Modeling the dynamics of cerebrovascular reactivity to carbon dioxide in fMRI under task and resting-state conditions

Conventionally, cerebrovascular reactivity (CVR) is estimated as the amplitude of the hemodynamic response to vascular stimuli, most commonly carbon dioxide (CO(2)). While the CVR amplitude has established clinical utility, the temporal characteristics of CVR (dCVR) have been increasingly explored and may yield even more pathology-sensitive parameters. This work is motivated by the current need to evaluate the feasibility of dCVR modeling in various experimental conditions. In this work, we present a comparison of several recently published/utilized model-based deconvolution (response estimation) approaches for estimating the CO(2) response function h(t), including maximum a posteriori likelihood (MAP), inverse logit (IL), canonical correlation analysis (CCA), and basis expansion (using Gamma and Laguerre basis sets). To aid the comparison, we devised a novel simulation framework that incorporates a wide range of SNRs, ranging from 10 to -7 dB, representative of both task and resting-state CO(2) changes. In addition, we built ground-truth h(t) into our simulation framework, overcoming the conventional limitation that the true h(t) is unknown. Moreover, to best represent realistic noise found in fMRI scans, we extracted noise from in-vivo resting-state scans. Furthermore, we introduce a simple optimization of the CCA method (CCA(opt)) and compare its performance to these existing methods. Our findings suggest that model-based methods can accurately estimate dCVR even amidst high noise (i.e. resting-state), and in a manner that is largely independent of the underlying model assumptions for each method. We also provide a quantitative basis for making methodological choices, based on the desired dCVR parameters, the estimation accuracy and computation time. The BEL method provided the highest accuracy and robustness, followed by the CCA(opt) and IL methods. Of the three, the CCA(opt) method has the lowest computational requirements. These findings lay the foundation for wider adoption of dCVR estimation in CVR mapping

Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery

PCA is one of the most widely used dimension reduction techniques. A related easier problem is "subspace learning" or "subspace estimation". Given relatively clean data, both are easily solved via singular value decomposition (SVD). The problem of subspace learning or PCA in the presence of outliers is called robust subspace learning or robust PCA (RPCA). For long data sequences, if one tries to use a single lower dimensional subspace to represent the data, the required subspace dimension may end up being quite large. For such data, a better model is to assume that it lies in a low-dimensional subspace that can change over time, albeit gradually. The problem of tracking such data (and the subspaces) while being robust to outliers is called robust subspace tracking (RST). This article provides a magazine-style overview of the entire field of robust subspace learning and tracking. In particular solutions for three problems are discussed in detail: RPCA via sparse+low-rank matrix decomposition (S+LR), RST via S+LR, and "robust subspace recovery (RSR)". RSR assumes that an entire data vector is either an outlier or an inlier. The S+LR formulation instead assumes that outliers occur on only a few data vector indices and hence are well modeled as sparse corruptions.Comment: To appear, IEEE Signal Processing Magazine, July 201