Multiresolution analysis in fMRI: sensitivity and specificity in the detection of brain activation

Multifaceted aspects of charge transfer

Charge transfer and charge transport are by far among the most important processes for sustaining life on Earth and for making our modern ways of living possible. Involving multiple electron-transfer steps, photosynthesis and cellular respiration have been principally responsible for managing the energy flow in the biosphere of our planet since the Great Oxygen Event. It is impossible to imagine living organisms without charge transport mediated by ion channels, or electron and proton transfer mediated by redox enzymes. Concurrently, transfer and transport of electrons and holes drive the functionalities of electronic and photonic devices that are intricate for our lives. While fueling advances in engineering, charge-transfer science has established itself as an important independent field, originating from physical chemistry and chemical physics, focusing on paradigms from biology, and gaining momentum from solar-energy research. Here, we review the fundamental concepts of charge transfer, and outline its core role in a broad range of unrelated fields, such as medicine, environmental science, catalysis, electronics and photonics. The ubiquitous nature of dipoles, for example, sets demands on deepening the understanding of how localized electric fields affect charge transfer. Charge-transfer electrets, thus, prove important for advancing the field and for interfacing fundamental science with engineering. Synergy between the vastly different aspects of charge-transfer science sets the stage for the broad global impacts that the advances in this field have.

Fast multiscale reconstruction for Cryo-EM

We present a multiscale reconstruction framework for single-particle analysis (SPA). The representation of three-dimensional (3D) objects with scaled basis functions permits the reconstruction of volumes at any desired scale in the real-space. This multiscale approach generates interesting opportunities in SPA for the stabilization of the initial volume problem or the 3D iterative refinement procedure. In particular, we show that reconstructions performed at coarse scale are more robust to angular errors and permit gains in computational speed. A key component of the proposed iterative scheme is its fast implementation. The costly step of reconstruction, which was previously hindering the use of advanced iterative methods in SPA, is formulated as a discrete convolution with a cost that does not depend on the number of projection directions. The inclusion of the contrast transfer function inside the imaging matrix is also done at no extra computational cost. By permitting full 3D regularization, the framework is by itself a robust alternative to direct methods for performing reconstruction in adverse imaging conditions (e.g., heavy noise, large angular misassignments, low number of projections). We present reconstructions obtained at different scales from a dataset of the 2015/2016 EMDataBank Map Challenge. The algorithm has been implemented in the Scipion package.

Gray matter changes and cognitive predictors of 2-year follow-up abnormalities in early-onset first-episode psychosis

This study aims to examine regional gray matter (GM) changes over a period of 2 years in patients diagnosed with early-onset first-episode psychosis (EO-FEP), and to identify baseline predictors of abnormalities at the follow-up. Fifty-nine patients with EO-FEP aged 11-17 years were assessed. Magnetic resonance imaging was carried out at admission and 2 years later. Changes over time were assessed with voxel-based morphometry. Fifty-nine patients (34 schizophrenia-SCZ, 15 bipolar disorder-BP, and 10 other psychotic disorders) and 70 healthy controls were assessed. At baseline no differences were found between the EO-FEP groups and control subjects. Over time, SCZ patients presented a larger GM decrease in the orbitofrontal cortex, anterior midline frontal cortex, cingulate, left caudate, and thalamus. BP patients also had a larger GM decrease in the right putamen, right orbitofrontal cortex, and anterior and midline region of the right superior frontal gyrus and left caudate, but with fewer areas showing significant differences than in the comparison between SCZ and controls. In the cross-sectional analysis, only SCZ patients showed differences with respect to controls in some GM areas. Significant baseline predictors of a 2-year reduction in GM were IQ and working memory. EO-FEP patients did not show differences in GM compared to controls at baseline. Both SCZ and BP patients showed a greater decrease in specific areas during the first 2 years. At follow-up, only SCZ patients differed significantly from controls in specific brain areas. The GM reduction was predicted by baseline cognitive variables.

