Activation detection in functional MRI using subspace modeling and maximum likelihood estimation

Adaptive Brain Activity Detection in Structured Interference and Partially Homogeneous Locally Correlated Disturbance

OBJECTIVE

In this paper, we aim to address the problem of subspace detection in the presence of locally-correlated complex Gaussian noise and interference. For applications like brain activity detection using functional magnetic resonance imaging (fMRI) data where the noise is possibly locally correlated, using the sample covariance estimator is not a suitable choice due to significant dependency of its accuracy on the number of observations.

METHODS

In this study, we take advantage of an assumed banded structure in the covariance matrix to model the local dependence in the noise and propose a new covariance estimation approach. In particular, we use the idea of fac-torizing the joint likelihood function into a few conditional likelihood terms and maximizing each term independently of the others. This process leads to an explicit estimator for banded covariance matrices which requires fewer observations to achieve the same accuracy as the sample covari-ance. This estimate is then fed into an adaptive matched filter, two-step Rao and two-step Wald tests for detection.

RESULTS

Simulation results reveal the superiority of the proposed methods over well known classical detectors. Finally, the proposed methods are applied to functional magnetic resonance imaging (fMRI) data to localize neural activities in the brain.

CONCLUSION

The proposed method can offer better activation maps in terms of accuracy and spatial smoothness.

SIGNIFICANCE

The proposed methods can be seen as alternatives for standard detection approaches which are not perfectly aligned with the properties of fMRI data.

Robust Subspace Detectors Based on α-Divergence With Application to Detection in Imaging

Robust variants of Wald, Rao and likelihood ratio (LR) tests for the detection of a signal subspace in a signal interference subspace corrupted by contaminated Gaussian noise are proposed in this paper. They are derived using the α- divergence, and the trade-off between the robustness and the power (the probability of detection) of the tests is adjustable using a single hyperparameter α . It is shown that when α→ 1 , these tests are equivalent to their well known classical counterparts. For example the robust LR test coincides with the LR test or the matched subspace detector (MSD). Asymptotic results are provided to support the proposed tests and robustness to outliers is obtained using values of . Numerical experiments illustrating the performance of these tests on simulated, real functional magnetic resonance imaging (fMRI), hyperspectral and synthetic aperture radar (SAR) data are also presented.

MOSES: A Streaming Algorithm for Linear Dimensionality Reduction

This paper introduces Memory-limited Online Subspace Estimation Scheme (MOSES) for both estimating the principal components of streaming data and reducing its dimension. More specifically, in various applications such as sensor networks, the data vectors are presented sequentially to a user who has limited storage and processing time available. Applied to such problems, MOSES can provide a running estimate of leading principal components of the data that has arrived so far and also reduce its dimension. MOSES generalises the popular incremental Singular Vale Decomposition (iSVD) to handle thin blocks of data, rather than just vectors. This minor generalisation in part allows us to complement MOSES with a comprehensive statistical analysis, thus providing the first theoretically-sound variant of iSVD, which has been lacking despite the empirical success of this method. This generalisation also enables us to concretely interpret MOSES as an approximate solver for the underlying non-convex optimisation program. We find that MOSES consistently surpasses the state of the art in our numerical experiments with both synthetic and real-world datasets, while being computationally inexpensive.

A Projection CCA Method for Effective fMRI Data Analysis

OBJECTIVE

Canonical correlation analysis (CCA) is a data-driven method that has been successfully used in functional magnetic resonance imaging (fMRI) data analysis. Standard CCA extracts meaningful information from a pair of data sets by seeking pairs of linear combinations from two sets of variables with maximum pairwise correlation. So far, however, this method has been used without incorporating prior information available for fMRI data. In this paper, we address this issue by proposing a new CCA method named pCCA (for projection CCA).

METHODS

The proposed method is obtained by projection onto a set of basis vectors that better characterize temporal information in the fMRI data set. A methodology is presented to describe the basis selection process using discrete cosine transform (DCT) basis functions. Employing DCT guides the estimated canonical variates, yielding a more computationally efficient CCA procedure.

