Three layered sparse dictionary learning algorithm for enhancing the subject wise segregation of brain networks

Independent component analysis (ICA) and dictionary learning (DL) are the most successful blind source separation (BSS) methods for functional magnetic resonance imaging (fMRI) data analysis. However, ICA to higher and DL to lower extent may suffer from performance degradation by the presence of anomalous observations in the recovered time courses (TCs) and high overlaps among spatial maps (SMs). This paper addressed both problems using a novel three-layered sparse DL (TLSDL) algorithm that incorporated prior information in the dictionary update process and recovered full-rank outlier-free TCs from highly corrupted measurements. The associated sequential DL model involved factorizing each subject's data into a multi-subject (MS) dictionary and MS sparse code while imposing a low-rank and a sparse matrix decomposition restriction on the dictionary matrix. It is derived by solving three layers of feature extraction and component estimation. The first and second layers captured brain regions with low and moderate spatial overlaps, respectively. The third layer that segregated regions with significant spatial overlaps solved a sequence of vector decomposition problems using the proximal alternating linearized minimization (PALM) method and solved a decomposition restriction using the alternating directions method (ALM). It learned outlier-free dynamics that integrate spatiotemporal diversities across brains and external information. It differs from existing DL methods owing to its unique optimization model, which incorporates prior knowledge, subject-wise/multi-subject representation matrices, and outlier handling. The TLSDL algorithm was compared with existing dictionary learning algorithms using experimental and synthetic fMRI datasets to verify its performance. Overall, the mean correlation value was found to be 26 % higher for the TLSDL than for the state-of-the-art subject-wise sequential DL (swsDL) technique.

A survey of brain functional network extraction methods using fMRI data

Functional network (FN) analyses play a pivotal role in uncovering insights into brain function and understanding the pathophysiology of various brain disorders. This paper focuses on classical and advanced methods for deriving brain FNs from functional magnetic resonance imaging (fMRI) data. We systematically review their foundational principles, advantages, shortcomings, and interrelations, encompassing both static and dynamic FN extraction approaches. In the context of static FN extraction, we present hypothesis-driven methods such as region of interest (ROI)-based approaches as well as data-driven methods including matrix decomposition, clustering, and deep learning. For dynamic FN extraction, both window-based and windowless methods are surveyed with respect to the estimation of time-varying FN and the subsequent computation of FN states. We also discuss the scope of application of the various methods and avenues for future improvements.

A novel subject-wise dictionary learning approach using multi-subject fMRI spatial and temporal components

The conventional dictionary learning (DL) algorithms aim to adapt the dictionary/sparse code to individual functional magnetic resonance imaging (fMRI) data. Thus, lacking the capability to consolidate the spatiotemporal diversities offered by other subjects. Considering that subject-wise (sw) data matrix can be decomposed into the sparse linear combination of multi-subject (MS) time courses and MS spatial maps, two new algorithms, sw sequential DL (swsDL) and sw block DL (swbDL), have been proposed. They are based on the novel framework, defined by the mixing model, where base matrices prepared by operating a computationally fast sparse spatiotemporal blind source separation method over multiple subjects are employed to adapt the mixing matrices to sw training data. They solve the optimization models formulated using [Formula: see text]/[Formula: see text]-norm penalization/constraints through dictionary/sparse code pair update and alternating minimization approach. They are unique because no existing sparse DL method can incorporate MS spatiotemporal components while updating sw atoms/sparse codes, which can eventually be assembled using neuroscience knowledge to extract group-level dynamics. Various fMRI datasets are used to evaluate and compare the performance of the proposed algorithms with existing state-of-the-art algorithms. Specifically, overall, a [Formula: see text] increase in the mean correlation value and [Formula: see text] reduction in the mean computation time exhibited by swsDL and swbDL, respectively, over the adaptive consistent sequential dictionary algorithm.

A Scalable Approach to Independent Vector Analysis by Shared Subspace Separation for Multi-Subject fMRI Analysis

Joint blind source separation (JBSS) has wide applications in modeling latent structures across multiple related datasets. However, JBSS is computationally prohibitive with high-dimensional data, limiting the number of datasets that can be included in a tractable analysis. Furthermore, JBSS may not be effective if the data's true latent dimensionality is not adequately modeled, where severe overparameterization may lead to poor separation and time performance. In this paper, we propose a scalable JBSS method by modeling and separating the "shared" subspace from the data. The shared subspace is defined as the subset of latent sources that exists across all datasets, represented by groups of sources that collectively form a low-rank structure. Our method first provides the efficient initialization of the independent vector analysis (IVA) with a multivariate Gaussian source prior (IVA-G) specifically designed to estimate the shared sources. Estimated sources are then evaluated regarding whether they are shared, upon which further JBSS is applied separately to the shared and non-shared sources. This provides an effective means to reduce the dimensionality of the problem, improving analyses with larger numbers of datasets. We apply our method to resting-state fMRI datasets, demonstrating that our method can achieve an excellent estimation performance with significantly reduced computational costs.

