Resampling methods for improved wavelet-based multiple hypothesis testing of parametric maps in functional MRI

Two- or three-dimensional wavelet transforms have been considered as a basis for multiple hypothesis testing of parametric maps derived from functional magnetic resonance imaging (fMRI) experiments. Most of the previous approaches have assumed that the noise variance is equally distributed across levels of the transform. Here we show that this assumption is unrealistic; fMRI parameter maps typically have more similarity to a 1/f-type spatial covariance with greater variance in 2D wavelet coefficients representing lower spatial frequencies, or coarser spatial features, in the maps. To address this issue we resample the fMRI time series data in the wavelet domain (using a 1D discrete wavelet transform [DWT]) to produce a set of permuted parametric maps that are decomposed (using a 2D DWT) to estimate level-specific variances of the 2D wavelet coefficients under the null hypothesis. These resampling-based estimates of the "wavelet variance spectrum" are substituted in a Bayesian bivariate shrinkage operator to denoise the observed 2D wavelet coefficients, which are then inverted to reconstitute the observed, denoised map in the spatial domain. Multiple hypothesis testing controlling the false discovery rate in the observed, denoised maps then proceeds in the spatial domain, using thresholds derived from an independent set of permuted, denoised maps. We show empirically that this more realistic, resampling-based algorithm for wavelet-based denoising and multiple hypothesis testing has good Type I error control and can detect experimentally engendered signals in data acquired during auditory-linguistic processing.     

利用独立成分分析技术和静息fMRI数据对脑功能区进行定位

目的 验证可否利用独立成分分析(ICA)技术和静息fMRI数据对脑功能区进行定位.方法 利用ICA方法,通过研究静息状态的脑功能联结来获取功能区的定位.静息数据的采集采用短TR,在低通滤波(截止频率0.08 Hz)后可以去除生理噪声的主要影响.在数据分析中,对ICA结果进行了可复制性分析,只保留可复制性较高的成分,之后将ICA结果与传统的"种子像素"方法获得的结果进行定量的一致性分析.结果 ICA能够在不设定"种子像素"的情况下从静息fMRI数据中分解出运动系统和初级视觉系统的功能联结图,并在所有被试上都与"种子像素"方法有较高一致性.ICA在同一数据中可以同时分解出上述两个系统的功能联结图. 结论 ICA克服了"种子像素"方法的主观性,稳定、准确地从静息fMRI数据中分解出了脑功能联结图.本研究支持初级功能系统内的联系要明显强于系统间的联系的假设,显示ICA方法具有良好的临床应用潜力.     

Single trial variability of EEG and fMRI responses to visual stimuli

Recent EEG-fMRI studies have suggested a novel method of data fusion which uses single trial (ST) estimates of event-related potentials in the fMRI analysis. This is potentially very powerful, but rests on the assumption that the ST variability observed in EEG is reflected in the fMRI signal. The current study investigated this assumption and compared two different data processing strategies for each modality. Five subjects underwent separate EEG and fMRI sessions with checkerboard stimuli at two contrasts. EEG data were preprocessed using wavelet denoising and independent component analysis (ICA), whilst the general linear model and ICA were used for fMRI. Amplitudes and latencies of the P1 and N2 components of the visual evoked potential (VEP) were calculated for each trial. For fMRI, the amplitudes and latencies of the ST haemodynamic responses (HR) were calculated. Within modality, the results for the two processing methods were significantly correlated in the majority of data sets. Across modality, the average amplitudes of the VEPs and HRs were also significantly correlated. Examination of ST variability demonstrated that the amplitudes of the mean VEPs and HRs are both influenced by the latency variability of the ST responses to a greater extent than the amplitude variability. For high contrast stimuli the latency variability in EEG and fMRI was significantly correlated, with a similar trend seen for the low contrast stimuli. The results confirm the validity of examining both the EEG and fMRI signals on an ST basis and suggest an underlying neuronal origin in both modalities.     

