Total variation regularization for fMRI-based prediction of behavior

How Not to Make the Joint Extended Kalman Filter Fail with Unstructured Mechanistic Models

The unstructured mechanistic model (UMM) allows for modeling the macro-scale of a phenomenon without known mechanisms. This is extremely useful in biomanufacturing because using the UMM for the joint estimation of states and parameters with an extended Kalman filter (JEKF) can enable the real-time monitoring of bioprocesses with unknown mechanisms. However, the UMM commonly used in biomanufacturing contains ordinary differential equations (ODEs) with unshared parameters, weak variables, and weak terms. When such a UMM is coupled with an initial state error covariance matrix P(t=0) and a process error covariance matrix Q with uncorrelated elements, along with just one measured state variable, the joint extended Kalman filter (JEKF) fails to estimate the unshared parameters and state simultaneously. This is because the Kalman gain corresponding to the unshared parameter remains constant and equal to zero. In this work, we formally describe this failure case, present the proof of JEKF failure, and propose an approach called SANTO to side-step this failure case. The SANTO approach consists of adding a quantity to the state error covariance between the measured state variable and unshared parameter in the initial P(t = 0) of the matrix Ricatti differential equation to compute the predicted error covariance matrix of the state and prevent the Kalman gain from being zero. Our empirical evaluations using synthetic and real datasets reveal significant improvements: SANTO achieved a reduction in root-mean-square percentage error (RMSPE) of up to approximately 17% compared to the classical JEKF, indicating a substantial enhancement in estimation accuracy.

Groupwise structural sparsity for discriminative voxels identification

This paper investigates the selection of voxels for functional Magnetic Resonance Imaging (fMRI) brain data. We aim to identify a comprehensive set of discriminative voxels associated with human learning when exposed to a neutral visual stimulus that predicts an aversive outcome. However, due to the nature of the unconditioned stimuli (typically a noxious stimulus), it is challenging to obtain sufficient sample sizes for psychological experiments, given the tolerability of the subjects and ethical considerations. We propose a stable hierarchical voting (SHV) mechanism based on stability selection to address this challenge. This mechanism enables us to evaluate the quality of spatial random sampling and minimizes the risk of false and missed detections. We assess the performance of the proposed algorithm using simulated and publicly available datasets. The experiments demonstrate that the regularization strategy choice significantly affects the results' interpretability. When applying our algorithm to our collected fMRI dataset, it successfully identifies sparse and closely related patterns across subjects and displays stable weight maps for three experimental phases under the fear conditioning paradigm. These findings strongly support the causal role of aversive conditioning in altering visual-cortical activity.

Benchmarking explanation methods for mental state decoding with deep learning models

Deep learning (DL) models find increasing application in mental state decoding, where researchers seek to understand the mapping between mental states (e.g., experiencing anger or joy) and brain activity by identifying those spatial and temporal features of brain activity that allow to accurately identify (i.e., decode) these states. Once a DL model has been trained to accurately decode a set of mental states, neuroimaging researchers often make use of methods from explainable artificial intelligence research to understand the model's learned mappings between mental states and brain activity. Here, we benchmark prominent explanation methods in a mental state decoding analysis of multiple functional Magnetic Resonance Imaging (fMRI) datasets. Our findings demonstrate a gradient between two key characteristics of an explanation in mental state decoding, namely, its faithfulness and its alignment with other empirical evidence on the mapping between brain activity and decoded mental state: explanation methods with high explanation faithfulness, which capture the model's decision process well, generally provide explanations that align less well with other empirical evidence than the explanations of methods with less faithfulness. Based on our findings, we provide guidance for neuroimaging researchers on how to choose an explanation method to gain insight into the mental state decoding decisions of DL models.

SPITFIR(e): a supermaneuverable algorithm for fast denoising and deconvolution of 3D fluorescence microscopy images and videos

Modern fluorescent microscopy imaging is still limited by the optical aberrations and the photon budget available in the specimen. A direct consequence is the necessity to develop flexible and "off-road" algorithms in order to recover structural details and improve spatial resolution, which is critical when restraining the illumination to low levels in order to limit photo-damages. Here, we report SPITFIR(e) a flexible method designed to accurately and quickly restore 2D-3D fluorescence microscopy images and videos (4D images). We designed a generic sparse-promoting regularizer to subtract undesirable out-of-focus background and we developed a primal-dual algorithm for fast optimization. SPITFIR(e) is a "swiss-knife" method for practitioners as it adapts to any microscopy techniques, to various sources of signal degradation (noise, blur), to variable image contents, as well as to low signal-to-noise ratios. Our method outperforms existing state-of-the-art algorithms, and is more flexible than supervised deep-learning methods requiring ground truth datasets. The performance, the flexibility, and the ability to push the spatiotemporal resolution limit of sub-diffracted fluorescence microscopy techniques are demonstrated on experimental datasets acquired with various microscopy techniques from 3D spinning-disk confocal up to lattice light sheet microscopy.

Inferring the Genetic Influences on Psychological Traits Using MRI Connectivity Predictive Models: Demonstration with Cognition

Introduction

Genetic correlations between brain and behavioral phenotypes in analyses from major genetic consortia have been weak and mostly nonsignificant. fMRI models of systems-level brain patterns may help improve our ability to link genes, brains, and behavior by identifying reliable and reproducible endophenotypes. Work using connectivity-based predictive modeling has generated brain-based proxies of behavioral and neuropsychological variables. If such models capture activity in inherited brain systems, they may offer a more powerful link between genes and behavior.

Method

As a proof of concept, we develop models predicting intelligence (IQ) based on fMRI connectivity and test their effectiveness as endophenotypes. We link brain and IQ in a model development dataset of N = 3,000 individuals and test the genetic correlations between brain models and measured IQ in a genetic validation sample of N = 13,092 individuals from the UK Biobank. We compare an additive connectivity-based model to multivariate LASSO and ridge models phenotypically and genetically. We also compare these approaches to single "candidate" brain areas.

