRI data before ICA, and spatial smoothing on the spatial maps after ICA. We evaluate the proposed methods using 82 resting-state fMRI datasets including 42 Schizophrenia patients and 40 healthy controls. The spatial map of the default mode network is used for classification, and each data augmentation is constrained to have the same numbers of samples for a fair comparison. The results show a 2%~15% increase in an average accuracy compared to the existing multiple-model-order method when adopting each of the proposed sample augmentation strategies. The spatial smoothing on the spatial maps is the most accurate among the three proposed methods. When using a combination of the proposed spatial smoothing on the spatial maps with the multiple-model-order method, the average accuracy increases above 90%.

Deep learning has contributed greatly to functional magnetic resonance imaging (fMRI) analysis, however, spatial maps derived from fMRI data by independent component analysis (ICA), as promising biomarkers, have rarely been directly used to perform individualized diagnosis. As such, this study proposes a novel framework combining ICA and convolutional neural network (CNN) for classifying schizophrenia patients (SZs) and healthy controls (HCs). ICA is first used to obtain components of interest which have been previously implicated in schizophrenia. Functionally informative slices of these components are then selected and labelled. CNN is finally employed to learn hierarchical diagnostic features from the slices and classify SZs and HCs. We use complex-valued fMRI data instead of magnitude fMRI data, in order to obtain more contiguous spatial activations. Spatial maps estimated by ICA with multiple model orders are employed for data argumentation to enhance the training process. Evaluations are performed using 82 resting-state complex-valued fMRI datasets including 42 SZs and 40 HCs. The proposed method shows an average accuracy of 72.65% in the default mode network and 78.34% in the auditory cortex for slice-level classification. When performing subject-level classification based on majority voting, the result shows 91.32% and 98.75% average accuracy, highlighting the potential of the proposed method for diagnosis of schizophrenia and other neurological diseases.

Canonical polyadic decomposition (CPD) may face a local optimal problem when analyzing multi-subject fMRI data with inter-subject variability. Beckmann and Smith proposed a tensor PICA approach that incorporated an independence constraint to the spatial modality by combining CPD with ICA, and alleviated the problem of inter-subject spatial map (SM) variability.This study extends tensor PICA to incorporate additional inter-subject time course (TC) variability and to connect CPD and ICA in a new way. Assuming multiple subjects share common TCs but with different time delays, we accommodate subject-dependent TC delays into the CP model based on the idea of shift-invariant CP (SCP). We use ICA as an initialization step to provide the aggregating mixing matrix for shift-invariant CPD to estimate shared TCs with subject-dependent delays and intensities. We then estimate shared SMs using a least-squares fit post shift-invariant CPD.Using simulated fMRI data as well as actual fMRI data we demonstrate that the proposed approach improves the estimates of the shared SMs and TCs, and the subject-dependent TC delays and intensities. The default mode component illustrates larger TC delays than the task-related component.The proposed approach shows improvements over tensor PICA in particular when TC delays are large, and also outperforms SCP with SM orthogonality constraint and SCP with ICA-based SM initialization.TCs with subject-dependent delays conform to the true situation of multi-subject fMRI data. The proposed approach is suitable for decomposing multi-subject fMRI data with large inter-subject temporal and spatial variability.

Electroencephalography (EEG) is one fundamental tool for functional brain imaging. EEG signals tend to be represented by a vector or a matrix to facilitate data processing and analysis with generally understood methodologies like time-series analysis, spectral analysis and matrix decomposition. Indeed, EEG signals are often naturally born with more than two modes of time and space, and they can be denoted by a multi-way array called as tensor. This review summarizes the current progress of tensor decomposition of EEG signals with three aspects. The first is about the existing modes and tensors of EEG signals. Second, two fundamental tensor decomposition models, canonical polyadic decomposition (CPD, it is also called parallel factor analysis-PARAFAC) and Tucker decomposition, are introduced and compared. Moreover, the applications of the two models for EEG signals are addressed. Particularly, the determination of the number of components for each mode is discussed. Finally, the N-way partial least square and higherorder partial least square are described for a potential trend to process and analyze brain signals of two modalities simultaneously peerReviewed

Background Complex-valued fMRI data can provide additional insights beyond magnitude-only data. However, independent vector analysis (IVA), which has exhibited great potential for group analysis of magnitude-only fMRI data, has rarely been applied to complex-valued fMRI data. The main challenges in this application include the extremely noisy nature and large variability of the source component vector (SCV) distribution. New method To address these challenges, we propose an adaptive fixed-point IVA algorithm for analyzing multiple-subject complex-valued fMRI data. We exploited a multivariate generalized Gaussian distribution (MGGD)- based nonlinear function to match varying SCV distributions in which the MGGD shape parameter was estimated using maximum likelihood estimation. To achieve our de-noising goal, we updated the MGGD-based nonlinearity in the dominant SCV subspace, and employed a post-IVA de-noising strategy based on phase information in the IVA estimates. We also incorporated the pseudo-covariance matrix of fMRI data into the algorithm to emphasize the noncircularity of complex-valued fMRI sources. Results Results from simulated and experimental fMRI data demonstrated the efficacy of our method. Comparison with existing method(s) Our approach exhibited significant improvements over typical complex-valued IVA algorithms, especially during higher noise levels and larger spatial and temporal changes. As expected, the proposed complex-valued IVA algorithm detected more contiguous and reasonable activations than the magnitude-only method for task-related (393%) and default mode (301%) spatial maps. Conclusions The proposed approach is suitable for decomposing multi-subject complex-valued fMRI data, and has great potential for capturing additional subject variability.