Topologically convergent and divergent functional connectivity patterns in unmedicated unipolar depression and bipolar disorder

Bipolar disorder (BD), particularly BD II, is frequently misdiagnosed as unipolar depression (UD), leading to inappropriate treatment and poor clinical outcomes. Although depressive symptoms may be expressed similarly in UD and BD, the similarities and differences in the architecture of brain functional networks between the two disorders are still unknown. In this study, we hypothesized that UD and BD II patients would show convergent and divergent patterns of disrupted topological organization of the functional connectome, especially in the default mode network (DMN) and the limbic network. Brain resting-state functional magnetic resonance imaging (fMRI) data were acquired from 32 UD-unmedicated patients, 31 unmedicated BD II patients (current episode depressed) and 43 healthy subjects. Using graph theory, we systematically studied the topological organization of their whole-brain functional networks at the following three levels: whole brain, modularity and node. First, both the UD and BD II patients showed increased characteristic path length and decreased global efficiency compared with the controls. Second, both the UD and BD II patients showed disrupted intramodular connectivity within the DMN and limbic system network. Third, decreased nodal characteristics (nodal strength and nodal efficiency) were found predominantly in brain regions in the DMN, limbic network and cerebellum of both the UD and BD II patients, whereas differences between the UD and BD II patients in the nodal characteristics were also observed in the precuneus and temporal pole. Convergent deficits in the topological organization of the whole brain, DMN and limbic networks may reflect overlapping pathophysiological processes in unipolar and bipolar depression. Our discovery of divergent regional connectivity that supports emotion processing could help to identify biomarkers that will aid in differentiating these disorders.

Abnormal structural connectivity between the basal ganglia, thalamus, and frontal cortex in patients with disorders of consciousness

Consciousness loss in patients with severe brain injuries is associated with reduced functional connectivity of the default mode network (DMN), fronto-parietal network, and thalamo-cortical network. However, it is still unclear if the brain white matter connectivity between the above mentioned networks is changed in patients with disorders of consciousness (DOC). In this study, we collected diffusion tensor imaging (DTI) data from 13 patients and 17 healthy controls, constructed whole-brain white matter (WM) structural networks with probabilistic tractography. Afterward, we estimated and compared topological properties, and revealed an altered structural organization in the patients. We found a disturbance in the normal balance between segregation and integration in brain structural networks and detected significantly decreased nodal centralities primarily in the basal ganglia and thalamus in the patients. A network-based statistical analysis detected a subnetwork with uniformly significantly decreased structural connections between the basal ganglia, thalamus, and frontal cortex in the patients. Further analysis indicated that along the WM fiber tracts linking the basal ganglia, thalamus, and frontal cortex, the fractional anisotropy was decreased and the radial diffusivity was increased in the patients compared to the controls. Finally, using the receiver operating characteristic method, we found that the structural connections within the NBS-derived component that showed differences between the groups demonstrated high sensitivity and specificity (>90%). Our results suggested that major consciousness deficits in DOC patients may be related to the altered WM connections between the basal ganglia, thalamus, and frontal cortex.

Wavelets and statistical analysis of functional magnetic resonance images of the human brain

Wavelets provide an orthonormal basis for multiresolution analysis and decorrelation or ‘whitening’ of nonstationary time series and spatial processes. Wavelets are particularly well suited to analysis of biological signals and images, such as human brain imaging data, which often have fractal or scale-invariant properties. We briefly define some key properties of the discrete wavelet transform (DWT) and review its applications to statistical analysis of functional magnetic resonance imaging (fMRI) data. We focus on time series resampling by ‘wavestrapping’ of wavelet coefficients, methods for efficient linear model estimation in the wavelet domain, and wavelet-based methods for multiple hypothesis testing, all of which are somewhat simplified by the decorrelating property of the DWT.

Statistical analysis of brain tissue images in the wavelet domain: wavelet-based morphometry

Wavelet-based methods have been developed for statistical analysis of functional MRI and PET data, where the wavelet transformation is employed as a tool for efficient signal representation. A number of studies using these approaches have reported better estimation capabilities, in terms of increased sensitivity and specificity, than the standard statistical analyses in the spatial domain. In line with these previous studies, the present report proposes a statistical analysis in the wavelet domain for the estimation of inter-group differences from structural MRI data. The procedure, called wavelet-based morphometry (WBM), was implemented under a voxel-based morphometry (VBM) style analysis. It was evaluated by comparing the gray-matter images of a group of 32 healthy subjects whose images were artificially altered to induce thinning of the cortex, with a different group of 32 healthy subjects whose images were unaltered. In order to quantify the performance of the reconstruction from a practical perspective, the same comparison was also conducted with standard VBM using SPM's Gaussian random fields and FSL's cluster-based statistics, family-wise error corrected, for datasets spatially-normalized via two different registration methods (i.e., SyN and FNIRT). The effect of using different amounts of smoothing, Battle-Lemarié filters and resolution levels in the wavelet transform was also investigated. Results support the proposed approach as a different and promising methodology to assess the structural morphometric differences between different populations of subjects.

