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39
Controlling the familywise error rate in functional neuroimaging: a comparative review
 Statistical Methods in Medical Research
, 2003
"... Functional neuroimaging data embodies a massive multiple testing problem, where 100 000 correlated test statistics must be assessed. The familywise error rate, the chance of any false positives is the standard measure of Type I errors in multiple testing. In this paper we review and evaluate three a ..."
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Cited by 167 (7 self)
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Functional neuroimaging data embodies a massive multiple testing problem, where 100 000 correlated test statistics must be assessed. The familywise error rate, the chance of any false positives is the standard measure of Type I errors in multiple testing. In this paper we review and evaluate three approaches to thresholding images of test statistics: Bonferroni, random �eld and the permutation test. Owing to recent developments, improved Bonferroni procedures, such as Hochberg’s methods, are now applicable to dependent data. Continuous random �eld methods use the smoothness of the image to adapt to the severity of the multiple testing problem. Also, increased computing power has made both permutation and bootstrap methods applicable to functional neuroimaging. We evaluate these approaches on t images using simulations and a collection of real datasets. We �nd that Bonferronirelated tests offer little improvement over Bonferroni, while the permutation method offers substantial improvement over the random �eld method for low smoothness and low degrees of freedom. We also show the limitations of trying to �nd an equivalent number of independent tests for an image of correlated test statistics. 1
Penalized Partially Linear Models Using Sparse Representations With an Application to fMRI Time Series
, 2005
"... In this paper, we consider modeling the nonparametric component in partially linear models (PLMs) using linear sparse representations, e.g., wavelet expansions. Two types of representations are investigated, namely, orthogonal bases (complete) and redundant overcomplete expansions. For bases, we int ..."
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Cited by 15 (0 self)
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In this paper, we consider modeling the nonparametric component in partially linear models (PLMs) using linear sparse representations, e.g., wavelet expansions. Two types of representations are investigated, namely, orthogonal bases (complete) and redundant overcomplete expansions. For bases, we introduce a regularized estimator of the nonparametric part. The important contribution here is that the nonparametric part can be parsimoniously estimated by choosing an appropriate penalty function for which the hard and soft thresholding estimators are special cases. This allows us to represent in an effective manner a broad class of signals, including stationary and/or nonstationary signals and avoids excessive bias in estimating the parametric component. We also give a fast estimation algorithm. The method is then generalized to handle the case of overcomplete representations. A largescale simulation study is conducted to illustrate the finite sample properties of the estimator. The estimator is finally applied to real neurophysiological functional magnetic resonance imaging (MRI) data sets that are suspected to contain both smooth and transient drift features.
Waveletbased multifractal analysis of fMRI time series., Neuroimage 22
, 2004
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Activelets: Wavelets for sparse representation of hemodynamic responses
 Signal Processing
, 2011
"... We propose a new framework to extract the activityrelated component in the BOLD functional Magnetic Resonance Imaging (fMRI) signal. As opposed to traditional fMRI signal analysis techniques, we do not impose any prior knowledge of the event timing. Instead, our basic assumption is that the activa ..."
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Cited by 8 (4 self)
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We propose a new framework to extract the activityrelated component in the BOLD functional Magnetic Resonance Imaging (fMRI) signal. As opposed to traditional fMRI signal analysis techniques, we do not impose any prior knowledge of the event timing. Instead, our basic assumption is that the activation pattern is a sequence of short and sparselydistributed stimuli, as is the case in slow eventrelated fMRI. We introduce new wavelet bases, termed “activelets”, which sparsify the activityrelated BOLD signal. These wavelets mimic the behavior of the differential operator underlying the hemodynamic system. To recover the sparse representation, we deploy a sparsesolution search algorithm. The feasibility of the method is evaluated using both synthetic and experimental fMRI data. The importance of the activelet basis and the nonlinear sparse recovery algorithm is demonstrated by comparison against classical Bspline wavelets and linear regularization, respectively.
Analysis of eventrelated fMRI data using best clustering bases
 IEEE Transactions on Medical Imaging
, 2003
"... Abstract—We explore a new paradigm for the analysis of eventrelated functional magnetic resonance images (fMRI) of brain activity. We regard the fMRI data as a very large set of time series @ A, indexed by the position of a voxel inside the brain. The decision that a voxel H is activated is based no ..."
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Cited by 7 (5 self)
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Abstract—We explore a new paradigm for the analysis of eventrelated functional magnetic resonance images (fMRI) of brain activity. We regard the fMRI data as a very large set of time series @ A, indexed by the position of a voxel inside the brain. The decision that a voxel H is activated is based not solely on the value of the fMRI signal at H, but rather on the comparison of all time series @ A in a small neighborhood around H. We construct basis functions on which the projection of the fMRI data reveals the organization of the time series @ A into activated and nonactivated clusters. These clustering basis functions are selected from large libraries of wavelet packets according to their ability to separate the fMRI time series into the activated cluster and a nonactivated cluster. This principle exploits the intrinsic spatial correlation that is present in the data. The construction of the clustering basis functions described in this paper is applicable to a large category of problems where time series are indexed by a spatial variable. Index Terms—Best clustering basis, brain mapping, fMRI, functional magnetic resonance imaging, wavelets. I.