Results

We found that predictive brain models were significantly phenotypically correlated with IQ and showed much stronger correlations than individual edges. Further, brain models were more heritable (h2 = 0.155-0.181) than single brain regions (h2 = 0.038-0.118) and captured about half of the genetic variance in IQ (rG = 0.422-0.576), while rGs with single brain measures were smaller and nonsignificant. For the different approaches, LASSO and ridge were similarly predictive, with slightly weaker performance of the additive model. LASSO model weights were highly theoretically interpretable and replicated known brain IQ associations. Finally, functional connectivity models trained in midlife showed genetic correlations with early life correlates of IQ, suggesting some stability in the prediction of fMRI models.

Conclusion

Multisystem predictive models hold promise as imaging endophenotypes that offer complex and theoretically relevant conclusions for future imaging genetics research.

Brain Regions Identified as Being Associated with Verbal Reasoning through the Use of Imaging Regression via Internal Variation

Brain-imaging data have been increasingly used to understand intellectual disabilities. Despite significant progress in biomedical research, the mechanisms for most of the intellectual disabilities remain unknown. Finding the underlying neurological mechanisms has been proved difficult, especially in children due to the rapid development of their brains. We investigate verbal reasoning, which is a reliable measure of individuals' general intellectual abilities, and develop a class of high-order imaging regression models to identify brain subregions which might be associated with this specific intellectual ability. A key novelty of our method is to take advantage of spatial brain structures, and specifically the piecewise smooth nature of most imaging coefficients in the form of high-order tensors. Our approach provides an effective and urgently needed method for identifying brain subregions potentially underlying certain intellectual disabilities. The idea behind our approach is a carefully constructed concept called Internal Variation (IV). The IV employs tensor decomposition and provides a computationally feasible substitution for Total Variation (TV), which has been considered in the literature to deal with similar problems but is problematic in high order tensor regression. Before applying our method to analyze the real data, we conduct comprehensive simulation studies to demonstrate the validity of our method in imaging signal identification. Then, we present our results from the analysis of a dataset based on the Philadelphia Neurodevelopmental Cohort for which we preprocessed the data including re-orienting, bias-field correcting, extracting, normalizing and registering the magnetic resonance images from 978 individuals. Our analysis identified a subregion across the cingulate cortex and the corpus callosum as being associated with individuals' verbal reasoning ability, which, to the best of our knowledge, is a novel region that has not been reported in the literature. This finding is useful in further investigation of functional mechansims for verbal reasoning.

Surface Estimation via Analysis Method: A Constrained Inverse Problem Approach

Ultrasonic imaging is a common technique in nondestructive evaluation, as it presents advantages such as low cost and safety of operation. In many industries, the interior inspection of objects with complex geometry has become a necessity. This kind of inspection requires the transducer to be coupled to the object with the use of some technique, such as immersing the object in water. When doing so, the geometry of the object surface must be known a priori or estimated. Recent methods for surface estimation start with an image of the interface between water and the specimen. Then, the surface is estimated by processing the image using different strategies. In this article, the strategy to extract the surface profile is based on an analysis-based inverse problem, hence named surface estimation via analysis method (SEAM). The problem formulation aims to reduce the noise in the estimate and also, by including priors, reach more accurate estimates. By using a second-order total variation regularization, which favors piecewise linear functions, the proposed method can describe a great range of surface profiles. Experiments were performed to evaluate the proposed method on surface profile estimation and results show good agreement with references and lower errors than methods in the literature. In addition, the estimated profiles enhance the imaging of the interior of objects, allowing better visualization of internal defects.

Correlation Guided Graph Learning to Estimate Functional Connectivity Patterns From fMRI Data

OBJECTIVE

Recently, functional magnetic resonance imaging (fMRI)-derived brain functional connectivity (FC) patterns have been used as fingerprints to predict individual differences in phenotypic measures, and cognitive dysfunction associated with brain diseases. In these applications, how to accurately estimate FC patterns is crucial yet technically challenging.

METHODS

In this article, we propose a correlation guided graph learning (CGGL) method to estimate FC patterns for establishing brain-behavior relationships. Different from the existing graph learning methods which only consider the graph structure across brain regions-of-interest (ROIs), our proposed CGGL takes into account both the temporal correlation of ROIs across time points, and the graph structure across ROIs. The resulting FC patterns reflect substantial inter-individual variations related to the behavioral measure of interest.

RESULTS

We validate the effectiveness of our proposed CGGL on the Philadelphia Neurodevelopmental Cohort data for separately predicting three behavioral measures based on resting-state fMRI. Experimental results demonstrate that the proposed CGGL outperforms other competing FC pattern estimation methods.

CONCLUSION

Our method increases the predictive power of the constructed FC patterns when establishing brain-behavior relationships, and gains meaningful insights into relevant biological mechanisms.

SIGNIFICANCE

The proposed CGGL offers a more powerful, and reliable method to estimate FC patterns, which can be used as fingerprints in many brain network studies.

Stable Anatomy Detection in Multimodal Imaging Through Sparse Group Regularization: A Comparative Study of Iron Accumulation in the Aging Brain

Multimodal neuroimaging provides a rich source of data for identifying brain regions associated with disease progression and aging. However, present studies still typically analyze modalities separately or aggregate voxel-wise measurements and analyses to the structural level, thus reducing statistical power. As a central example, previous works have used two quantitative MRI parameters-R2* and quantitative susceptibility (QS)-to study changes in iron associated with aging in healthy and multiple sclerosis subjects, but failed to simultaneously account for both. In this article, we propose a unified framework that combines information from multiple imaging modalities and regularizes estimates for increased interpretability, generalizability, and stability. Our work focuses on joint region detection problems where overlap between effect supports across modalities is encouraged but not strictly enforced. To achieve this, we combine L ₁ (lasso), total variation (TV), and L ₂ group lasso penalties. While the TV penalty encourages geometric regularization by controlling estimate variability and support boundary geometry, the group lasso penalty accounts for similarities in the support between imaging modalities. We address the computational difficulty in this regularization scheme with an alternating direction method of multipliers (ADMM) optimizer. In a neuroimaging application, we compare our method against independent sparse and joint sparse models using a dataset of R2* and QS maps derived from MRI scans of 113 healthy controls: our method produces clinically-interpretable regions where specific iron changes are associated with healthy aging. Together with results across multiple simulation studies, we conclude that our approach identifies regions that are more strongly associated with the variable of interest (e.g., age), more accurate, and more stable with respect to training data variability. This work makes progress toward a stable and interpretable multimodal imaging analysis framework for studying disease-related changes in brain structure and can be extended for classification and disease prediction tasks.