RESULTS

The performance gain of the proposed pCCA algorithm over standard and regularized CCA is illustrated on both simulated and real fMRI datasets from resting state, block paradigm task-related and event-related experiments. The results have shown that the proposed pCCA successfully extracts latent components from the task as well as resting-state datasets with increased specificity of the activated voxels.

CONCLUSION

In addition to offering a new CCA approach, when applied on fMRI data, the proposed algorithm adapts to variations of brain activity patterns and reveals the functionally connected brain regions.

SIGNIFICANCE

The proposed method can be seen as a regularized CCA method where regularization is introduced via basis expansion, which has the advantage of enforcing smoothness on canonical components.

Asymptotic performance of PCA for high-dimensional heteroscedastic data

Principal Component Analysis (PCA) is a classical method for reducing the dimensionality of data by projecting them onto a subspace that captures most of their variation. Effective use of PCA in modern applications requires understanding its performance for data that are both high-dimensional and heteroscedastic. This paper analyzes the statistical performance of PCA in this setting, i.e., for high-dimensional data drawn from a low-dimensional subspace and degraded by heteroscedastic noise. We provide simplified expressions for the asymptotic PCA recovery of the underlying subspace, subspace amplitudes and subspace coefficients; the expressions enable both easy and efficient calculation and reasoning about the performance of PCA. We exploit the structure of these expressions to show that, for a fixed average noise variance, the asymptotic recovery of PCA for heteroscedastic data is always worse than that for homoscedastic data (i.e., for noise variances that are equal across samples). Hence, while average noise variance is often a practically convenient measure for the overall quality of data, it gives an overly optimistic estimate of the performance of PCA for heteroscedastic data.

Dynamic contrast-enhanced MRI of the patellar bone: How to quantify perfusion

Purpose

To identify the optimal combination of pharmacokinetic model and arterial input function (AIF) for quantitative analysis of blood perfusion in the patellar bone using dynamic contrast‐enhanced magnetic resonance imaging (DCE‐MRI).

Materials and Methods

This method design study used a random subset of five control subjects from an Institutional Review Board (IRB)‐approved case–control study into patellofemoral pain, scanned on a 3T MR system with a contrast‐enhanced time‐resolved imaging of contrast kinetics (TRICKS) sequence. We systematically investigated the reproducibility of pharmacokinetic parameters for all combinations of Orton and Parker AIF models with Tofts, Extended Tofts (ETofts), and Brix pharmacokinetic models. Furthermore, we evaluated if the AIF should use literature parameters, be subject‐specific, or group‐specific. Model selection was based on the goodness‐of‐fit and the coefficient of variation of the pharmacokinetic parameters inside the patella. This extends previous studies that were not focused on the patella and did not evaluate as many combinations of arterial and pharmacokinetic models.

Results

The vascular component in the ETofts model could not reliably be recovered (coefficient of variation [CV] of v_p >50%) and the Brix model parameters showed high variability of up to 20% for k_el across good AIF models. Compared to group‐specific AIF, the subject‐specific AIF's mostly had higher residual. The best reproducibility and goodness‐of‐fit were obtained by combining Tofts' pharmacokinetic model with the group‐specific Parker AIF.

Conclusion

We identified several good combinations of pharmacokinetic models and AIF for quantitative analysis of perfusion in the patellar bone. The recommended combination is Tofts pharmacokinetic model combined with a group‐specific Parker AIF model.

Level of Evidence: 2

Technical Efficacy: Stage 1

J. Magn. Reson. Imaging 2018;47:848–858.

Sequential Dictionary Learning From Correlated Data: Application to fMRI Data Analysis

Sequential dictionary learning via the K-SVD algorithm has been revealed as a successful alternative to conventional data driven methods, such as independent component analysis for functional magnetic resonance imaging (fMRI) data analysis. fMRI data sets are however structured data matrices with notions of spatio-temporal correlation and temporal smoothness. This prior information has not been included in the K-SVD algorithm when applied to fMRI data analysis. In this paper, we propose three variants of the K-SVD algorithm dedicated to fMRI data analysis by accounting for this prior information. The proposed algorithms differ from the K-SVD in their sparse coding and dictionary update stages. The first two algorithms account for the known correlation structure in the fMRI data by using the squared Q, R-norm instead of the Frobenius norm for matrix approximation. The third and last algorithms account for both the known correlation structure in the fMRI data and the temporal smoothness. The temporal smoothness is incorporated in the dictionary update stage via regularization of the dictionary atoms obtained with penalization. The performance of the proposed dictionary learning algorithms is illustrated through simulations and applications on real fMRI data.

