Nonstationary noise estimation in functional MRI
ABSTRACT An important issue in functional MRI analysis is accurate characterisation of the noise processes present in the data. Whilst conventional fMRI noise representations often assume stationarity (or time-invariance) in the noise generating sources, such approaches may serve to suppress important dynamic information about brain function. As an alternative to these fixed temporal assumptions, we present in this paper two time-varying procedures for examining nonstationary noise structure in fMRI data. In the first procedure, we approximate nonstationary behaviour by means of a collection of simple but numerous time-varying parametric models. This is accomplished through the derivation of a locally parametric AutoRegressive (AR) plus drift model which tracks temporal covariance by allowing the model parameters to evolve over time. Before exploring time variation in these parameters, window-widths (bandwidths) that are well suited to the latent time-varying noise structure must be determined. To do this, we employ a bandwidth selection mechanism based on Stein's Unbiased Risk Estimator (SURE) criterion. In the second procedure, we describe the fMRI noise using a nonparametric method based on Functional Data Analysis (FDA). This process generates well-conditioned nonstationary covariance estimates that reflect temporal continuity in the underlying data structure whilst penalizing effective model dimension. We demonstrate both methods on simulated data and investigate the presence of nonstationary noise in resting fMRI data using the whitening capabilities of the locally parametric procedure. We evaluate the comparative behaviour of the stationary and nonstationary AR-based methods on data acquired at 1.5, 3 and 7 T magnetic field strengths and show that incorporation of time variation in the AR parameters leads to an overall decrease in the level of residual structure in the data. The FDA noise modelling technique is formulated within an activation mapping procedure and compared to the SPM (Statistical Parametric Mapping) toolbox on a cognitive face recognition task. Both the SPM and FDA methods show good sensitivity on this task, but we find that inclusion of the nonstationary FDA noise model seems to improve detection power in important task-related medial temporal regions.
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- "Romance speaker data set but is commonly encountered with functional data sets due to their often high-dimensionality (e.g. Long et al. (2005)). Rank deficiency obstructs using CVA to obtain numerical solutions to CFA. "
ABSTRACT: Evolutionary models of languages are usually considered to take the form of trees. With the development of so-called tree constraints the plausibility of the tree model assumptions can be addressed by checking whether the moments of observed variables lie within regions consistent with trees. In our linguistic application, the data set comprises acoustic samples (audio recordings) from speakers of five Romance languages or dialects. We wish to assess these functional data for compatibility with a hereditary tree model at the language level. A novel combination of canonical function analysis (CFA) with a separable covariance structure provides a method for generating a representative basis for the data. This resulting basis is formed of components which emphasize language differences whilst maintaining the integrity of the observational language-groupings. A previously unexploited Gaussian tree constraint is then applied to component-by-component projections of the data to investigate adherence to an evolutionary tree. The results indicate that while a tree model is unlikely to be suitable for modeling all aspects of the acoustic linguistic data, certain features of the spoken Romance languages highlighted by the separable-CFA basis may indeed be suitably modeled as a tree.
- "Physiological factors such as cardiac beat or breathing cycle may also contribute to this scaling phenomenon since they may contaminate the BOLD signal with properties depending on the sampling period of data (i.e., short/long time of repetition (TR))   . Early investigations therefore considered these space-varying low frequency components as noise, which are responsible for potential non stationarities   . Hence, to fulfill the assumptions underlying the classical model-based localization techniques of brain activity, most neuropsychologists resort to high-pass filtering to remove these trends. "
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- "Viviani et al. (2005) used FPCA to single subject to extract the features of hemodynamic response in fMRI studies, and showed that FPCA outperformed multivariate PCA. Long et al. (2005) used FPCA on multiple subjects to estimate the subject-wise spatially varying non-stationary noise covariance kernel. As with multivariate PCA, FPCA explores the variance–covariance and the correlation structure. "
ABSTRACT: Functional data analysis (FDA) considers the continuity of the curves or functions, and is a topic of increasing interest in the statistics community. FDA is commonly applied to time-series and spatial-series studies. The development of functional brain imaging techniques in recent years made it possible to study the relationship between brain and mind over time. Consequently, an enormous amount of functional data is collected and needs to be analyzed. Functional techniques designed for these data are in strong demand. This paper discusses three statistically challenging problems utilizing FDA techniques in functional brain imaging analysis. These problems are dimension reduction (or feature extraction), spatial classification in functional magnetic resonance imaging studies, and the inverse problem in magneto-encephalography studies. The application of FDA to these issues is relatively new but has been shown to be considerably effective. Future efforts can further explore the potential of FDA in functional brain imaging studies.Frontiers in Psychology 10/2010; 1:35. DOI:10.3389/fpsyg.2010.00035 · 2.80 Impact Factor