Incorporating structured assumptions with probabilistic graphical models in fMRI data analysis

With the wide adoption of functional magnetic resonance imaging (fMRI) by cognitive neuroscience researchers, large volumes of brain imaging data have been accumulated in recent years. Aggregating these data to derive scientific insights often faces the challenge that fMRI data are high-dimensional, heterogeneous across people, and noisy. These challenges demand the development of computational tools that are tailored both for the neuroscience questions and for the properties of the data. We review a few recently developed algorithms in various domains of fMRI research: fMRI in naturalistic tasks, analyzing full-brain functional connectivity, pattern classification, inferring representational similarity and modeling structured residuals. These algorithms all tackle the challenges in fMRI similarly: they start by making clear statements of assumptions about neural data and existing domain knowledge, incorporate those assumptions and domain knowledge into probabilistic graphical models, and use those models to estimate properties of interest or latent structures in the data. Such approaches can avoid erroneous findings, reduce the impact of noise, better utilize known properties of the data, and better aggregate data across groups of subjects. With these successful cases, we advocate wider adoption of explicit model construction in cognitive neuroscience. Although we focus on fMRI, the principle illustrated here is generally applicable to brain data of other modalities.

Regularized Bagged Canonical Component Analysis for Multiclass Learning in Brain Imaging

A fundamental problem of supervised learning algorithms for brain imaging applications is that the number of features far exceeds the number of subjects. In this paper, we propose a combined feature selection and extraction approach for multiclass problems. This method starts with a bagging procedure which calculates the sign consistency of the multivariate analysis (MVA) projection matrix feature-wise to determine the relevance of each feature. This relevance measure provides a parsimonious matrix, which is combined with a hypothesis test to automatically determine the number of selected features. Then, a novel MVA regularized with the sign and magnitude consistency of the features is used to generate a reduced set of summary components providing a compact data description. We evaluated the proposed method with two multiclass brain imaging problems: 1) the classification of the elderly subjects in four classes (cognitively normal, stable mild cognitive impairment (MCI), MCI converting to AD in 3 years, and Alzheimer's disease) based on structural brain imaging data from the ADNI cohort; 2) the classification of children in 3 classes (typically developing, and 2 types of Attention Deficit/Hyperactivity Disorder (ADHD)) based on functional connectivity. Experimental results confirmed that each brain image (defined by 29.852 features in the ADNI database and 61.425 in the ADHD) could be represented with only 30 - 45% of the original features. Furthermore, this information could be redefined into two or three summary components, providing not only a gain of interpretability but also classification rate improvements when compared to state-of-art reference methods.

Sign-Consistency Based Variable Importance for Machine Learning in Brain Imaging

An important problem that hinders the use of supervised classification algorithms for brain imaging is that the number of variables per single subject far exceeds the number of training subjects available. Deriving multivariate measures of variable importance becomes a challenge in such scenarios. This paper proposes a new measure of variable importance termed sign-consistency bagging (SCB). The SCB captures variable importance by analyzing the sign consistency of the corresponding weights in an ensemble of linear support vector machine (SVM) classifiers. Further, the SCB variable importances are enhanced by means of transductive conformal analysis. This extra step is important when the data can be assumed to be heterogeneous. Finally, the proposal of these SCB variable importance measures is completed with the derivation of a parametric hypothesis test of variable importance. The new importance measures were compared with a t-test based univariate and an SVM-based multivariate variable importances using anatomical and functional magnetic resonance imaging data. The obtained results demonstrated that the new SCB based importance measures were superior to the compared methods in terms of reproducibility and classification accuracy.

Analyzing Neuroimaging Data Through Recurrent Deep Learning Models

The application of deep learning (DL) models to neuroimaging data poses several challenges, due to the high dimensionality, low sample size, and complex temporo-spatial dependency structure of these data. Even further, DL models often act as black boxes, impeding insight into the association of cognitive state and brain activity. To approach these challenges, we introduce the DeepLight framework, which utilizes long short-term memory (LSTM) based DL models to analyze whole-brain functional Magnetic Resonance Imaging (fMRI) data. To decode a cognitive state (e.g., seeing the image of a house), DeepLight separates an fMRI volume into a sequence of axial brain slices, which is then sequentially processed by an LSTM. To maintain interpretability, DeepLight adapts the layer-wise relevance propagation (LRP) technique. Thereby, decomposing its decoding decision into the contributions of the single input voxels to this decision. Importantly, the decomposition is performed on the level of single fMRI volumes, enabling DeepLight to study the associations between cognitive state and brain activity on several levels of data granularity, from the level of the group down to the level of single time points. To demonstrate the versatility of DeepLight, we apply it to a large fMRI dataset of the Human Connectome Project. We show that DeepLight outperforms conventional approaches of uni- and multivariate fMRI analysis in decoding the cognitive states and in identifying the physiologically appropriate brain regions associated with these states. We further demonstrate DeepLight's ability to study the fine-grained temporo-spatial variability of brain activity over sequences of single fMRI samples.

Interindividual Covariations of Brain Functional and Structural Connectivities Are Decomposed Blindly to Subnetworks: A Fusion-Based Approach

BACKGROUND

Studying brain interindividual variations has recently gained interest to understand different human behaviors. It is particularly important to investigate how a variety of functional differences can be associated with a few differences in brain structure. It would be more meaningful if such an investigation is performed jointly at the network level to connect structural building blocks to functional variations modules.

PURPOSE

To decompose the interindividual variations of brain in the form of mutual functional and structural subnetworks based on a data-driven approach.

STUDY TYPE

Retrospective.

POPULATION

In all, 92 healthy subjects.

FIELD STRENGTH/SEQUENCE

3T Siemens/MPRAGE, diffusion spectrum imaging (DSI) acquisition protocol, gradient echo sequence.

ASSESSMENT

The proposed approach was quantitatively assessed by examining the consistency of the networks against the number of subjects. Distribution of the obtained components across brain regions was studied and their relevance was qualitatively evaluated by comparison to variations that had been independently reported previously.