Prewhitening High-Dimensional fMRI Data Sets Without Eigendecomposition

This letter proposes an algorithm for linear whitening that minimizes the mean squared error between the original and whitened data without using the truncated eigendecomposition (ED) of the covariance matrix of the original data. This algorithm uses Lanczos vectors to accurately approximate the major eigenvectors and eigenvalues of the covariance matrix of the original data. The major advantage of the proposed whitening approach is its low computational cost when compared with that of the truncated ED. This gain comes without sacrificing accuracy, as illustrated with an experiment of whitening a high-dimensional fMRI data set.

Spatiotemporal Segregation of Neural Response to Auditory Stimulation: An fMRI Study Using Independent Component Analysis and Frequency-Domain Analysis

Although auditory processing has been widely studied with conventional parametric methods, there have been a limited number of independent component analysis (ICA) applications in this area. The purpose of this study was to examine spatiotemporal behavior of brain networks in response to passive auditory stimulation using ICA. Continuous broadband noise was presented binaurally to 19 subjects with normal hearing. ICA was performed to segregate spatial networks, which were subsequently classified according to their temporal relation to the stimulus using power spectrum analysis. Classification of separated networks resulted in 3 stimulus-activated, 9 stimulus-deactivated, 2 stimulus-neutral (stimulus-dependent but not correlated with the stimulation timing), and 2 stimulus-unrelated (fluctuations that did not follow the stimulus cycles) components. As a result of such classification, spatiotemporal subdivisions were observed in a number of cortical structures, namely auditory, cingulate, and sensorimotor cortices, where parts of the same cortical network responded to the stimulus with different temporal patterns. The majority of the classified networks seemed to comprise subparts of the known resting-state networks (RSNs); however, they displayed different temporal behavior in response to the auditory stimulus, indicating stimulus-dependent temporal segregation of RSNs. Only one of nine deactivated networks coincided with the “classic” default-mode network, suggesting the existence of a stimulus-dependent default-mode network, different from that commonly accepted.

Concurrent bias correction in hemodynamic data assimilation

Low-frequency drift in fMRI datasets can be caused by various sources and are generally not of interest in a conventional task-based fMRI experiment. This feature complicates the assimilation approach that is always under specific assumption on statistics of system uncertainties. In this paper, we present a novel approach to the assimilation of nonlinear hemodynamic system with stochastic biased noise. By treating the drift variation as a random-walk process, the assimilation problem was translated into the identification of a nonlinear system in the presence of time-varying bias. We developed a bias aware unscented Kalman estimator to efficiently handle this problem. In this framework, the estimates of bias-free states and drift are separately carried out in two parallel filters, the optimal estimates of the system states then are corrected from bias-free states with drift estimates. The approach can simultaneously deal with the fMRI responses and drift in an assimilation cycle in an on-line fashion. It makes no assumptions of the structure and statistics of the drift, thereby is particularly suited for fMRI imaging where the formulation of real drift remains difficult to acquire. Experiments with synthetic data and real fMRI data are performed to demonstrate feasibility of our approach and to explore its potential advantages over classic polynomial approach. Moreover, we include the comparison of the variability of observables from the scanner and of normalized signal used in assimilation procedure in Appendix.