Latency (in)sensitive ICA. Group independent component analysis of fMRI data in the temporal frequency domain

Independent component analysis (ICA), a data-driven approach utilizing high-order statistical moments to find maximally independent sources, has found fruitful application in functional magnetic resonance imaging (fMRI). A limitation of the standard fMRI ICA model is that a given component's time course is required to have the same delay at every voxel. As spatially varying delays (SVDs) may be found in fMRI data, using an ICA model with a fixed temporal delay for each source will have two implications. Larger SVDs can result in the splitting of regions with different delays into different components. Second, smaller SVDs can result in a biased ICA amplitude estimate due to only a slight delay difference. We propose a straightforward approach for incorporating this prior temporal information and removing the limitation of a fixed source delay by performing ICA on the amplitude spectrum of the original fMRI data (thus removing latency information). A latency map is then estimated for each component using the resulting component images and the raw data. We show that voxels with similar time courses, but different delays, are grouped into the same component. Additionally, when using traditional ICA, the amplitudes of motor areas are diminished due to systematic delay differences between visual and motor areas. The amplitudes are more accurately estimated when using a latency-insensitive ICA approach. The resulting time courses, the component maps, and the latency maps may prove useful as an addition to the collection of methods for fMRI data analysis.     

Noise reduction in BOLD-based fMRI using component analysis

Principle Component Analysis (PCA) and Independent Component Analysis (ICA) were used to decompose the fMRI time series signal and separate the BOLD signal change from the structured and random noise. Rather than using component analysis to identify spatial patterns of activation and noise, the approach we took was to identify PCA or ICA components contributing primarily to the noise. These noise components were identified using an unsupervised algorithm that examines the Fourier decomposition of each component time series. Noise components were then removed before subsequent reconstruction of the time series data. The BOLD contrast sensitivity (CS(BOLD)), defined as the ability to detect a BOLD signal change in the presence of physiological and scanner noise, was then calculated for all voxels. There was an increase in CS(BOLD) values of activated voxels after noise reduction as a result of decreased image-to-image variability in the time series of each voxel. A comparison of PCA and ICA revealed significant differences in their treatment of both structured and random noise. ICA proved better for isolation and removal of structured noise, while PCA was superior for isolation and removal of random noise. This provides a framework for using and evaluating component analysis techniques for noise reduction in fMRI.     

Automatic independent component labeling for artifact removal in fMRI

Blood oxygenation level dependent (BOLD) signals in functional magnetic resonance imaging (fMRI) are often small compared to the level of noise in the data. The sources of noise are numerous including different kinds of motion artifacts and physiological noise with complex patterns. This complicates the statistical analysis of the fMRI data. In this study, we propose an automatic method to reduce fMRI artifacts based on independent component analysis (ICA). We trained a supervised classifier to distinguish between independent components relating to a potentially task-related signal and independent components clearly relating to structured noise. After the components had been classified as either signal or noise, a denoised fMR time-series was reconstructed based only on the independent components classified as potentially task-related. The classifier was a novel global (fixed structure) decision tree trained in a Neyman-Pearson (NP) framework, which allowed the shape of the decision regions to be controlled effectively. Additionally, the conservativeness of the classifier could be tuned by modifying the NP threshold. The classifier was tested against the component classifications by an expert with the data from a category learning task. The test set as well as the expert were different from the data used for classifier training and the expert labeling the training set. The misclassification rate was between 0.2 and 0.3 for both the event-related and blocked designs and it was consistent among variety of different NP thresholds. The effects of denoising on the group-level statistical analyses were as expected: The denoising generally decreased Z-scores in the white matter, where extreme Z-values can be expected to reflect artifacts. A similar but weaker decrease in Z-scores was observed in the gray matter on average. These two observations suggest that denoising was likely to reduce artifacts from gray matter and could be useful to improve the detection of activations. We conclude that automatic ICA-based denoising offers a potentially useful approach to improve the quality of fMRI data and consequently increase the accuracy of the statistical analysis of these data.     