STATISTICAL TESTS

Permutation test, two-sample t-test, Pearson correlation coefficient.

RESULTS

Ten pairs of components including functional and structural subnetworks were obtained. Assessing the reproducibility of the proposed method with respect to the sample size indicated reliable detection of connections (above 70%) for all components by reducing the number of subjects to 70. Specifically, one of the functional subnetworks can be used to distinguish left-handed from right-handed people (P = 2.6 × 10^-8 ) as the basic interindividual variation. This functional subnetwork has a main overlap (40.18%) with the somatomotor system and the Broca part was captured in its corresponding structural subnetwork.

DATA CONCLUSION

These results show that the proposed method can reveal intersubject variations systematically through a mathematical algorithm of joint independent component analysis. They confirm that intersubject variations can be expressed in the form of building blocks. In contrast to the functional subnetworks that were discoverable independently, their structural counterparts were found and interpreted only in conjunction with the functional subnetworks.

LEVEL OF EVIDENCE

3 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2020;51:1779-1788.

Computational and Informatic Advances for Reproducible Data Analysis in Neuroimaging

The reproducibility of scientific research has become a point of critical concern. We argue that openness and transparency are critical for reproducibility, and we outline an ecosystem for open and transparent science that has emerged within the human neuroimaging community. We discuss the range of open data-sharing resources that have been developed for neuroimaging data, as well as the role of data standards (particularly the brain imaging data structure) in enabling the automated sharing, processing, and reuse of large neuroimaging data sets. We outline how the open source Python language has provided the basis for a data science platform that enables reproducible data analysis and visualization. We also discuss how new advances in software engineering, such as containerization, provide the basis for greater reproducibility in data analysis. The emergence of this new ecosystem provides an example for many areas of science that are currently struggling with reproducibility.

Spatially regularized estimation of the tissue homogeneity model parameters in DCE-MRI using proximal minimization

PURPOSE

The Tofts and the extended Tofts models are the pharmacokinetic models commonly used in dynamic contrast-enhanced MRI (DCE-MRI) perfusion analysis, although they do not provide two important biological markers, namely, the plasma flow and the permeability-surface area product. Estimates of such markers are possible using advanced pharmacokinetic models describing the vascular distribution phase, such as the tissue homogeneity model. However, the disadvantage of the advanced models lies in biased and uncertain estimates, especially when the estimates are computed voxelwise. The goal of this work is to improve the reliability of the estimates by including information from neighboring voxels.

THEORY AND METHODS

Information from the neighboring voxels is incorporated in the estimation process through spatial regularization in the form of total variation. The spatial regularization is applied on five maps of perfusion parameters estimated using the tissue homogeneity model. Since the total variation is not differentiable, two proximal techniques of convex optimization are used to solve the problem numerically.

RESULTS

The proposed algorithm helps to reduce noise in the estimated perfusion-parameter maps together with improving accuracy of the estimates. These conclusions are proved using a numerical phantom. In addition, experiments on real data show improved spatial consistency and readability of perfusion maps without considerable lowering of the quality of fit.

CONCLUSION

The reliability of the DCE-MRI perfusion analysis using the tissue homogeneity model can be improved by employing spatial regularization. The proposed utilization of modern optimization techniques implies only slightly higher computational costs compared to the standard approach without spatial regularization.

Spatially Regularized Shape Analysis of the Hippocampus Using P-Spline Based Shape Regression

Shape analysis is increasingly becoming important to study changes in brain structures in relation to clinical neurological outcomes. This is a challenging task due to the high dimensionality of shape representations and the often limited number of available shapes. Current techniques counter the poor ratio between dimensions and sample size by using regularization in shape space, but do not take into account the spatial relations within the shapes. This can lead to models that are biologically implausible and difficult to interpret. We propose to use P-spline based regression, which combines a generalized linear model (GLM) with the coefficients described as B-splines and a penalty term that constrains the regression coefficients to be spatially smooth. Owing to the GLM, this method can naturally predict both continuous and discrete outcomes and can include non-spatial covariates without penalization. We evaluated our method on hippocampus shapes extracted from magnetic resonance (MR) images of 510 non-demented, elderly people. We related the hippocampal shape to age, memory score, and sex. The proposed method retained the good performance of current techniques, such as ridge regression, but produced smoother coefficient fields that are easier to interpret.

Incorporating prior information with fused sparse group lasso: Application to prediction of clinical measures from neuroimages

Predicting clinical variables from whole-brain neuroimages is a high-dimensional problem that can potentially benefit from feature selection or extraction. Penalized regression is a popular embedded feature selection method for high-dimensional data. For neuroimaging applications, spatial regularization using the ℓ 1 or ℓ 2 norm of the image gradient has shown good performance, yielding smooth solutions in spatially contiguous brain regions. Enormous resources have been devoted to establishing structural and functional brain connectivity networks that can be used to define spatially distributed yet related groups of voxels. We propose using the fused sparse group lasso (FSGL) penalty to encourage structured, sparse, and interpretable solutions by incorporating prior information about spatial and group structure among voxels. We present optimization steps for FSGL penalized regression using the alternating direction method of multipliers algorithm. With simulation studies and in application to real functional magnetic resonance imaging data from the Autism Brain Imaging Data Exchange, we demonstrate conditions under which fusion and group penalty terms together outperform either of them alone.

Empirical Functional PCA for 3D Image Feature Extraction Through Fractal Sampling

Medical image classification is currently a challenging task that can be used to aid the diagnosis of different brain diseases. Thus, exploratory and discriminative analysis techniques aiming to obtain representative features from the images play a decisive role in the design of effective Computer Aided Diagnosis (CAD) systems, which is especially important in the early diagnosis of dementia. In this work, we present a technique that allows using specific time series analysis techniques with 3D images. This is achieved by sampling the image using a fractal-based method which preserves the spatial relationship among voxels. In addition, a method called Empirical functional PCA (EfPCA) is presented, which combines Empirical Mode Decomposition (EMD) with functional PCA to express an image in the space spanned by a basis of empirical functions, instead of using components computed by a predefined basis as in Fourier or Wavelet analysis. The devised technique has been used to classify images from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) and the Parkinson Progression Markers Initiative (PPMI), achieving accuracies up to 93% and 92% differential diagnosis tasks (AD versus controls and PD versus Controls, respectively). The results obtained validate the method, proving that the information retrieved by our methodology is significantly linked to the diseases.

