A Data-Driven Sparse GLM for fMRI Analysis Using Sparse Dictionary Learning With MDL Criterion

Abstract

We propose a novel statistical analysis method for functional magnetic resonance imaging (fMRI) to overcome the drawbacks of conventional data-driven methods such as the independent component analysis (ICA). Although ICA has been broadly applied to fMRI due to its capacity to separate spatially or temporally independent components, the assumption of independence has been challenged by recent studies showing that ICA does not guarantee independence of simultaneously occurring distinct activity patterns in the brain. Instead, sparsity of the signal has been shown to be more promising. This coincides with biological findings such as sparse coding in V1 simple cells, electrophysiological experiment results in the human medial temporal lobe, etc. The main contribution of this paper is, therefore, a new data driven fMRI analysis that is derived solely based upon the sparsity of the signals. A compressed sensing based data-driven sparse generalized linear model is proposed that enables estimation of spatially adaptive design matrix as well as sparse signal components that represent synchronous, functionally organized and integrated neural hemodynamics. Furthermore, a minimum description length (MDL)-based model order selection rule is shown to be essential in selecting unknown sparsity level for sparse dictionary learning. Using simulation and real fMRI experiments, we show that the proposed method can adapt individual variation better compared to the conventional ICA methods.

Characterizing and differentiating task-based and resting state fMRI signals via two-stage sparse representations

“…(1) during the optimization. It should be noted that we employ the same assumption as in previous studies (Li et al, 2009; Lee et al, 2011; Li et al, 2012; Oikonomou et al, 2012; Lee et al, 2013; Abolghasemi et al, 2013) that the atomic components (which are dictionary atoms in D in our work) involved in each voxel’s fMRI signal are a few major ones and the neural integration of those components is linear. In this work, the value of λ and dictionary size m were determined experimentally ( λ =0.1, k =400) (Lv et al, 2014a; Lv et al, 2014b).…”

“…Inspired by the successes of using sparse representation in pattern recognition (Mairal et al, 2009; Kreutz-Delgado et al, 2003; Aharon et al, 2006; Lewicki and Sejnowski 2000) and in brain functional imaging analysis (Lee et al, 2011; Li et al, 2012; Yamashita et al, 2008; Li et al, 2009; Lv et al, 2014a; Lv et al, 2014b), in this paper, we propose a novel two-stage sparse representation framework to obtain a groupwise characterization of fMRI signals obtained during various tasks (or during resting-state), which have the capability of addressing the abovementioned three challenges. Specifically, for the first challenge, the sparse-constrained dictionary learning method has been algorithmically shown to be capable of identifying the representative components from the given fMRI dataset as the activation maps from the fMRI study are usually with little overlapping ( Daubechies et al, 2009).…”

Distributed rank-1 dictionary learning: Towards fast and scalable solutions for fMRI big data analytics

“…The algorithm alternates updating u (randomly initialized before the first iteration) and v until the convergence of u: (2) One dictionary basis [u, v] can be estimated after the convergence of Eq. 2.…”

“…In the current field of functional neuroimaging research, one of the most effective approaches for fMRI data analysis is the functional network decomposition based on Dictionary Learning methods [1,2]. Dictionary learning derives a set of vectors that sparsely code the input fMRI data.…”

“…Following the previous success in using dictionary learning for functional network decomposition [1,2], in this work we developed a novel distributed rank-1 dictionary learning (D-r1DL) framework [19], using the Apache Spark platform. All code presented in this work can be found in the Github repository https://github.com/quinngroup/dr1dl-pyspark Dictionary learning has been in the center of attention of researchers in variety of disciplines, but less effort has been made to create new algorithms using it.…”