Muhammad Usman Khalid

Improving functional connectivity detection in FMRI by combining sparse dictionary learning and canonical correlation analysis

In this paper a novel framework that combines data-driven methods is proposed for functional connectivity analysis of functional magnetic resonance imaging (fMRI) data. The basic idea is to overcome the shortcomings of compressed sensing based data-driven method by incorporating canonical correlation analysis (CCA) to extract a more meaningful temporal profile that is based solely on underlying brain hemodynamics, which can be further investigated to detect functional connectivity using regression analysis. We apply our method on synthetic and task-related fMRI data to show that the combined framework which better adapts to individual variations of distinct activity patterns in the brain is an effective approach to reveal functionally connected brain regions.

A single SVD sparse dictionary learning algorithm for FMRI data analysis

Data driven analysis methods such as independent component analysis (ICA) have proven to be well suited for analyzing functional magnetic resonance imaging (fMRI) data. Instead of using the independence assumption as in ICA approaches, we use the sparsity assumption to propose a novel overcomplete dictionary learning algorithm for statistical analysis of fMRI data. The proposed method differs from recent dictionary learning algorithms for sparse representation by updating all the dictionary atoms in parallel using only one SVD. Using both simulated and experimental fMRI data we show that the proposed method produces results comparable to those achieved with popular dictionary learning algorithms, but is more computationally efficient since the dictionary update is done using only one SVD.

Constrained maximum likelihood based efficient dictionary learning for fMRI analysis

A principal component analysis (PCA) based dictionary initialization approach accompanied by a computationally efficient dictionary learning algorithm for statistical analysis of functional magnetic resonance imaging (fMRI) is proposed. It replaces a singular value decomposition (SVD) computation with an approximate solution to obtain a local minima for a given initial dictionary. The K-SVD has been recently used to develop a data-driven sparse general linear model (GLM) framework for fMRI analysis solely based on the sparsity of signals. However, the K-SVD algorithm is computationally demanding and may require many iterations to converge. Replacing SVD with an approximate solution for the dictionary update combined with an optimal dictionary initialization, the desired results for a sparse GLM can be improved and achieved in few iterations.

Multi-subject fMRI connectivity analysis using sparse dictionary learning and multiset canonical correlation analysis

In this paper, we propose an effective technique to analyze task-based functional connectivity across multiple subjects for functional magnetic resonance imaging (fMRI) data. Instead of applying the assumption of group-independence or multiset correlation maximization, an alternative approach is adopted based on a combined framework of sparse dictionary learning (SDL) and multi-set canonical correlation analysis (MCCA) to obtain connectivity maps. The proposed technique encapsulates commonality and uniqueness solely based on sparsity of cross dataset corresponding components. It is validated using real fMRI data and its superior performance is illustrated using a simulation study, which shows its better capability in obtaining connectivity maps that are more specific.

Is first-order vector autoregressive model optimal for fmri data?

We consider the problem of selecting the optimal orders of vector autoregressive (VAR) models for fMRI data. Many previous studies used model order of one and ignored that it may vary considerably across data sets depending on different data dimensions, subjects, tasks, and experimental designs. In addition, the classical information criteria (IC) used (e.g., the Akaike IC (AIC)) are biased and inappropriate for the high-dimensional fMRI data typically with a small sample size. We examine the mixed results on the optimal VAR orders for fMRI, especially the validity of the order-one hypothesis, by a comprehensive evaluation using different model selection criteria over three typical data types—a resting state, an event-related design, and a block design data set—with varying time series dimensions obtained from distinct functional brain networks. We use a more balanced criterion, Kullback’s IC (KIC) based on Kullback’s symmetric divergence combining two directed divergences. We also consider the bias-corrected versions (AICc and KICc) to improve VAR model selection in small samples. Simulation results show better small-sample selection performance of the proposed criteria over the classical ones. Both bias-corrected ICs provide more accurate and consistent model order choices than their biased counterparts, which suffer from overfitting, with KICc performing the best. Results on real data show that orders greater than one were selected by all criteria across all data sets for the small to moderate dimensions, particularly from small, specific networks such as the resting-state default mode network and the task-related motor networks, whereas low orders close to one but not necessarily one were chosen for the large dimensions of full-brain networks.

Sparse dictionary learning for fMRI analysis using autocorrelation maximization.