Traction force microscopy with optimized regularization and automated Bayesian parameter selection for comparing cells

Adherent cells exert traction forces on to their environment which allows them to migrate, to maintain tissue integrity, and to form complex multicellular structures during developmental morphogenesis. Traction force microscopy (TFM) enables the measurement of traction forces on an elastic substrate and thereby provides quantitative information on cellular mechanics in a perturbation-free fashion. In TFM, traction is usually calculated via the solution of a linear system, which is complicated by undersampled input data, acquisition noise, and large condition numbers for some methods. Therefore, standard TFM algorithms either employ data filtering or regularization. However, these approaches require a manual selection of filter- or regularization parameters and consequently exhibit a substantial degree of subjectiveness. This shortcoming is particularly serious when cells in different conditions are to be compared because optimal noise suppression needs to be adapted for every situation, which invariably results in systematic errors. Here, we systematically test the performance of new methods from computer vision and Bayesian inference for solving the inverse problem in TFM. We compare two classical schemes, L1- and L2-regularization, with three previously untested schemes, namely Elastic Net regularization, Proximal Gradient Lasso, and Proximal Gradient Elastic Net. Overall, we find that Elastic Net regularization, which combines L1 and L2 regularization, outperforms all other methods with regard to accuracy of traction reconstruction. Next, we develop two methods, Bayesian L2 regularization and Advanced Bayesian L2 regularization, for automatic, optimal L2 regularization. Using artificial data and experimental data, we show that these methods enable robust reconstruction of traction without requiring a difficult selection of regularization parameters specifically for each data set. Thus, Bayesian methods can mitigate the considerable uncertainty inherent in comparing cellular tractions in different conditions.

Glucose metabolic brain patterns to discriminate amyotrophic lateral sclerosis from Parkinson plus syndromes

Background

¹⁸F-FDG brain PET measures metabolic changes in neurodegenerative disorders and may discriminate between different diseases even at an early stage. The objective of this study was to classify patients with amyotrophic lateral sclerosis (ALS) and Parkinson plus syndromes (PP). To this end, different approaches were evaluated using generalized linear models and corresponding glucose metabolic brain patterns. Besides direct classification, healthy controls were also included to generate disease-specific metabolic brain patterns and to perform a classification using disease expression scores.

Methods

ALS patients (n = 70) and PP patients (n = 33: 20 PSP, 3 CBD, and 10 MSA) were available from an existing database of patients with neuromuscular and movement disorders while age-matched healthy controls (n = 29) were selected from a prospective study. To generate both disease-discriminative (direct classification) and disease-specific (classification versus controls) metabolic brain patterns, data were spatially normalized and a principal component analysis (PCA) was performed prior to classification using either logistic regression (PCA-LR) or a support vector machine (PCA-SVM). Furthermore, a direct SVM approach was considered. To compare the three different approaches, Pearson correlations (r) between pattern expression scores and metabolic brain patterns were evaluated, while pairs of ALS- and PP-specific pattern expression scores were compared using the RV coefficient.

Results

Classification between ALS and PP resulted in a sensitivity and specificity ≥ 0.82 for both direct classification and classification according to disease-specific pattern expression scores. PCA-LR, PCA-SVM, and SVM generated very similar metabolic brain patterns with voxelwise correlations ≥ 0.66, while all patterns allowed straightforward identification of ALS- and PP-specific brain regions of hyper- and hypometabolism. Moreover, pattern expression scores were highly correlated among different classifiers with a mean r of 0.94 while a RV coefficient ≥ 0.91 was found between pairs of ALS- and PP-specific pattern expression scores.

Conclusion

We demonstrated that a classification between ALS and PP using expression scores of an ALS and PP metabolic brain pattern leads to a similar and high prediction accuracy as direct classification between ALS and PP. Classification performance and disease-specific metabolic patterns, which could support visual reading and improve insight in brain pathology, were very related for different classifiers.

Improved Application of Sparse Representation Classifier in fMRI-based Brain State Decoding

Multivariate pattern analysis techniques have been widely applied to decode brain states using functional magnetic resonance imaging (fMRI). Among various multivariate pattern analysis methods, sparse representation classifier (SRC) exhibit state-of-the-art classification performance for image classification. However, SRC has rarely been applied to fMRI-based decoding. This study aimed to investigate the feasibility of SRC in fMRI-based decoding and how to improve the performance of SRC. In this study, two SRC variants were proposed to improve SRC. We performed experimental tests on real fMRI data to compare the performance of SRC, the non-negative SRC (NSRC), two SRC variants, and the support vector machine (SVM). The results of the real fMRI experiments showed that the two SRC variants and NSRC exhibited much better classification performance than the SRC. Moreover, the performance of the second SRC variant is the best among the five classifiers.

Continuation of Nesterov's Smoothing for Regression With Structured Sparsity in High-Dimensional Neuroimaging

Predictive models can be used on high-dimensional brain images to decode cognitive states or diagnosis/prognosis of a clinical condition/evolution. Spatial regularization through structured sparsity offers new perspectives in this context and reduces the risk of overfitting the model while providing interpretable neuroimaging signatures by forcing the solution to adhere to domain-specific constraints. Total variation (TV) is a promising candidate for structured penalization: it enforces spatial smoothness of the solution while segmenting predictive regions from the background. We consider the problem of minimizing the sum of a smooth convex loss, a non-smooth convex penalty (whose proximal operator is known) and a wide range of possible complex, non-smooth convex structured penalties such as TV or overlapping group Lasso. Existing solvers are either limited in the functions they can minimize or in their practical capacity to scale to high-dimensional imaging data. Nesterov's smoothing technique can be used to minimize a large number of non-smooth convex structured penalties. However, reasonable precision requires a small smoothing parameter, which slows down the convergence speed to unacceptable levels. To benefit from the versatility of Nesterov's smoothing technique, we propose a first order continuation algorithm, CONESTA, which automatically generates a sequence of decreasing smoothing parameters. The generated sequence maintains the optimal convergence speed toward any globally desired precision. Our main contributions are: gap to probe the current distance to the global optimum in order to adapt the smoothing parameter and the To propose an expression of the duality convergence speed. This expression is applicable to many penalties and can be used with other solvers than CONESTA. We also propose an expression for the particular smoothing parameter that minimizes the number of iterations required to reach a given precision. Furthermore, we provide a convergence proof and its rate, which is an improvement over classical proximal gradient smoothing methods. We demonstrate on both simulated and high-dimensional structural neuroimaging data that CONESTA significantly outperforms many state-of-the-art solvers in regard to convergence speed and precision.