TWave: high-order analysis of functional MRI

The traditional approach to functional image analysis models images as matrices of raw voxel intensity values. Although such a representation is widely utilized and heavily entrenched both within neuroimaging and in the wider data mining community, the strong interactions among space, time, and categorical modes such as subject and experimental task inherent in functional imaging yield a dataset with "high-order" structure, which matrix models are incapable of exploiting. Reasoning across all of these modes of data concurrently requires a high-order model capable of representing relationships between all modes of the data in tandem. We thus propose to model functional MRI data using tensors, which are high-order generalizations of matrices equivalent to multidimensional arrays or data cubes. However, several unique challenges exist in the high-order analysis of functional medical data: naïve tensor models are incapable of exploiting spatiotemporal locality patterns, standard tensor analysis techniques exhibit poor efficiency, and mixtures of numeric and categorical modes of data are very often present in neuroimaging experiments. Formulating the problem of image clustering as a form of Latent Semantic Analysis and using the WaveCluster algorithm as a baseline, we propose a comprehensive hybrid tensor and wavelet framework for clustering, concept discovery, and compression of functional medical images which successfully addresses these challenges. Our approach reduced runtime and dataset size on a 9.3GB finger opposition motor task fMRI dataset by up to 98% while exhibiting improved spatiotemporal coherence relative to standard tensor, wavelet, and voxel-based approaches. Our clustering technique was capable of automatically differentiating between the frontal areas of the brain responsible for task-related habituation and the motor regions responsible for executing the motor task, in contrast to a widely used fMRI analysis program, SPM, which only detected the latter region. Furthermore, our approach discovered latent concepts suggestive of subject handedness nearly 100× faster than standard approaches. These results suggest that a high-order model is an integral component to accurate scalable functional neuroimaging.

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.

Discriminating brain activity from task-related artifacts in functional MRI: fractal scaling analysis simulation and application

Functional magnetic resonance imaging (fMRI) signal changes can be separated from background noise by various processing algorithms, including the well-known deconvolution method. However, discriminating signal changes due to task-related brain activities from those due to task-related head motion or other artifacts correlated in time to the task has been little addressed. We examine whether three exploratory fractal scaling analyses correctly classify these possibilities by capturing temporal self-similarity; namely, fluctuation analysis, wavelet multi-resolution analysis, and detrended fluctuation analysis (DFA). We specifically evaluate whether these fractal analytic methods can be effective and reliable in discriminating activations from artifacts. DFA is indeed robust for such classification. Brain activation maps derived by DFA are similar, but not identical, to maps derived by deconvolution. Deconvolution explicitly utilizes task timing to extract the signals whereas DFA does not, so these methods reveal somewhat different information from the data. DFA is better than deconvolution for distinguishing fMRI activations from task-related artifacts, although a combination of these approaches is superior to either one taken alone. We also present a method for estimating noise levels in fMRI data, validated with numerical simulations suggesting that Birn's model is effective for simulating fMRI signals. Simulations further corroborate that DFA is excellent at discriminating signal changes due to task-related brain activities from those due to task-related artifacts, under a range of conditions.

Assessing a signal model and identifying brain activity from fMRI data by a detrending-based fractal analysis

One of the major challenges of functional magnetic resonance imaging (fMRI) data analysis is to develop simple and reliable methods to correlate brain regions with functionality. In this paper, we employ a detrending-based fractal method, called detrended fluctuation analysis (DFA), to identify brain activity from fMRI data. We perform three tasks: (a) Estimating noise level from experimental fMRI data; (b) Assessing a signal model recently introduced by Birn et al.; and (c) Evaluating the effectiveness of DFA for discriminating brain activations from artifacts. By computing the receiver operating characteristic (ROC) curves, we find that the ROC curve for experimental data is similar to the curve for simulated data with similar signal-to-noise ratio (SNR). This suggests that the proposed algorithm for estimating noise level is very effective and that Birn's model fits our experimental data very well. The brain activation maps for experimental data derived by DFA are similar to maps derived by deconvolution using a widely used software, AFNI. Considering that deconvolution explicitly uses the information about the experimental paradigm to extract the activation patterns whereas DFA does not, it remains to be seen whether one can effectively integrate the two methods to improve accuracy for detecting brain areas related to functional activity.