A data-driven sparse GLM for fMRI analysis using sparse dictionary learning with MDL criterion

We propose a novel statistical analysis method for functional magnetic resonance imaging (fMRI) to overcome the drawbacks of conventional data-driven methods such as the independent component analysis (ICA). Although ICA has been broadly applied to fMRI due to its capacity to separate spatially or temporally independent components, the assumption of independence has been challenged by recent studies showing that ICA does not guarantee independence of simultaneously occurring distinct activity patterns in the brain. Instead, sparsity of the signal has been shown to be more promising. This coincides with biological findings such as sparse coding in V1 simple cells, electrophysiological experiment results in the human medial temporal lobe, etc. The main contribution of this paper is, therefore, a new data driven fMRI analysis that is derived solely based upon the sparsity of the signals. A compressed sensing based data-driven sparse generalized linear model is proposed that enables estimation of spatially adaptive design matrix as well as sparse signal components that represent synchronous, functionally organized and integrated neural hemodynamics. Furthermore, a minimum description length (MDL)-based model order selection rule is shown to be essential in selecting unknown sparsity level for sparse dictionary learning. Using simulation and real fMRI experiments, we show that the proposed method can adapt individual variation better compared to the conventional ICA methods.

Likelihood-based hypothesis tests for brain activation detection from MRI data disturbed by colored noise: a simulation study

Functional magnetic resonance imaging (fMRI) data that are corrupted by temporally colored noise are generally preprocessed (i.e., prewhitened or precolored) prior to functional activation detection. In this paper, we propose likelihood-based hypothesis tests that account for colored noise directly within the framework of functional activation detection. Three likelihood-based tests are proposed: the generalized likelihood ratio (GLR) test, the Wald test, and the Rao test. The fMRI time series is modeled as a linear regression model, where one regressor describes the task-related hemodynamic response, one regressor accounts for a constant baseline and one regressor describes potential drift. The temporal correlation structure of the noise is modeled as an autoregressive (AR) model. The order of the AR model is determined from practical null data sets using Akaike's information criterion (with penalty factor 3) as order selection criterion. The tests proposed are based on exact expressions for the likelihood function of the data. Using Monte Carlo simulation experiments, the performance of the proposed tests is evaluated in terms of detection rate and false alarm rate properties and compared to the current general linear model (GLM) test, which estimates the coloring of the noise in a separate step. Results show that theoretical asymptotic distributions of the GLM, GLR, and Wald test statistics cannot be reliably used for computing thresholds for activation detection from finite length time series. Furthermore, it is shown that, for a fixed false alarm rate, the detection rate of the proposed GLR test statistic is slightly, but (statistically) significantly improved compared to that of the common GLM-based tests. Finally, simulations results reveal that all tests considered show seriously inferior performance if the order of the AR model is not chosen sufficiently high to give an adequate description of the correlation structure of the noise, whereas the effects of (slightly) overmodeling are observed to be less harmful.

Lesion detection in dynamic FDG-PET using matched subspace detection

We describe a matched subspace detection algorithm to assist in the detection of small tumors in dynamic positron emission tomography (PET) images. The algorithm is designed to differentiate tumors from background using the time activity curves (TACs) that characterize the uptake of PET tracers. TACs are modeled using linear subspaces with additive Gaussian noise. Using TACs from a primary tumor region of interest (ROI) and one or more background ROIs, each identified by a human observer, two linear subspaces are identified. Applying a matched subspace detector to these identified subspaces on a voxel-by-voxel basis throughout the dynamic image produces a test statistic at each voxel which on thresholding indicates potential locations of secondary or metastatic tumors. The detector is derived for three cases: using a single TAC with white noise of unknown variance, using a single TAC with known noise covariance, and detection using multiple TACs within a small ROI with known noise covariance. The noise covariance is estimated for the reconstructed image from the observed sinogram data. To evaluate the proposed method, a simulation-based receiver operating characteristic (ROC) study for dynamic PET tumor detection is designed. The detector uses a dynamic sequence of frame-by-frame 2-D reconstructions as input. We compare the performance of the subspace detectors with that of a Hotelling observer applied to a single frame image and of the Patlak method applied to the dynamic data. We also show examples of the application of each detection approach to clinical PET data from a breast cancer patient with metastatic disease.