Early Findings on Functional Connectivity Correlates of Behavioral Outcomes of Brain-Computer Interface Stroke Rehabilitation Using Machine Learning

The primary goal of this work was to apply data-driven machine learning regression to assess if resting state functional connectivity (rs-FC) could estimate measures of behavioral domains in stroke subjects who completed brain-computer interface (BCI) intervention for motor rehabilitation. The study cohort consisted of 20 chronic-stage stroke subjects exhibiting persistent upper-extremity motor deficits who received the intervention using a closed-loop neurofeedback BCI device. Over the course of this intervention, resting state functional MRI scans were collected at four distinct time points: namely, pre-intervention, mid-intervention, post-intervention and 1-month after completion of intervention. Behavioral assessments were administered outside the scanner at each time-point to collect objective measures such as the Action Research Arm Test, Nine-Hole Peg Test, and Barthel Index as well as subjective measures including the Stroke Impact Scale. The present analysis focused on neuroplasticity and behavioral outcomes measured across pre-intervention, post-intervention and 1-month post-intervention to study immediate and carry-over effects. Rs-FC, changes in rs-FC within the motor network and the behavioral measures at preceding stages were used as input features and behavioral measures and associated changes at succeeding stages were used as outcomes for machine-learning-based support vector regression (SVR) models. Potential clinical confounding factors such as age, gender, lesion hemisphere, and stroke severity were included as additional features in each of the regression models. Sequential forward feature selection procedure narrowed the search for important correlates. Behavioral outcomes at preceding time-points outperformed rs-FC-based correlates. Rs-FC and changes associated with bilateral primary motor areas were found to be important correlates of across several behavioral outcomes and were stable upon inclusion of clinical variables as well. NIH Stroke Scale and motor impairment severity were the most influential clinical variables. Comparatively, linear SVR models aided in evaluation of contribution of individual correlates and seed regions while non-linear SVR models achieved higher performance in prediction of behavioral outcomes.

Representation, Pattern Information, and Brain Signatures: From Neurons to Neuroimaging

Human neuroimaging research has transitioned from mapping local effects to developing predictive models of mental events that integrate information distributed across multiple brain systems. Here we review work demonstrating how multivariate predictive models have been utilized to provide quantitative, falsifiable predictions; establish mappings between brain and mind with larger effects than traditional approaches; and help explain how the brain represents mental constructs and processes. Although there is increasing progress toward the first two of these goals, models are only beginning to address the latter objective. By explicitly identifying gaps in knowledge, research programs can move deliberately and programmatically toward the goal of identifying brain representations underlying mental states and processes.

Reproducibility of importance extraction methods in neural network based fMRI classification

Recent advances in machine learning allow faster training, improved performance and increased interpretability of classification techniques. Consequently, their application in neuroscience is rapidly increasing. While classification approaches have proved useful in functional magnetic resonance imaging (fMRI) studies, there are concerns regarding extraction, reproducibility and visualization of brain regions that contribute most significantly to the classification. We addressed these issues using an fMRI classification scheme based on neural networks and compared a set of methods for extraction of category-related voxel importances in three simulated and two empirical datasets. The simulation data revealed that the proposed scheme successfully detects spatially distributed and overlapping activation patterns upon successful classification. Application of the proposed classification scheme to two previously published empirical fMRI datasets revealed robust importance maps that extensively overlap with univariate maps but also provide complementary information. Our results demonstrate increased statistical power of importance maps compared to univariate approaches for both detection of overlapping patterns and patterns with weak univariate information.

A decomposition model and voxel selection framework for fMRI analysis to predict neural response of visual stimuli

This paper presents an fMRI signal analysis methodology using geometric mean curve decomposition (GMCD) and mutual information-based voxel selection framework. Previously, the fMRI signal analysis has been conducted using empirical mean curve decomposition (EMCD) model and voxel selection on raw fMRI signal. The erstwhile methodology loses frequency component, while the latter methodology suffers from signal redundancy. Both challenges are addressed by our methodology in which the frequency component is considered by decomposing the raw fMRI signal using geometric mean rather than arithmetic mean and the voxels are selected from EMCD signal using GMCD components, rather than raw fMRI signal. The proposed methodologies are adopted for predicting the neural response. Experimentations are conducted in the openly available fMRI data of six subjects, and comparisons are made with existing decomposition models and voxel selection frameworks. Subsequently, the effect of degree of selected voxels and the selection constraints are analyzed. The comparative results and the analysis demonstrate the superiority and the reliability of the proposed methodology.

Significant Anatomy Detection Through Sparse Classification: A Comparative Study

We present a comparative study for discriminative anatomy detection in high dimensional neuroimaging data. While most studies solve this problem using mass univariate approaches, recent works show better accuracy and variable selection using a sparse classification model. Two types of image-based regularization methods have been proposed in the literature based on either a Graph Net (GN) model or a total variation (TV) model. These studies showed increased classification accuracy and interpretability of results when using image-based regularization, but did not look at the accuracy and quality of the recovered significant regions. In this paper, we theoretically prove bounds on the recovered sparse coefficients and the corresponding selected image regions in four models (two based on GN penalty and two based on TV penalty). Practically, we confirm the theoretical findings by measuring the accuracy of selected regions compared with ground truth on simulated data. We also evaluate the stability of recovered regions over cross-validation folds using real MRI data. Our findings show that the TV penalty is superior to the GN model. In addition, we showed that adding an l₂ penalty improves the accuracy of estimated coefficients and selected significant regions for the both types of models.