Constrained CPD of Complex-Valued Multi-Subject fMRI Data via Alternating Rank-R and Rank-1 Least Squares

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.

Adaptive Brain Activity Detection in Structured Interference and Partially Homogeneous Locally Correlated Disturbance

OBJECTIVE

In this paper, we aim to address the problem of subspace detection in the presence of locally-correlated complex Gaussian noise and interference. For applications like brain activity detection using functional magnetic resonance imaging (fMRI) data where the noise is possibly locally correlated, using the sample covariance estimator is not a suitable choice due to significant dependency of its accuracy on the number of observations.

METHODS

In this study, we take advantage of an assumed banded structure in the covariance matrix to model the local dependence in the noise and propose a new covariance estimation approach. In particular, we use the idea of fac-torizing the joint likelihood function into a few conditional likelihood terms and maximizing each term independently of the others. This process leads to an explicit estimator for banded covariance matrices which requires fewer observations to achieve the same accuracy as the sample covari-ance. This estimate is then fed into an adaptive matched filter, two-step Rao and two-step Wald tests for detection.

RESULTS

Simulation results reveal the superiority of the proposed methods over well known classical detectors. Finally, the proposed methods are applied to functional magnetic resonance imaging (fMRI) data to localize neural activities in the brain.

CONCLUSION

The proposed method can offer better activation maps in terms of accuracy and spatial smoothness.

SIGNIFICANCE

The proposed methods can be seen as alternatives for standard detection approaches which are not perfectly aligned with the properties of fMRI data.

A Computational Neural Model for Mapping Degenerate Neural Architectures

Degeneracy in biological systems refers to a many-to-one mapping between physical structures and their functional (including psychological) outcomes. Despite the ubiquity of the phenomenon, traditional analytical tools for modeling degeneracy in neuroscience are extremely limited. In this study, we generated synthetic datasets to describe three situations of degeneracy in fMRI data to demonstrate the limitations of the current univariate approach. We describe a novel computational approach for the analysis referred to as neural topographic factor analysis (NTFA). NTFA is designed to capture variations in neural activity across task conditions and participants. The advantage of this discovery-oriented approach is to reveal whether and how experimental trials and participants cluster into task conditions and participant groups. We applied NTFA on simulated data, revealing the appropriate degeneracy assumption in all three situations and demonstrating NTFA's utility in uncovering degeneracy. Lastly, we discussed the importance of testing degeneracy in fMRI data and the implications of applying NTFA to do so.

Dictionary Learning-Based Ultrasound Image Combined with Gastroscope for Diagnosis of Helicobacter pylori-Caused Gastrointestinal Bleeding

The study is aimed at evaluating the application value of ultrasound combined with gastroscopy in diagnosing gastrointestinal bleeding (GIB) caused by Helicobacter pylori (HP). An ultrasound combined with a gastroscopy diagnostic model based on improved K-means Singular Value Decomposition (N-KSVD) was proposed first. 86 patients with Peptic ulcer (PU) and GIB admitted to our Hospital were selected and defined as the test group, and 86 PU patients free of GIB during the same period were selected as the control group. The two groups were observed for clinical manifestations and HP detection results. The results showed that when the noise ρ was 10, 30, 50, and 70, the Peak Signal to Noise Ratio (PSNR) values of N-KSVD dictionary after denoising were 35.55, 30.47, 27.91, and 26.08, respectively, and the structure similarity index measure (SSIM) values were 0.91, 0.827, 0.763, and 0.709, respectively. Those were greater than those of DCT dictionary and Global dictionary and showed statistically significant differences versus the DCT dictionary (P < 0.05). In the test group, there were 60 HP-positives and 26 HP-negatives, and there was significant difference in the numbers of HP-positives and HP-negatives (P < 0.05), but no significant difference in gender and age (P > 0.05). Of the subjects with abdominal pain, HP-positives accounted for 59.02% and HP-negatives accounted for 37.67%, showing significant differences (P < 0.05). Finally, the size of the ulcer lesion in HP-positives and HP-negatives was compared. It was found that 71.57% of HP-positives had ulcers with a diameter of 0-1 cm, and 28.43% had ulcers with a diameter of ≥1 cm. Compared with HP-negatives, the difference was statistically significant (P < 0.05). In conclusion, N-KSVD-based ultrasound combined with gastroscopy demonstrated good denoising effects and was effective in the diagnosis of GIB caused by HP.

Enhanced design matrix for task-related fMRI data analysis

In this paper, we introduce a novel methodology for the analysis of task-related fMRI data. In particular, we propose an alternative way for constructing the design matrix, based on the newly suggested Information-Assisted Dictionary Learning (IADL) method. This technique offers an enhanced potential, within the conventional GLM framework, (a) to efficiently cope with uncertainties in the modeling of the hemodynamic response function, (b) to accommodate unmodeled brain-induced sources, beyond the task-related ones, as well as potential interfering scanner-induced artifacts, uncorrected head-motion residuals and other unmodeled physiological signals, and (c) to integrate external knowledge regarding the natural sparsity of the brain activity that is associated with both the experimental design and brain atlases. The capabilities of the proposed methodology are evaluated via a realistic synthetic fMRI-like dataset, and demonstrated using a test case of a challenging fMRI study, which verifies that the proposed approach produces substantially more consistent results compared to the standard design matrix method. A toolbox extension for SPM is also provided, to facilitate the use and reproducibility of the proposed methodology.