Deriving meaning: Distinct neural mechanisms for metaphoric, literal, and non-meaningful sentences

In this study, we used a novel cognitive paradigm and event-related functional magnetic resonance imaging (ER-fMRI) to investigate the neural substrates involved in processing three different types of sentences. Participants read either metaphoric (Some surgeons are butchers), literal (Some surgeons are fathers), or non-meaningful sentences (Some surgeons are shelves) and had to decide whether they made sense or not. We demonstrate that processing of the different sentence types relied on distinct neural mechanisms. Activation of the left inferior frontal gyrus (LIFG), BA 47, was shared by both non-meaningful and metaphoric sentences but not by literal sentences. Furthermore, activation of the left thalamus appeared to be specifically involved in deriving meaning from metaphoric sentences despite lack of reaction times differences between literals and metaphors. We assign this to the ad hoc concept construction and open-endedness of metaphoric interpretation. In contrast to previous studies, our results do not support the view the right hemispheric is specifically involved in metaphor comprehension.

Development of computer-generated phantoms for FMRI software evaluation

Functional magnetic resonance imaging (FMRI) is a major tool for the evaluation of brain function and architecture. It is widely used by physicians, neuroscientists, psychologists and others. In order to process the data collected using FMRI, it is necessary to use post-acquisition processing software that employs motion correction and statistical modeling capabilities. These types of programs permit the user to extract the information about areas of brain activations that have occurred during a study. How well a particular motion-correction technique works and what effect it has on statistical processing are difficult to evaluate, since the level of activation present is not known a priori. This paper provides a description of the construction of a software phantom for use with FMRI post-acquisition processing tools with the properties that it is based on real subject data, has known locations and levels of activation, has known amounts of rigid body motion and noise added, and can be used to evaluate a processing system as if it were a real data set. Versions of the software phantom are available for downloading at the website: .

How metaphors influence semantic relatedness judgments: The role of the right frontal cortex

We used event-related fMRI (ER-fMRI) to test the hypothesis that metaphors bias cognitive processing of semantic relatedness towards a search for a wider range of associations. Twelve right-handed male volunteers read a mixture of metaphoric and literal sentences, each sentence being followed by a single word, which could be semantically related or not to the preceding sentence context. We found that judging unrelated words as contextually irrelevant was associated with increased blood oxygenation level-dependent (BOLD) signal in the right ventrolateral prefrontal cortex in the metaphoric but not in the literal condition. The same region was also activated when subjects endorsed a semantic relation between words and metaphoric sentence primes but not between words and literal sentence primes. We argue that these results are consistent with the notion of semantic open-endedness, whereby figurative statements bias cognitive processing towards a search for a wider range of semantic relationships compared to literal statements, and thus lend further support to the view that coarse semantic coding occurs preferentially in the right hemisphere.

Estimation of false discovery rates for wavelet-denoised statistical parametric maps

Correction for multiple comparisons in neuroimaging data is an important area of research. Recently, wavelet-based methods have gained popularity and have been reported to achieve better sensitivity compared to spatial domain methods. However, these techniques produce smoothed statistical maps which are difficult to interpret. The generated maps have to be thresholded again in the spatial domain to delineate active from inactive regions. The selection of a proper threshold satisfying the required error rate control is not straightforward. In this paper, a framework is proposed for thresholding wavelet-denoised maps in which a rejection region is fixed, and the achieved false discovery rate (FDR) is estimated. This approach provides a meaningful strategy to choose thresholds for wavelet-denoised statistical parametric maps (SPMs). Two FDR estimation algorithms were used to assess the achieved error rate control when thresholding wavelet filtered SPMs at various rejection regions. Their performance was evaluated using both simulated and resting fMRI data. The proposed framework was also applied on in vivo data.

A wavelet-based statistical analysis of FMRI data: I. motivation and data distribution modeling

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 magnetic resonance imaging (MRI) and fMRI to empirically estimate the distribution of the wavelet coefficients of the data both across individuals and 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 frequency-adaptive wavelet shrinkage scheme is employed to obtain essentially optimal estimations of the signals in the wavelet space. The empirical distributions of the signals on all the regions are computed in a compressed wavelet space. These are modeled by heavy-tail distributions because their histograms exhibit slower tail decay than the Gaussian. We discovered that the Cauchy, Bessel K Forms, 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 atlas-based wavelet space representation. In the second part of our investigation, we will apply this technique to analyze a large fMRI dataset involving repeated presentation of sensory-motor response stimuli in young, elderly, and demented subjects.