Independent vector analysis (IVA) has exhibited great potential for the group analysis of magnitude-only fMRI data, but has rarely been applied to native complex-valued fMRI data. We propose an adaptive fixed-point IVA algorithm by taking into account the extremely noisy nature, large variability of the source component vector (SCV) distribution, and non-circularity of the complex-valued fMRI data. The multivariate generalized Gaussian distribution (MGGD) is exploited to match the SCV distribution based on nonlinearity, the shape parameter of MGGD is estimated using maximum likelihood estimation, and the nonlinearity is updated in the dominant SCV subspace to achieve denoising goal. In addition, the pseudo-covariance matrix is incorporated into the algorithm to represent the non-circularity. Experimental results from simulated and actual fMRI data demonstrate significant improvements of our algorithm over a complex-valued IVA-G algorithm and several circular and noncircular fixed-point IVA variants.

Background ICA of complex-valued fMRI data is challenging because of the ambiguous and noisy nature of the phase. A typical solution is to remove noisy regions from fMRI data prior to ICA. However, it may be more optimal to carry out ICA of full complex-valued fMRI data, since any filtering or voxel-based processing may disrupt information that can be useful to ICA. New method We enable ICA of the full complex-valued fMRI data by utilizing phase information of estimated spatial maps (SMs). The SM phases are first adjusted to properly represent spatial phase changes of all voxels based on estimated time courses (TCs), and then these are used to segment the voxels into BOLD-related and unwanted voxels based on a criterion of TC real-part power maximization. Single-subject and group phase masks are finally constructed to remove the unwanted voxels from the individual and group SM estimates. Results Our method efficiently estimated not only the task-related component but also the non-task-related component DMN. Comparison with existing method(s) Our method extracted 139–331% more contiguous and reasonable activations than magnitude-only infomax for the task-related component and DMN at |Z| > 2.5, and detected more BOLD-related voxels, but eliminated more unwanted voxels than ICA of complex-valued fMRI data with pre-ICA de-noising. Our TC-based phase de-ambiguity exhibited higher accuracy and robustness than the SM-based method. Conclusions The TC-based phase de-ambiguity is essential to prepare the SM phases. The SM phases provide a new post-ICA index for reliably identifying and suppressing the unwanted voxels.

Tensor decomposition of fMRI data has gradually drawn attention since it can explore the multi-way data's structure which exists inherently in brain imaging. For multi-subject fMRI data analysis, time shifts occur inevitably among different participants, therefore, shift-invariant tensor decomposition should be used. This method allows for arbitrary shifts along one modality, and can yield satisfactory results for analyzing multi-set fMRI data with time shifts of different datasets. In this study, we presented the first application of shift-invariant tensor decomposition to simulated multi-subject fMRI data with shifts of time courses and variations of spatial maps. By this method, time shifts, spatial maps, time courses, and subjects' amplitudes were better estimated in contrast to group independent component analysis. Therefore, shift-invariant tensor decomposition is promising for real multi-set fMRI data analysis.

Magnitude-only resting-state fMRI data have been largely investigated via independent component analysis (ICA) for exacting spatial maps (SMs) and time courses. However, the native complex-valued fMRI data have rarely been studied. Motivated by the significant improvements achieved by ICA of complex-valued task fMRI data than magnitude-only task fMRI data, we present an efficient method for de-noising SM estimates which makes full use of complex-valued resting-state fMRI data. Our two main contributions include: (1) The first application of a post-ICA phase de-noising method, originally proposed for task fMRI data, to resting-state data, which recognizes voxels within a specific phase range as desired voxels. (2) A new phase range detection strategy for a specific SM component based on correlation with its reference. We continuously change the phase range within a larger range, and compute a set of correlation coefficients between each de-noised SM and its reference. The phase range with the maximal correlation determines the final selection. The detected results by the proposed approach confirm the correctness of the post-ICA phase de-noising method in the analysis of resting-state complex-valued fMRI data.

Independent vector analysis (IVA) has exhibited promising applications to complex-valued fMRI data, however model order effects on complex-valued IVA have not yet been studied. As such, we investigate model order effects on IVA using 16 task-based complex-valued fMRI data sets. A noncircular fixed-point complex-valued IVA (non-FIVA) algorithm was utilized. The model orders were varied from 10 to 160. The ICASSO toolbox was modified for selecting the best spatial estimates across all runs to assess the IVA stability. Non-FIVA was compared to a complex-valued independent component analysis (ICA) algorithm as well as to real-valued IVA and ICA algorithms which analyzed magnitude-only fMRI data. The complex-valued analysis detected component splitting at higher model orders, but in a different way from the magnitude-only analysis in that a complete component and its sub-components exist simultaneously. This suggests that the incorporation of phase fMRI data may better preserve the integrity of the larger networks. Good stability was also achieved by non-FIVA with different orders.