A WaveletBased Statistical Analysis of fMRI data
 I. Motivation and Data Distribution Modeling, in press, NeuroInformatics
, 2005
"... We propose a new method for statistical analysis of functional magnetic resonance imaging (fMRI) data. The discrete wavelet transformation is employed as a tool for efficient and robust signal representation. We use structural MRI and functional fMRI to empirically estimate the distribution of the w ..."
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Cited by 6 (2 self)
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We propose a new method for statistical analysis of functional magnetic resonance imaging (fMRI) data. The discrete wavelet transformation is employed as a tool for efficient and robust signal representation. We use structural MRI and functional fMRI to empirically estimate the distribution of the wavelet coefficients of the data both across individuals and across spatial locations. An anatomical subvolume probabilistic atlas is used to tessellate the structural and functional signals into smaller regions each of which is processed separately. A frequencyadaptive wavelet shrinkage scheme is employed to obtain essentially optimal estimations of the signals in the wavelet space. The empirical distributions of the signals are computed on all regions in compressed wavelet space. These are modeled by heavytail distributions because their histograms exhibit slower tail decay than the Gaussian. We discovered that Cauchy, Bessel KForms and Pareto distributions provide the most accurate asymptotic models for the distribution of the wavelet coefficients of the data. Finally, we propose a new model for statistical analysis of functional MRI data using this atlasbased waveletspace representation. In the second part of our investigation we will apply this technique to analyze a large fMRI data set involving repeated presentation of sensorymotor response stimuli in young, elderly and demented subjects.
BOLD noise assumptions in fMRI
 J. Biomed. Imag
"... This paper discusses the assumption of Gaussian noise in the bloodoxygenationdependent (BOLD) contrast for functional MRI (fMRI). In principle, magnitudes in MRI images follow a Rice distribution. We start by reviewing differences between Rician and Gaussian noise. An analytic expression is derive ..."
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Cited by 6 (0 self)
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This paper discusses the assumption of Gaussian noise in the bloodoxygenationdependent (BOLD) contrast for functional MRI (fMRI). In principle, magnitudes in MRI images follow a Rice distribution. We start by reviewing differences between Rician and Gaussian noise. An analytic expression is derived for the null (restingstate) distribution of the difference between two Rician distributed images. This distribution is shown to be symmetric, and an exact expression for its standard deviation is derived. This distribution can be well approximated by a Gaussian, with very high precision for high SNR, and high precision for lower SNR. Tests on simulated and real MR images show that subtracting the timeseries mean in fMRI yields asymmetrically distributed temporal noise. Subtracting a restingstate time series from the first results in symmetric and nearly Gaussian noise. This has important consequences for fMRI analyses using standard statistical tests. Copyright © 2006 A. M. Wink and J. B. T. M. Roerdink. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.
A comparative evaluation of waveletbased methods for hypothesis testing of brain activation maps
, 2004
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Spatiotemporal wavelet analysis for functional MRI
 NeuroImage
, 2004
"... Characterizing the spatiotemporal behavior of the BOLD signal in functional Magnetic Resonance Imaging (fMRI) is a central issue in understanding brain function. While the nature of functional activation clusters is fundamentally heterogeneous, many current analysis approaches use spatially invarian ..."
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Cited by 4 (0 self)
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Characterizing the spatiotemporal behavior of the BOLD signal in functional Magnetic Resonance Imaging (fMRI) is a central issue in understanding brain function. While the nature of functional activation clusters is fundamentally heterogeneous, many current analysis approaches use spatially invariant models that can degrade anatomic boundaries and distort the underlying spatiotemporal signal. Furthermore, few analysis approaches use true spatiotemporal continuity in their statistical formulations. To address these issues, we present a novel spatiotemporal wavelet procedure that uses a stimulusconvolved hemodynamic signal plus correlated noise model. The wavelet fits, computed by spatially constrained maximumlikelihood estimation, provide efficient multiscale representations of heterogeneous brain structures and give wellidentified, parsimonious spatial activation estimates that are modulated by the temporal fMRI dynamics. In a study of both simulated data and actual fMRI memory task experiments, our new method gave lower meansquared error and seemed to result in more localized fMRI activation maps compared to models using standard wavelet or smoothing techniques. Our spatiotemporal wavelet framework suggests a useful tool for the analysis of fMRI studies.