Activation detection in diffuse optical imaging by means of the general linear model

Due to its non-invasive nature and low cost, diffuse optical imaging (DOI) is becoming a commonly used technique to assess functional activation in the brain. When imaging with DOI, two major issues arise in the data analysis: (i) the separation of noise of physiological origin and the recovery of the functional response; (ii) the tomographic image reconstruction problem. This paper focuses on the first issue. Although the general linear model (GLM) has been extensively used in functional magnetic resonance imaging (fMRI), DOI has mostly relied on filtering and averaging of raw data to recover brain functional activation. This is mainly due to the high temporal resolution of DOI which implies a new design of the drift basis modelling physiology. In this paper, we provide (i) a filtering method based on cosine functions that is more adapted than standard averaging techniques for DOI specifically; (ii) a new mode-locking technique to recover small signals and locate them temporally with high precision (shift method). Results on real data show the capability of the shift method to retrieve HbR and HbO(2) peak locations.

Using voxel-specific hemodynamic response function in EEG-fMRI data analysis: An estimation and detection model

Research groups who study epileptic spikes with simultaneous EEG-fMRI have used mostly the general linear model (GLM). A shortcoming of the GLM is that the specification of a simple hemodynamic response function (HRF) may lead to biased results. Other methods, which predict the hemodynamic response from the measured data, have been termed "recognition models". The merit of recognition models lies in the power of estimating the region-specific or voxel-specific HRF. We propose an approach that merges these two models in a general framework: estimate the HRF on the training data sets, and applying the estimated HRF on the other part of the data sets. The merit of this framework is that it can utilize the advantages of both models. A comparison of performance is made between the GLM with three fixed HRFs and the new model with voxel-specific HRFs. The main results are as follows: (1) in 18 of the 21 patients, the new model has a higher adjusted coefficient of multiple determination than the GLM with fixed HRF; (2) in some subjects, with the new model, we found areas of activation that had not been detected with the three fixed HRFs at our threshold of significance. The results suggest that the new model can do better than the fixed HRF GLM for the analysis of epileptic activity with EEG-fMRI.

Implications of the Rician distribution for fMRI generalized likelihood ratio tests

In functional magnetic resonance imaging (fMRI), the general linear model test (GLMT) is widely used for brain activation detection. However, the GLMT relies on the assumption that the noise corrupting the data is Gaussian distributed. Because the majority of fMRI studies employ magnitude image reconstructions, which are Rician distributed, this assumption is invalid and has significant consequences in case the signal-to-noise ratio (SNR) is low. In this study, we show that the GLMT should not be used at low SNR. Furthermore, we propose a generalized likelihood ratio test for magnitude MR data that has the same performance compared to the GLMT for high SNR, but performs significantly better than the GLMT for low SNR.

Adaptive Denoising of Event-Related Functional Magnetic Resonance Imaging Data Using Spectral Subtraction

A new adaptive signal-preserving technique for noise suppression in event-related functional magnetic resonance imaging (fMRI) data is proposed based on spectral subtraction. The proposed technique estimates a parametric model for the power spectrum of random noise from the acquired data based on the characteristics of the Rician statistical model. This model is subsequently used to estimate a noise-suppressed power spectrum for any given pixel time course by simple subtraction of power spectra. The new technique is tested using computer simulations and real data from event-related fMRI experiments. The results show the potential of the new technique in suppressing noise while preserving the other deterministic components in the signal. Moreover, we demonstrate that further analysis using principal component analysis and independent component analysis shows a significant improvement in both convergence and clarity of results when the new technique is used. Given its simple form, the new method does not change the statistical characteristics of the signal or cause correlated noise to be present in the processed signal. This suggests the value of the new technique as a useful preprocessing step for fMRI data analysis.