FReM - Scalable and stable decoding with fast regularized ensemble of models

Brain decoding relates behavior to brain activity through predictive models. These are also used to identify brain regions involved in the cognitive operations related to the observed behavior. Training such multivariate models is a high-dimensional statistical problem that calls for suitable priors. State of the art priors -eg small total-variation- enforce spatial structure on the maps to stabilize them and improve prediction. However, they come with a hefty computational cost. We build upon very fast dimension reduction with spatial structure and model ensembling to achieve decoders that are fast on large datasets and increase the stability of the predictions and the maps. Our approach, fast regularized ensemble of models (FReM), includes an implicit spatial regularization by using a voxel grouping with a fast clustering algorithm. In addition, it aggregates different estimators obtained across splits of a cross-validation loop, each time keeping the best possible model. Experiments on a large number of brain imaging datasets show that our combination of voxel clustering and model ensembling improves decoding maps stability and reduces the variance of prediction accuracy. Importantly, our method requires less samples than state-of-the-art methods to achieve a given level of prediction accuracy. Finally, FreM is much faster than other spatially-regularized methods and, in addition, it can better exploit parallel computing resources.

Euler Elastica Regularized Logistic Regression for Whole-Brain Decoding of fMRI Data

OBJECTIVE

Multivariate pattern analysis methods have been widely applied to functional magnetic resonance imaging (fMRI) data to decode brain states. Due to the "high features, low samples" in fMRI data, machine learning methods have been widely regularized using various regularizations to avoid overfitting. Both total variation (TV) using the gradients of images and Euler's elastica (EE) using the gradient and the curvature of images are the two popular regulations with spatial structures. In contrast to TV, EE regulation is able to overcome the disadvantage of TV regulation that favored piecewise constant images over piecewise smooth images. In this study, we introduced EE to fMRI-based decoding for the first time and proposed the EE regularized multinomial logistic regression (EELR) algorithm for multi-class classification.

METHODS

We performed experimental tests on both simulated and real fMRI data to investigate the feasibility and robustness of EELR. The performance of EELR was compared with sparse logistic regression (SLR) and TV regularized LR (TVLR).

RESULTS

The results showed that EELR was more robustness to noises and showed significantly higher classification performance than TVLR and SLR. Moreover, the forward models and weights patterns revealed that EELR detected larger brain regions that were discriminative to each task and activated by each task than TVLR.

CONCLUSION

The results suggest that EELR not only performs well in brain decoding but also reveals meaningful discriminative and activation patterns.

SIGNIFICANCE

This study demonstrated that EELR showed promising potential in brain decoding and discriminative/activation pattern detection.

Functional brain networks reconstruction using group sparsity-regularized learning

Investigating functional brain networks and patterns using sparse representation of fMRI data has received significant interests in the neuroimaging community. It has been reported that sparse representation is effective in reconstructing concurrent and interactive functional brain networks. To date, most of data-driven network reconstruction approaches rarely take consideration of anatomical structures, which are the substrate of brain function. Furthermore, it has been rarely explored whether structured sparse representation with anatomical guidance could facilitate functional networks reconstruction. To address this problem, in this paper, we propose to reconstruct brain networks utilizing the structure guided group sparse regression (S2GSR) in which 116 anatomical regions from the AAL template, as prior knowledge, are employed to guide the network reconstruction when performing sparse representation of whole-brain fMRI data. Specifically, we extract fMRI signals from standard space aligned with the AAL template. Then by learning a global over-complete dictionary, with the learned dictionary as a set of features (regressors), the group structured regression employs anatomical structures as group information to regress whole brain signals. Finally, the decomposition coefficients matrix is mapped back to the brain volume to represent functional brain networks and patterns. We use the publicly available Human Connectome Project (HCP) Q1 dataset as the test bed, and the experimental results indicate that the proposed anatomically guided structure sparse representation is effective in reconstructing concurrent functional brain networks.

Generalized Scalar-on-Image Regression Models via Total Variation

The use of imaging markers to predict clinical outcomes can have a great impact in public health. The aim of this paper is to develop a class of generalized scalar-on-image regression models via total variation (GSIRM-TV), in the sense of generalized linear models, for scalar response and imaging predictor with the presence of scalar covariates. A key novelty of GSIRM-TV is that it is assumed that the slope function (or image) of GSIRM-TV belongs to the space of bounded total variation in order to explicitly account for the piecewise smooth nature of most imaging data. We develop an efficient penalized total variation optimization to estimate the unknown slope function and other parameters. We also establish nonasymptotic error bounds on the excess risk. These bounds are explicitly specified in terms of sample size, image size, and image smoothness. Our simulations demonstrate a superior performance of GSIRM-TV against many existing approaches. We apply GSIRM-TV to the analysis of hippocampus data obtained from the Alzheimers Disease Neuroimaging Initiative (ADNI) dataset.

Transient networks of spatio-temporal connectivity map communication pathways in brain functional systems

The study of brain dynamics enables us to characterize the time-varying functional connectivity among distinct neural groups. However, current methods suffer from the absence of structural connectivity information. We propose to integrate infra-slow neural oscillations and anatomical-connectivity maps, as derived from functional and diffusion MRI, in a multilayer-graph framework that captures transient networks of spatio-temporal connectivity. These networks group anatomically wired and temporary synchronized brain regions and encode the propagation of functional activity on the structural connectome. In a group of 71 healthy subjects, we find that these transient networks demonstrate power-law spatial and temporal size, globally organize into well-known functional systems and describe wave-like trajectories of activation across anatomically connected regions. Within the transient networks, activity propagates through polysynaptic paths that include selective ensembles of structural connections and differ from the structural shortest paths. In the light of the communication-through-coherence principle, the identified spatio-temporal networks could encode communication channels' selection and neural assemblies, which deserves further attention. This work contributes to the understanding of brain structure-function relationships by considering the time-varying nature of resting-state interactions on the axonal scaffold, and it offers a convenient framework to study large-scale communication mechanisms and functional dynamics.