A comparative evaluation of wavelet-based methods for hypothesis testing of brain activation maps

Wavelet-based methods for hypothesis testing are described and their potential for activation mapping of human functional magnetic resonance imaging (fMRI) data is investigated. In this approach, we emphasise convergence between methods of wavelet thresholding or shrinkage and the problem of hypothesis testing in both classical and Bayesian contexts. Specifically, our interest will be focused on the trade-off between type I probability error control and power dissipation, estimated by the area under the ROC curve. We describe a technique for controlling the false discovery rate at an arbitrary level of error in testing multiple wavelet coefficients generated by a 2D discrete wavelet transform (DWT) of spatial maps of fMRI time series statistics. We also describe and apply change-point detection with recursive hypothesis testing methods that can be used to define a threshold unique to each level and orientation of the 2D-DWT, and Bayesian methods, incorporating a formal model for the anticipated sparseness of wavelet coefficients representing the signal or true image. The sensitivity and type I error control of these algorithms are comparatively evaluated by analysis of "null" images (acquired with the subject at rest) and an experimental data set acquired from five normal volunteers during an event-related finger movement task. We show that all three wavelet-based algorithms have good type I error control (the FDR method being most conservative) and generate plausible brain activation maps (the Bayesian method being most powerful). We also generalise the formal connection between wavelet-based methods for simultaneous multiresolution denoising/hypothesis testing and methods based on monoresolution Gaussian smoothing followed by statistical testing of brain activation maps.     

Modeling both the magnitude and phase of complex-valued fMRI data

In MRI and fMRI, images or voxel measurement are complex valued or bivariate at each time point. Recently, (Rowe, D.B., Logan, B.R., 2004. A complex way to compute fMRI activation. NeuroImage 23 (3), 1078-1092) introduced an fMRI magnitude activation model that utilized both the real and imaginary data in each voxel. This model, following traditional beliefs, specified that the phase time course were fixed unknown quantities which may be estimated voxel-by-voxel. Subsequently, (Rowe, D.B., Logan, B.R., 2005. Complex fMRI analysis with unrestricted phase is equivalent to a magnitude-only model. NeuroImage 24 (2), 603-606) generalized the model to have no restrictions on the phase time course. They showed that this unrestricted phase model was mathematically equivalent to the usual magnitude-only data model including regression coefficients and voxel activation statistic but philosophically different due to it derivation from complex data. Recent findings by (Hoogenrad, F.G., Reichenbach, J.R., Haacke, E.M., Lai, S., Kuppusamy, K., Sprenger, M., 1998. In vivo measurement of changes in venous blood-oxygenation with high resolution functional MRI at .95 Tesla by measuring changes in susceptibility and velocity. Magn. Reson. Med. 39 (1), 97-107) and (Menon, R.S., 2002. Postacquisition suppression of large-vessel BOLD signals in high-resolution fMRI. Magn. Reson. Med. 47 (1), 1-9) indicate that the voxel phase time course may exhibit task related changes. In this paper, a general complex fMRI activation model is introduced that describes both the magnitude and phase in complex data which can be used to specifically characterize task related change in both. Hypotheses regarding task related magnitude and/or phase changes are evaluated using derived activation statistics. It was found that the Rowe-Logan complex constant phase model strongly biases against voxels with task related phase changes and that the current very general complex linear phase model can be cast to address several different hypotheses sensitive to different magnitude/phase changes.     

fMRI数据去噪处理对FastICA检测精度的影响

目的 探讨fMRI数据中白噪声及去噪预处理方法对于采用FastICA算法检测人脑激活区精度的影响。方法 采用模拟和真实fMRI数据进行测试。实验重复50次,以比较未去噪、高斯平滑和两种正交小波方法去噪预处理后FastICA算法分离激活信号的能力。对不同阈值条件下检测的激活体素进行统计分析。用ROC曲线评价检测质量。结果 模拟实验显示,当fMRI数据的SNR为15 db时,去噪预处理能显著提高FastICA检测准确率;SNR为20 db时,去噪对提高FastICA检测准确率影响较小。采用不同的小波基及不同参数去噪处理结果差异较大,存在经db4小波去噪处理后激活区检测结果的敏感度和特异度反而降低的现象,但随着激活区减小,这种现象消失。结论 对于FastICA而言,小波去噪与传统的高斯平滑方法相比未显示出更好的敏感度和特异度;在低SNR情况下,有必要进行去噪预处理;在高SNR情况下,不恰当的去噪方法反而可导致FastICA检测精度降低。     