Quantile estimation to derive optimized test thresholds for random field statistics

We present a numerical method to estimate the true threshold values in random fields needed to determine the significance of apparent signals observed in noisy images. To accomplish this, a quantile estimation algorithm is applied to derive the threshold with a predefined confidence interval from a large number of simulated random fields. Also, a computationally efficient method for generating a random field simulation is presented using resampling techniques. Applying these techniques, thresholds have been determined for a large variety of parameter settings (smoothness, voxel size, brain shape, type of statistics). By means of interpolation techniques, thresholds for additional arbitrary settings can be quickly derived without the need to run individual simulations. Compared to the parametric approach of Worsley et al. (1996) (Worsley, K.J., Marrett, S., Neelin P., Vandal, A.C., Friston, K.J., Evans, A.C., 1996. A unified statistical approach for determining significant signals in images of cerebral activation. Hum. Brain Mapp. 4, 58-73) and Friston et al. (1991) (Friston, K.J., Frith, C.D., Liddle, P.F., Frackowiak, R.S. 1991. Comparing functional (PET) images: the assessment of significant change. J. Cereb. Blood Flow Metab. 11(4), 690-699), and to the Bonferroni approach, these optimized thresholds lead to higher levels of significance (i.e., lower p values) with a specific amount of activation especially with fields of moderate smoothness (i.e., with a relative full width half maximum between 2 and 6). Alternatively, the threshold for a specified level of significance can be lowered. This improved statistical sensitivity is illustrated by the analysis of an actual event related functional magnetic resonance data set, and its limitations are tested by determining the false positive rate with experimental MR noise data. The grid of estimated threshold values as well as the interpolation algorithm to derive thresholds for arbitrary parameter settings are made available over the internet (http://neuro2.med.uni-magdeburg.de/quantile_estimation).

Generalized likelihood ratio tests for complex fMRI data: a simulation study

Statistical tests developed for the analysis of (intrinsically complex valued) functional magnetic resonance time series, are generally applied to the data's magnitude components. However, during the past five years, new tests were developed that incorporate the complex nature of fMRI data. In particular, a generalized likelihood ratio test (GLRT) was proposed based on a constant phase model. In this work, we evaluate the sensitivity of GLRTs for complex data to small misspecifications of the phase model by means of simulation experiments. It is argued that, in practical situations, GLRTs based on magnitude data are likely to perform better compared to GLRTs based on complex data in terms of detection rate and constant false alarm rate properties.

ROC evaluation of statistical wavelet-based analysis of brain activation in [15O]-H2O PET scans

This paper presents and evaluates a wavelet-based statistical analysis of PET images for the detection of brain activation areas. Brain regions showing significant activations were obtained by performing Student's t tests in the wavelet domain, reconstructing the final image from only those wavelet coefficients that passed the statistical test at a given significance level, and discarding artifacts introduced during the reconstruction process. Using Receiver Operating Characteristic (ROC) curves, we have compared this statistical analysis in the wavelet domain to the conventional image-domain Statistical Parametric Mapping (SPM) method. For obtaining an accurate assessment of sensitivity and specificity, we have simulated realistic single subject [15O]-H2O PET studies with different hyperactivation levels of the thalamic region. The results obtained from an ROC analysis show that the wavelet approach outperforms conventional SPM in identifying brain activation patterns. Using the wavelet method, activation areas detected were closer in size and shape to the region actually activated in the reference image.

Unsupervised learning and mapping of active brain functional MRI signals based on hidden semi-Markov event sequence models

In this paper, a novel functional magnetic resonance imaging (fMRI) brain mapping method is presented within the statistical modeling framework of hidden semi-Markov event sequence models (HSMESMs). Neural activation detection is formulated at the voxel level in terms of time coupling between the sequence of hemodynamic response onsets (HROs) observed in the fMRI signal, and an HSMESM of the hidden sequence of task-induced neural activations. The sequence of HRO events is derived from a continuous wavelet transform (CWT) of the fMRI signal. The brain activation HSMESM is built from the timing information of the input stimulation protocol. The rich mathematical framework of HSMESMs makes these models an effective and versatile approach for fMRI data analysis. Solving for the HSMESM Evaluation and Learning problems enables the model to automatically detect neural activation embedded in a given set of fMRI signals, without requiring any template basis function or prior shape assumption for the fMRI response. Solving for the HSMESM Decoding problem allows to enrich brain mapping with activation lag mapping, activation mode visualizing, and hemodynamic response function analysis. Activation detection results obtained on synthetic and real epoch-related fMRI data demonstrate the superiority of the HSMESM mapping method with respect to a real application case of the statistical parametric mapping (SPM) approach. In addition, the HSMESM mapping method appears clearly insensitive to timing variations of the hemodynamic response, and exhibits low sensitivity to fluctuations of its shape.