Model-independent method for fMRI analysis

This paper presents a fast method for delineation of activated areas of the brain from functional magnetic resonance imaging (fMRI) time series data. The steps of the work accomplished are as follows. 1) It is shown that the detection performance evaluated by the area under the receiver operating characteristic curve is directly related to the signal-to-noise ratio (SNR) of the composite image generated in the detection process. 2) Detection and segmentation of activated areas are formulated in a vector space framework. In this formulation, a linear transformation (image combination method) is shown to be desirable to maximize the SNR of the activated areas subject to the constraint of removing inactive areas. 3) An analytical solution for the problem is found. 4) Image pixel vectors and expected time series pattern (signature) for inactive pixels are used to calculate weighting vector and identify activated regions. 5) Signatures of the activated regions are used to segment different activities. 6) Segmented images by the proposed method are compared with those generated by the conventional methods (correlation, t-statistic, and z statistic). Detection performance and SNRs of the images are compared. The proposed approach outperforms the conventional methods of fMRI analysis. In addition, it is model-independent and does not require a priori knowledge of the fMRI response to the paradigm. Since the method is linear and most of the work is done analytically, numerical implementation and execution of the method are much faster than the conventional methods.

Model assessment and model building in fMRI

Model quality is rarely assessed in fMRI data analyses and less often reported. This may have contributed to several shortcomings in the current fMRI data analyses, including: (1) Model mis-specification, leading to incorrect inference about the activation-maps, SPM[t] and SPM[F]; (2) Improper model selection based on the number of activated voxels, rather than on model quality; (3) Under-utilization of systematic model building, resulting in the common but suboptimal practice of using only a single, pre-specified, usually over-simplified model; (4) Spatially homogenous modeling, neglecting the spatial heterogeneity of fMRI signal fluctuations; and (5) Lack of standards for formal model comparison, contributing to the high variability of fMRI results across studies and centers. To overcome these shortcomings, it is essential to assess and report the quality of the models used in the analysis. In this study, we applied images of the Durbin-Watson statistic (DW-map) and the coefficient of multiple determination (R(2)-map) as complementary tools to assess the validity as well as goodness of fit, i.e., quality, of models in fMRI data analysis. Higher quality models were built upon reduced models using classic model building. While inclusion of an appropriate variable in the model improved the quality of the model, inclusion of an inappropriate variable, i.e., model mis-specification, adversely affected it. Higher quality models, however, occasionally decreased the number of activated voxels, whereas lower quality or inappropriate models occasionally increased the number of activated voxels, indicating that the conventional approach to fMRI data analysis may yield sub-optimal or incorrect results. We propose that model quality maps become part of a broader package of maps for quality assessment in fMRI, facilitating validation, optimization, and standardization of fMRI result across studies and centers. Hum. Brain Mapping 20:227-238, 2003.

Detection and quantification of a wide range of fMRI temporal responses using a physiologically-motivated basis set

The temporal dynamics of fMRI responses can span a broad range, indicating a rich underlying physiology, but also posing a significant challenge for detection. For instance, in human auditory cortex, prolonged sound stimuli ( approximately 30 sec) can evoke responses ranging from sustained to highly phasic (i.e., characterized by prominent peaks just after sound onset and offset). In the present study, we developed a method capable of detecting a wide variety of responses, while simultaneously extracting information about individual response components, which may have different neurophysiological underpinnings. Specifically, we implemented the general linear model using a novel set of basis functions chosen to reflect temporal features of cortical fMRI responses. This physiologically-motivated basis set (the "OSORU" basis set) was tested against (1) the commonly employed "sustained-only" basis "set" (i.e., a single smoothed "boxcar" function), and (2) a sinusoidal basis set, which is capable of detecting a broad range of responses, but lacks a direct relationship to individual response components. On data that included many different temporal responses, the OSORU basis set performed far better overall than the sustained-only set, and as well or better than the sinusoidal basis set. The OSORU basis set also proved effective in exploring brain physiology. As an example, we demonstrate that the OSORU basis functions can be used to spatially map the relative amount of transient vs. sustained activity within auditory cortex. The OSORU basis set provides a powerful means for response detection and quantification that should be broadly applicable to any brain system and to both human and non-human species.