Mapping Transient, Randomly Occurring Neuropsychological Events Using Independent Component Analysis

The feasibility of mapping transient, randomly occurring neuropsychological events using independent component analysis (ICA) was evaluated in an auditory sentence-monitoring fMRI experiment, in which prerecorded short sentences of random content were presented in varying temporal patterns. The efficacy of ICA on fMRI data with such temporal characteristics was assessed by a series of simulation studies, as well as by human activation studies. The effects of contrast-to-noise ratio level, spatially varied hemodynamic response within a brain region, time lags of the responses among brain regions, and different simulated activation locations on the ICA were investigated in the simulations. Component maps obtained from the auditory sentence-monitoring experiments in each subject using ICA showed distinct activation in bilateral auditory and language cortices, as well as in superior sensorimotor cortices, consistent with previous PET studies. The associated time courses in the activated brain regions matched well to the timing of the sentence presentation, as evidenced by the recorded button-press response signals. Methods for ICA component ordering that may rank highly the components of primary interest in such experiments were developed. The simulation results characterized the performance of ICA under various conditions and may provide useful information for experimental design and data interpretation.     

采用独立分量分析观察经皮穴位电针刺激对脑功能的影响

目的使用独立分量分析方法探索督脉穴位经皮电刺激对脑功能的影响。方法使用1.5T GE Signa Excite核磁成像仪对一位女性脑外伤患者进行BOLD成像。采用组块设计,静息期与刺激期交替,组块长度均为30 s。数据处理采用GIFT、SPM5和MRIcro软件进行,并将独立分量分析与SPM软件处理的结果进行比较。结果采用GIFT中的扩展Infomax算法进行独立分量分析,显示有13个独立成分,每一独立成分包含一空间图和相应的时间变化曲线。任务相关性独立成分的空间激活图与SPM5的分析结果类似,但并不完全相同。此外,这些任务相关性独立成分的时间曲线与SPM所用的经典血流动力相应函数模型的形状并不一致。结论在使用模型依赖的数据分析方法如SPM之前,可以使用独立分量分析探索fMRI数据并获得先验知识。     

Improving human brain mapping via joint inversion of brain electrodynamics and the BOLD signal

We present several methods to improve the resolution of human brain mapping by combining information obtained from surface electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) of the same participants performing the same task in separate imaging sessions. As an initial step in our methods we used independent component analysis (ICA) to obtain task-related sources for both EEG and fMRI. We then used that information in an integrated cost function that attempts to match both data sources and trades goodness of fit in one regime for another. We compared the performance and drawbacks of each method in localizing sources for a dual visual evoked response experiment, and we contrasted the results of adding fMRI information to simple EEG-only inversion methods. We found that adding fMRI information in a variety of ways gives superior results to classical minimum norm source estimation. Our findings lead us to favor a method which attempts to match EEG scalp dynamics along with voxel power obtained from ICA-processed blood oxygenation level dependent (BOLD) data; this method of joint inversion enables us to treat the two data sources as symmetrically as possible.     

Dual tree complex wavelet transform based denoising of optical microscopy images

Photon shot noise is the main noise source of optical microscopy images and can be modeled by a Poisson process. Several discrete wavelet transform based methods have been proposed in the literature for denoising images corrupted by Poisson noise. However, the discrete wavelet transform (DWT) has disadvantages such as shift variance, aliasing, and lack of directional selectivity. To overcome these problems, a dual tree complex wavelet transform is used in our proposed denoising algorithm. Our denoising algorithm is based on the assumption that for the Poisson noise case threshold values for wavelet coefficients can be estimated from the approximation coefficients. Our proposed method was compared with one of the state of the art denoising algorithms. Better results were obtained by using the proposed algorithm in terms of image quality metrics. Furthermore, the contrast enhancement effect of the proposed method on collagen fıber images is examined. Our method allows fast and efficient enhancement of images obtained under low light intensity conditions.OCIS codes: (100.0100) Image processing, (100.7410) Wavelets, (100.3020) Image reconstruction-restoration     