In this paper, the effect of temporal autocorrelations in functional magnetic resonance imaging (fMRI) data on sparse dictionary learning (SDL) is addressed. For sparse general linear model (sGLM), the fMRI time-series is modeled as a linear mixture of several signals such as neural dynamics, structured noise, random noise and unexplained signal variations on the basis of spatial sparseness. These signals are considered as underlying sources and SDL is used to estimate them. However, the sparse GLM model does not take into account the autocorrelations in fMRI data. To address this shortcoming, a new model is proposed to incorporate the prior knowledge about lag-1 autocorrelation into dictionary update stage. This helps improve the sensitivity and specificity of the fMRI data during statistical analysis. Using a simulation study, the effect of the proposed dictionary update on sGLM is compared to conventional sGLM by utilizing various detrending techniques. Furthermore, the proposed update is validated in an sGLM framework for real fMRI datasets, which shows its better capability to estimate neural dynamics in presence of spatiotemporal dependencies.

Adaptive 2DCCA Based Approach for Improving Spatial Specificity of Activation Detection in Functional MRI

The univariate approach without a smoothing filter for detecting activation patterns in functional magnetic resonance imaging (fMRI) data suffers from a low sensitivity due to presence of high noise. The poor performance of univariate methods such as ordinary correlation is due to lack of their ability to take advantage of spatial correlation that exists in fMR images among group of neighboring voxels. To rectify this problem multivariate approaches such as canonical correlation analysis (CCA), adaptive canonical correlation analysis (ACCA) and spatial Gaussian smoothing accompanied with univariate correlation has already been applied to fMR images to improve both sensitivity and specificity. In this work idea of smoothing fMR images with ACCA has been extended to adaptive two-dimensional canonical correlation analysis (A2DCCA) to obtain improvements in detection performance in terms of specificity. It is shown on synthetic and real fMRI data that A2DCCA produces better specificity than ACCA and Gaussian smoothing.

Learning dictionaries from correlated data: Application to fMRI data analysis

Sequential dictionary learning via the K-SVD algorithm has been revealed as a successful alternative to conventional data driven methods such as independent component analysis (ICA) for functional magnetic resonance imaging (fMRI) data analysis. fMRI data sets are however structured data matrices with notions of spatio-temporal correlation. This prior information has not been included in the K-SVD algorithm when applied in fMRI data analysis. In this paper we remedy to this situation by proposing a variant of the K-SVD algorithm dedicated to fMRI data analysis by taking into account this prior information. The proposed algorithm accounts for the known correlation structure in the fMRI data by using the squared Q, R-norm instead of the Frobenius norm for rank one approximation in the dictionary update stage. The performance of the proposed algorithm is illustrated through simulations and applications on a real fMRI data set.

Comparing causality measures of fMRI data using PCA, CCA and vector autoregressive modelling

Extracting the directional interaction between activated brain areas from functional magnetic resonance imaging (fMRI) time series measurements of their activity is a significant step in understanding the process of brain functions. In this paper, the directional interaction between fMRI time series characterizing the activity of two neuronal sites is quantified using two measures; one derived based on univariate autoregressive and autoregressive exogenous (AR/ARX) and other derived based on multivariate vector autoregressive and vector autoregressive exogenous (VAR/VARX) models. The significance and effectiveness of these measures is illustrated on both simulated and real fMRI data sets. It has been revealed that VAR modelling of the regions of interest is robust in inferring true causality compared to principal component analysis (PCA) and canonical correlation analysis (CCA) based causality methods.

Unsupervised detrending technique using sparse dictionary learning for fMRI preprocessing and analysis

This paper addresses the problem of scanner induced low frequency drift estimation in order to improve the significance of functional magnetic resonance imaging (fMRI) data for statistical analysis. A novel technique is presented to estimate the drift parameters using a sparse general linear model (sGLM) framework. The fMRI signal is modeled as a linear mixture of several signals such as low frequency trend, brain hemodynamic, physiological noise and unexplained signal variations. These signals are considered as underlying sources and sparse dictionary learning (SDL) is used to estimate them. The superior performance of the proposed technique compared to other detrending techniques is illustrated using a simulation study. Furthermore, the proposed technique is validated using real fMRI data, which shows its better capability to estimate drift in presence of spatiotemporal dependencies.