Clustered components analysis for functional MRI

A common method of increasing hemodynamic response (SNR) in functional magnetic resonance imaging (fMRI) is to average signal timecourses across voxels. This technique is potentially problematic because the hemodynamic response may vary across the brain. Such averaging may destroy significant features in the temporal evolution of the fMRI response that stem from either differences in vascular coupling to neural tissue or actual differences in the neural response between two averaged voxels. Two novel techniques are presented in this paper in order to aid in an improved SNR estimate of the hemodynamic response while preserving statistically significant voxel-wise differences. The first technique is signal subspace estimation for periodic stimulus paradigms that involves a simple thresholding method. This increases SNR via dimensionality reduction. The second technique that we call clustered components analysis is a novel amplitude-independent clustering method based upon an explicit statistical data model. It includes an unsupervised method for estimating the number of clusters. Our methods are applied to simulated data for verification and comparison to other techniques. A human experiment was also designed to stimulate different functional cortices. Our methods separated hemodynamic response signals into clusters that tended to be classified according to tissue characteristics.

Activation detection in fMRI using a maximum energy ratio statistic obtained by adaptive spatial filtering

An adaptive spatial filtering method is proposed that takes into account contextual information in fMRI activation detection. This filter replaces the time series of each voxel with a weighted average of time series of a small neighborhood around it. The filter coefficients at each voxel are derived so as to maximize a test statistic designed to indicate the presence of activation. This statistic is the ratio of the energy of the filtered time series in a signal subspace to the energy of the residuals. It is shown that the filter coefficients and the maximum energy ratio can be found through a generalized eigenproblem. This approach equates the filter coefficients to the elements of an eigenvector corresponding to the largest eigenvalue of a specific matrix, while the largest eigenvalue itself becomes the maximum energy ratio that can be used as a statistic for detecting activation. The distribution of this statistic under the null hypothesis is derived by a nonparametric permutation technique in the wavelet domain. Also, in this paper we introduce a new set of basis vectors that define the signal subspace. The space spanned by these basis vectors covers a wide range of possible hemodynamic response functions (HRF) and is applicable to both event related and block design fMRI signal analysis. This approach circumvents the need for a priori assumptions about the exact shape of the HRF. Resting-state experimental fMRI data were used to assess the specificity of the method, showing that the actual false-alarm rate of the proposed method is equal or less than its expected value. Analysis of simulated data and motor task fMRI datasets from six volunteers using the method proposed here showed an improved sensitivity as compared to a conventional test with a similar statistic applied to spatially smoothed data.

Multiresolution fMRI activation detection using translation invariant wavelet transform and statistical analysis based on resampling

A new method is proposed for activation detection in event-related functional magnetic resonance imaging (fMRI). The method is based on the analysis of selected resolution levels (a subspace) in translation invariant wavelet transform (TIWT) domain. Using a priori knowledge about the activation signal and trends, we analyze their power in different resolution levels in TIWT domain and select an optimal set of resolution levels. A randomization-based statistical test is then applied in the wavelet domain for activation detection. This approach suppresses the effects of trends and enhances the detection sensitivity. In addition, since TIWT is insensitive to signal translations, the power analysis is robust with respect to signal shifts. The randomization test alleviates the need for assumptions about fMRI noise. The method has been applied to simulated and experimental fMRI datasets. Comparisons have been made between the results of the proposed method, a similar method in the time domain and the cross-correlation method. The proposed method has shown superior sensitivity compared to the other methods.

Functional MRI activity characterization using response time shift estimates from curve evolution

Characterizing the response of the brain to a stimulus based on functional magnetic resonance imaging data is a major challenge due to the fact that the response time delay of the brain may be different from one stimulus phase to the next and from pixel to pixel. To enhance detectability, this work introduces the use of a curve evolution approach that provides separate estimates of the response time shifts at each phase of the stimulus on a pixel-by-pixel basis. The approach relies on a parsimonious but simple model that is nonlinear in the time shifts of the response relative to the stimulus and linear in the gains. To effectively use the response time shift estimates in a subspace detection framework, we implement a robust hypothesis test based on a Laplacian noise model. The algorithm provides a pixel-by-pixel functional characterization of the brain's response. The results based on experimental data show that response time shift estimates, when properly implemented, enhance detectability without sacrificing robustness.