Wavelet denoising of displacement estimates in elastography

Wavelet shrinkage denoising of the displacement estimates to reduce noise artefacts, especially at high overlaps in elastography, is presented in this paper. Correlated errors in the displacement estimates increase dramatically with an increase in the overlap between the data segments. These increased correlated errors (due to the increased correlation or similarity between consecutive displacement estimates) generate the so-called "worm" artefact in elastography. However, increases in overlap on the order of 90% or higher are essential to improve axial resolution in elastography. The use of wavelet denoising significantly reduces errors in the displacement estimates, thereby reducing the worm artefacts, without compromising on edge (high-frequency or detail) information in the elastogram. Wavelet denoising is a term used to characterize noise rejection by thresholding the wavelet coefficients. Worm artefacts can also be reduced using a low-pass filter; however, low-pass filtering of the displacement estimates does not preserve local information such as abrupt change in slopes, causing the smoothing of edges in the elastograms. Simulation results using the analytic 2-D model of a single inclusion phantom illustrate that wavelet denoising produces elastograms with the closest correspondence to the ideal mechanical strain image. Wavelet denoising applied to experimental data obtained from an in vitro thermal lesion phantom generated using radiofrequency (RF) ablation also illustrates the improvement in the elastogram noise characteristics.     

Wavelets and functional magnetic resonance imaging of the human brain

The discrete wavelet transform (DWT) is widely used for multiresolution analysis and decorrelation or "whitening" of nonstationary time series and spatial processes. Wavelets are naturally appropriate for analysis of biological data, such as functional magnetic resonance images of the human brain, which often demonstrate scale invariant or fractal properties. We provide a brief formal introduction to key properties of the DWT and review the growing literature on its application to fMRI. We focus on three applications in particular: (i) wavelet coefficient resampling or "wavestrapping" of 1-D time series, 2- to 3-D spatial maps and 4-D spatiotemporal processes; (ii) wavelet-based estimators for signal and noise parameters of time series regression models assuming the errors are fractional Gaussian noise (fGn); and (iii) wavelet shrinkage in frequentist and Bayesian frameworks to support multiresolution hypothesis testing on spatially extended statistic maps. We conclude that the wavelet domain is a rich source of new concepts and techniques to enhance the power of statistical analysis of human fMRI data.     

fMRI Applications in Schizophrenia Research

fMRI has unique potential in the study of psychiatric patients, particularly in characterizing individual variations and changes over time. We have performed four studies of patients with schizophrenia, using three different fMRI acquisition protocols: (1) 3-D echo-shifted FLASH, a multishot volumetric approach; (2) 3-D PRESTO, a hybid of multishot and echo-planar imaging (EPI) methods that also acquires true volumetric data; and (3) a whole-brain isotropic, multislice EPI technique. Patients were studied during sensorimotor activation and during a novel “Nback” working memory paradigm. In general, patients show normal sensorimotor activation responses, although motor cortical activation tends to be less completely lateralized. Prefrontal activation during working memory tends to be reduced in patients with schizophrenia even when performance is normal. A major potential confound in studying this patient population with fMRI is the effect of motion. We propose several methodological standards to address this problem, including comparisons of motion corrections parameters, voxel variances, and the use of an “internal activation standard.”     