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.

A multiresolution approach to orientation assignment in 3D electron microscopy of single particles

Three-dimensional (3D) electron microscopy (3DEM) aims at the determination of the spatial distribution of the Coulomb potential of macromolecular complexes. The 3D reconstruction of a macromolecule using single-particle techniques involves thousands of 2D projections. One of the key parameters required to perform such a 3D reconstruction is the orientation of each projection image as well as its in-plane orientation. This information is unknown experimentally and must be determined using image-processing techniques. We propose the use of wavelets to match the experimental projections with those obtained from a reference 3D model. The wavelet decomposition of the projection images provides a framework for a multiscale matching algorithm in which speed and robustness to noise are gained. Furthermore, this multiresolution approach is combined with a novel orientation selection strategy. Results obtained from computer simulations as well as experimental data encourage the use of this approach.

Wavelet variance components in image space for spatiotemporal neuroimaging data

Neuroimaging studies place great emphasis on not only the estimation but also the standard error estimates of underlying parameters derived from a temporal model. This allows inferences to be made about the signal estimates and resulting conclusions to be drawn about the underlying data. It can often be advantageous to interrogate temporal models after spatial transformation of the data into the wavelet domain. Wavelet bases provide a multiresolution decomposition of the spatial data dimension and an ensuing reduction in spatial correlation. However, widespread acceptance of these wavelet techniques has been hampered by the limited ability to reconstruct both parametric and error estimates into the image domain after analysis of temporal models in the wavelet domain. This paper introduces a derivation and a fast implementation of a method for the calculation of the variance of the parametric images obtained from wavelet filters. The technique is proposed for a class of estimators that have been shown to be useful in neuroimaging studies. The techniques are demonstrated for both functional magnetic resonance imaging (fMRI) and positron emission tomography (PET) data sets.

Integrated wavelet processing and spatial statistical testing of fMRI data

We introduce an integrated framework for detecting brain activity from fMRI data, which is based on a spatial discrete wavelet transform. Unlike the standard wavelet-based approach for fMRI analysis, we apply the suitable statistical test procedure in the spatial domain. For a desired significance level, this scheme has one remaining degree of freedom, characterizing the wavelet processing, which is optimized according to the principle of minimal approximation error. This allows us to determine the threshold values in a way that does not depend on data. While developing our framework, we make only conservative assumptions. Consequently, the detection of activation is based on strong evidence. We have implemented this framework as a toolbox (WSPM) for the SPM2 software, taking advantage of multiple options and functions of SPM such as the setup of the linear model and the use of the hemodynamic response function. We show by experimental results that our method is able to detect activation patterns; the results are comparable to those obtained by SPM even though statistical assumptions are more conservative.

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.

Wavelet statistics of functional MRI data and the general linear model

PURPOSE

To improve the signal-to-noise ratio (SNR) of functional magnetic resonance imaging (fMRI) data, an approach is developed that combines wavelet-based methods with the general linear model.

MATERIALS AND METHODS

Ruttimann et al. (1) developed a wavelet-based statistical procedure to test wavelet-space partitions for significant wavelet coefficients. Their method is applicable for the detection of differences between images acquired under two experimental conditions using long blocks of stimulation. However, many neuropsychological questions require more complicated event-related paradigms and more experimental conditions. Therefore, in order to apply wavelet-based methods to a wide range of experiments, we present a new approach that is based on the general linear model and wavelet thresholding.

RESULTS

In contrast to a monoresolution filter, the application of the wavelet method increased the SNR and showed a set of clearly dissociable activations. Furthermore, no relevant decrease of the local maxima was observed.

CONCLUSION

Wavelet-based methods can increase the SNR without diminishing the signal amplitude, while preserving the spatial resolution of the image. The anatomical localization is strongly improved.