Slice-Based Online Convolutional Dictionary Learning

Convolutional dictionary learning (CDL) aims to learn a structured and shift-invariant dictionary to decompose signals into sparse representations. While yielding superior results compared to traditional sparse coding methods on various signal and image processing tasks, most CDL methods have difficulties handling large data, because they have to process all images in the dataset in a single pass. Therefore, recent research has focused on online CDL (OCDL) which updates the dictionary with sequentially incoming signals. In this article, a novel OCDL algorithm is proposed based on a local, slice-based representation of sparse codes. Such representation has been found useful in batch CDL problems, where the convolutional sparse coding and dictionary learning problem could be handled in a local way similar to traditional sparse coding problems, but it has never been explored under online scenarios before. We show, in this article, that the proposed algorithm is a natural extension of the traditional patch-based online dictionary learning algorithm, and the dictionary is updated in a similar memory efficient way too. On the other hand, it can be viewed as an improvement of existing second-order OCDL algorithms. Theoretical analysis shows that our algorithm converges and has lower time complexity than existing counterpart that yields exactly the same output. Extensive experiments are performed on various benchmarking datasets, which show that our algorithm outperforms state-of-the-art batch and OCDL algorithms in terms of reconstruction objectives.

Deep Generative Model of Individual Variability in fMRI Images of Psychiatric Patients

Neuroimaging techniques, such as the resting-state functional magnetic resonance imaging (fMRI), have been investigated to find objective biomarkers of neuro-logical and psychiatric disorders. Objective biomarkers potentially provide a refined diagnosis and quantitative measurements of the effects of treatment. However, fMRI images are sensitive to individual variability, such as functional topography and personal attributes. Suppressing the irrelevant individual variability is crucial for finding objective biomarkers for multiple subjects. Herein, we propose a structured generative model based on deep learning (i.e., a deep generative model) that considers such individual variability. The proposed model builds a joint distribution of (preprocessed) fMRI images, state (with or without a disorder), and individual variability. It can thereby discriminate individual variability from the subject's state. Experimental results demonstrate that the proposed model can diagnose unknown subjects with greater accuracy than conventional approaches. Moreover, the diagnosis is fairer to gender and state, because the proposed model extracts subject attributes (age, gender, and scan site) in an unsupervised manner.

Independent vector analysis for common subspace analysis: Application to multi-subject fMRI data yields meaningful subgroups of schizophrenia

The extraction of common and distinct biomedical signatures among different populations allows for a more detailed study of the group-specific as well as distinct information of different populations. A number of subspace analysis algorithms have been developed and successfully applied to data fusion, however they are limited to joint analysis of only a couple of datasets. Since subspace analysis is very promising for analysis of multi-subject medical imaging data as well, we focus on this problem and propose a new method based on independent vector analysis (IVA) for common subspace extraction (IVA-CS) for multi-subject data analysis. IVA-CS leverages the strength of IVA in identification of a complete subspace structure across multiple datasets along with an efficient solution that uses only second-order statistics. We propose a subset analysis approach within IVA-CS to mitigate issues in estimation in IVA due to high dimensionality, both in terms of components estimated and the number of datasets. We introduce a scheme to determine a desirable size for the subset that is high enough to exploit the dependence across datasets and is not affected by the high dimensionality issue. We demonstrate the success of IVA-CS in extracting complex subset structures and apply the method to analysis of functional magnetic resonance imaging data from 179 subjects and show that it successfully identifies shared and complementary brain patterns from patients with schizophrenia (SZ) and healthy controls group. Two components with linked resting-state networks are identified to be unique to the SZ group providing evidence of functional dysconnectivity. IVA-CS also identifies subgroups of SZs that show significant differences in terms of their brain networks and clinical symptoms.

An α -Divergence-Based Approach for Robust Dictionary Learning

In this paper, a robust sequential dictionary learning (DL) algorithm is presented. The proposed algorithm is motivated from the maximum likelihood perspective on dictionary learning and its link to the minimization of the Kullback-Leibler divergence. It is obtained by using a robust loss function in the data fidelity term of the DL objective instead of the usual quadratic loss. The proposed robust loss function is derived from the α -divergence as an alternative to the Kullback-Leibler divergence, which leads to a quadratic loss. Compared to other robust approaches, the proposed loss has the advantage of belonging to class of redescending M-estimators, guaranteeing inference stability from large deviations from the Gaussian nominal noise model. The algorithm is obtained by solving a sequence of penalized rank-1 matrix approximation problems, where the l₁ -norm is introduced as a penalty promoting sparsity and then using a block coordinate descent approach to estimate the unknowns. Performance comparison with similar robust DL algorithms on digit recognition, background removal, and gray-scale image denoising is performed highlighting efficacy of the proposed algorithm.