功能磁共振图像小波域分析结果的修正

目的改进f MRI数据小波域分析方法。方法通过在原始空间域对传统小波方法检测出的激活区再进行检验来修正传统小波方法的缺点,并以SPM99为标准,通过比较传统小波方法和修正方法对一组手动实验数据的分析结果来说明修正方法的效果。结果修正方法能较好地除去或减小传统小波方法中激活区的扩散和伪影。结论小波域分析f MRI图像是一种快速灵敏的方法,但重建后激活区扩散且有伪影。本文提出的修正方法是一种快速且较传统小波方法准确的f MRI数据分析方法。     

Independent vector analysis (IVA): multivariate approach for fMRI group study

Independent component analysis (ICA) of fMRI data generates session/individual specific brain activation maps without a priori assumptions regarding the timing or pattern of the blood-oxygenation-level-dependent (BOLD) signal responses. However, because of a random permutation among output components, ICA does not offer a straightforward solution for the inference of group-level activation. In this study, we present an independent vector analysis (IVA) method to address the permutation problem during fMRI group data analysis. In comparison to ICA, IVA offers an analysis of additional dependent components, which were assigned for use in the automated grouping of dependent activation patterns across subjects. Upon testing using simulated trial-based fMRI data, our proposed method was applied to real fMRI data employing both a single-trial task-paradigm (right hand motor clenching and internal speech generation tasks) and a three-trial task-paradigm (right hand motor imagery task). A generalized linear model (GLM) and the group ICA of the fMRI toolbox (GIFT) were also applied to the same data set for comparison to IVA. Compared to GLM, IVA successfully captured activation patterns even when the functional areas showed variable hemodynamic responses that deviated from a hypothesized response. We also showed that IVA effectively inferred group-activation patterns of unknown origins without the requirement for a pre-processing stage (such as data concatenation in ICA-based GIFT). IVA can be used as a potential alternative or an adjunct to current ICA-based fMRI group processing methods.     

Investigation of spatial resolution, partial volume effects and smoothing in functional MRI using artificial 3D time series

This work addresses the balance between temporal signal-to-noise ratio (tSNR) and partial volume effects (PVE) in functional magnetic resonance imaging (fMRI) and investigates the impact of the choice of spatial resolution and smoothing. In fMRI, since physiological time courses are monitored, tSNR is of greater importance than image SNR. Improving SNR by an increase in voxel volume may be of negligible benefit when physiological fluctuations dominate the noise. Furthermore, at large voxel volumes, PVE are more pronounced, leading to an overall loss in performance. Artificial fMRI time series, based on high-resolution anatomical data, were used to simulate BOLD activation in a controlled manner. The performance was subsequently quantified as a measure of how well the resulted activation matched the simulated activation. The performance was highly dependent on the spatial resolution. At high contrast-to-noise ratio (CNR), the optimal voxel volume was small, i.e. in the region of 2(3) mm(3). It was also shown that using a substantially larger voxel volume in this case could potentially negate the CNR benefits. The optimal smoothing kernel width was dependent on the CNR, being larger at poor CNR. At CNR >1, little or no smoothing proved advantageous. The use of artificial time series gave an opportunity to quantitatively investigate the effects of partial volume and smoothing in single subject fMRI. It was shown that a proper choice of spatial resolution and smoothing kernel width is important for fMRI performance.     

A spatio-temporal regression model for the analysis of functional MRI data

The standard method for analyzing functional magnetic resonance imaging (fMRI) data applies the general linear model to the time series of each voxel separately. Such a voxelwise approach, however, does not consider the spatial autocorrelation between neighboring voxels in its model formulation and parameter estimation. We propose a spatio-temporal regression analysis for detecting activation in fMRI data. Its main features are that (1) each voxel has a regression model that involves the time series of the neighboring voxels together with its own, (2) the regression coefficient assigned to the center voxel is estimated so that the time series of these multiple voxels will best fit the model, (3) a generalized least squares (GLS) method was employed instead of the ordinary least squares (OLS) to put intrinsic autocorrelation structures into the model, and (4) the underlying spatial and temporal correlation structures are modeled using a separable model which expresses the combined correlation structures as a product of the two. We evaluated the statistical power of our model in comparison with voxelwise OLS/GLS models and a multivoxel OLS model. Our model's power to detect clustered activation was higher than that of the two voxelwise models and comparable to that of the multivoxel OLS. We examined the usefulness and goodness of fit of our model using real experimental data. Our model successfully detected neural activity in expected brain regions and realized better fit than the other models. These results suggest that our spatio-temporal regression model can serve as a reliable analysis suited for the nature of fMRI data.