Activation of attention networks using frequency analysis of a simple auditory-motor paradigm

The purpose of this study was to devise a paradigm that stimulates attention using a frequency-based analysis of the data acquired during a motor task. Six adults (30-40 years of age) and one child (10 years) were studied. Each subject was requested to attend to "start" and "stop" commands every 20 s alternatively and had to respond with the motor task every second time. Attention was stimulated during a block-designed, motor paradigm in which a start-stop commands cycle produced activation at the fourth harmonic of the motor frequency. We disentangled the motor and attention functions using statistical analysis with subspaces spanned by vectors generated by a truncated trigonometric series of motor and attention frequency. During our auditory-motor paradigm, all subjects showed activation in areas that belong to an extensive attention network. Attention and motor functions were coactivated but with different frequencies. While the motor-task-related areas were activated with slower frequency than attention, the activation in the attention-related areas was enhanced every time the subject had to start or end the motor task. We suggest that although a simple block-designed, auditory-motor paradigm stimulates the attention network, motor preparation, and motor inhibition concurrently, a frequency-based analysis can distinguish attention from motor functions. Due to its simplicity the paradigm can be valuable in studying children with attention deficit disorders.

A sensor array processing approach to object region detection

This paper presents a new approach for medical image analysis. It translates the object region-detection problem into a sensor array processing framework and detects the number of object regions based on the signal eigenstructure of the converted array system. The theoretical and experimental results obtained by using this approach on various medical images were in good agreement.

Contextual clustering for analysis of functional MRI data

We present a contextual clustering procedure for statistical parametric maps (SPM) calculated from time varying three-dimensional images. The algorithm can be used for the detection of neural activations from functional magnetic resonance images (fMRI). An important characteristic of SPM is that the intensity distribution of background (nonactive area) is known whereas the distributions of activation areas are not. The developed contextual clustering algorithm divides an SPM into background and activation areas so that the probability of detecting false activations by chance is controlled, i.e., hypothesis testing is performed. Unlike the much used voxel-by-voxel testing, neighborhood information is utilized, an important difference. This is achieved by using a Markov random field prior and iterated conditional modes (ICM) algorithm. However, unlike in the conventional use of ICM algorithm, the classification is based only on the distribution of background. The results from our simulations and human fMRI experiments using visual stimulation demonstrate that a better sensitivity is achieved with a given specificity in comparison to the voxel-by-voxel thresholding technique. The algorithm is computationally efficient and can be used to detect and delineate objects from a noisy background in other applications.

Detection of neural activity in functional MRI using canonical correlation analysis

A novel method for detecting neural activity in functional magnetic resonance imaging (fMRI) data is introduced. It is based on canonical correlation analysis (CCA), which is a multivariate extension of the univariate correlation analysis widely used in fMRI. To detect homogeneous regions of activity, the method combines a subspace modeling of the hemodynamic response and the use of spatial relationships. The spatial correlation that undoubtedly exists in fMR images is completely ignored when univariate methods such as as t-tests, F-tests, and ordinary correlation analysis are used. Such methods are for this reason very sensitive to noise, leading to difficulties in detecting activation and significant contributions of false activations. In addition, the proposed CCA method also makes it possible to detect activated brain regions based not only on thresholding a correlation coefficient, but also on physiological parameters such as temporal shape and delay of the hemodynamic response. Excellent performance on real fMRI data is demonstrated. Magn Reson Med 45:323-330, 2001.

Application of Bayesian inference to fMRI data analysis

The methods of Bayesian statistics are applied to the analysis of fMRI data. Three specific models are examined. The first is the familiar linear model with white Gaussian noise. In this section, the Jeffreys' Rule for noninformative prior distributions is stated and it is shown how the posterior distribution may be used to infer activation in individual pixels. Next, linear time-invariant (LTI) systems are introduced as an example of statistical models with nonlinear parameters. It is shown that the Bayesian approach can lead to quite complex bimodal distributions of the parameters when the specific case of a delta function response with a spatially varying delay is analyzed. Finally, a linear model with auto-regressive noise is discussed as an alternative to that with uncorrelated white Gaussian noise. The analysis isolates those pixels that have significant temporal correlation under the model. It is shown that the number of pixels that have a significantly large auto-regression parameter is dependent on the terms used to account for confounding effects.