Sparsity Is Better with Stability: Combining Accuracy and Stability for Model Selection in Brain Decoding

Structured sparse methods have received significant attention in neuroimaging. These methods allow the incorporation of domain knowledge through additional spatial and temporal constraints in the predictive model and carry the promise of being more interpretable than non-structured sparse methods, such as LASSO or Elastic Net methods. However, although sparsity has often been advocated as leading to more interpretable models it can also lead to unstable models under subsampling or slight changes of the experimental conditions. In the present work we investigate the impact of using stability/reproducibility as an additional model selection criterion¹ on several different sparse (and structured sparse) methods that have been recently applied for fMRI brain decoding. We compare three different model selection criteria: (i) classification accuracy alone; (ii) classification accuracy and overlap between the solutions; (iii) classification accuracy and correlation between the solutions. The methods we consider include LASSO, Elastic Net, Total Variation, sparse Total Variation, Laplacian and Graph Laplacian Elastic Net (GraphNET). Our results show that explicitly accounting for stability/reproducibility during the model optimization can mitigate some of the instability inherent in sparse methods. In particular, using accuracy and overlap between the solutions as a joint optimization criterion can lead to solutions that are more similar in terms of accuracy, sparsity levels and coefficient maps even when different sparsity methods are considered.

Interpretability of Multivariate Brain Maps in Linear Brain Decoding: Definition, and Heuristic Quantification in Multivariate Analysis of MEG Time-Locked Effects

Brain decoding is a popular multivariate approach for hypothesis testing in neuroimaging. Linear classifiers are widely employed in the brain decoding paradigm to discriminate among experimental conditions. Then, the derived linear weights are visualized in the form of multivariate brain maps to further study spatio-temporal patterns of underlying neural activities. It is well known that the brain maps derived from weights of linear classifiers are hard to interpret because of high correlations between predictors, low signal to noise ratios, and the high dimensionality of neuroimaging data. Therefore, improving the interpretability of brain decoding approaches is of primary interest in many neuroimaging studies. Despite extensive studies of this type, at present, there is no formal definition for interpretability of multivariate brain maps. As a consequence, there is no quantitative measure for evaluating the interpretability of different brain decoding methods. In this paper, first, we present a theoretical definition of interpretability in brain decoding; we show that the interpretability of multivariate brain maps can be decomposed into their reproducibility and representativeness. Second, as an application of the proposed definition, we exemplify a heuristic for approximating the interpretability in multivariate analysis of evoked magnetoencephalography (MEG) responses. Third, we propose to combine the approximated interpretability and the generalization performance of the brain decoding into a new multi-objective criterion for model selection. Our results, for the simulated and real MEG data, show that optimizing the hyper-parameters of the regularized linear classifier based on the proposed criterion results in more informative multivariate brain maps. More importantly, the presented definition provides the theoretical background for quantitative evaluation of interpretability, and hence, facilitates the development of more effective brain decoding algorithms in the future.

MWPCR: Multiscale Weighted Principal Component Regression for High-dimensional Prediction

We propose a multiscale weighted principal component regression (MWPCR) framework for the use of high dimensional features with strong spatial features (e.g., smoothness and correlation) to predict an outcome variable, such as disease status. This development is motivated by identifying imaging biomarkers that could potentially aid detection, diagnosis, assessment of prognosis, prediction of response to treatment, and monitoring of disease status, among many others. The MWPCR can be regarded as a novel integration of principal components analysis (PCA), kernel methods, and regression models. In MWPCR, we introduce various weight matrices to prewhitten high dimensional feature vectors, perform matrix decomposition for both dimension reduction and feature extraction, and build a prediction model by using the extracted features. Examples of such weight matrices include an importance score weight matrix for the selection of individual features at each location and a spatial weight matrix for the incorporation of the spatial pattern of feature vectors. We integrate the importance score weights with the spatial weights in order to recover the low dimensional structure of high dimensional features. We demonstrate the utility of our methods through extensive simulations and real data analyses of the Alzheimer's disease neuroimaging initiative (ADNI) data set.

Assessing and tuning brain decoders: Cross-validation, caveats, and guidelines

Decoding, i.e. prediction from brain images or signals, calls for empirical evaluation of its predictive power. Such evaluation is achieved via cross-validation, a method also used to tune decoders' hyper-parameters. This paper is a review on cross-validation procedures for decoding in neuroimaging. It includes a didactic overview of the relevant theoretical considerations. Practical aspects are highlighted with an extensive empirical study of the common decoders in within- and across-subject predictions, on multiple datasets -anatomical and functional MRI and MEG- and simulations. Theory and experiments outline that the popular "leave-one-out" strategy leads to unstable and biased estimates, and a repeated random splits method should be preferred. Experiments outline the large error bars of cross-validation in neuroimaging settings: typical confidence intervals of 10%. Nested cross-validation can tune decoders' parameters while avoiding circularity bias. However we find that it can be favorable to use sane defaults, in particular for non-sparse decoders.

Real-time estimation of dynamic functional connectivity networks

Two novel and exciting avenues of neuroscientific research involve the study of task-driven dynamic reconfigurations of functional connectivity networks and the study of functional connectivity in real-time. While the former is a well-established field within neuroscience and has received considerable attention in recent years, the latter remains in its infancy. To date, the vast majority of real-time fMRI studies have focused on a single brain region at a time. This is due in part to the many challenges faced when estimating dynamic functional connectivity networks in real-time. In this work, we propose a novel methodology with which to accurately track changes in time-varying functional connectivity networks in real-time. The proposed method is shown to perform competitively when compared to state-of-the-art offline algorithms using both synthetic as well as real-time fMRI data. The proposed method is applied to motor task data from the Human Connectome Project as well as to data obtained from a visuospatial attention task. We demonstrate that the algorithm is able to accurately estimate task-related changes in network structure in real-time. Hum Brain Mapp 38:202-220, 2017. © 2016 Wiley Periodicals, Inc.

A Bayesian probit model with spatially varying coefficients for brain decoding using fMRI data

Recent advances in human neuroimaging have shown that it is possible to accurately decode how the brain perceives information based only on non-invasive functional magnetic resonance imaging measurements of brain activity. Two commonly used statistical approaches, namely, univariate analysis and multivariate pattern analysis often lead to distinct patterns of selected voxels. One current debate in brain decoding concerns whether the brain's representation of sound categories is localized or distributed. We hypothesize that the distributed pattern of voxels selected by most multivariate pattern analysis models can be an artifact due to the spatial correlation among voxels. Here, we propose a Bayesian spatially varying coefficient model, where the spatial correlation is modeled through the variance-covariance matrix of the model coefficients. Combined with a proposed region selection strategy, we demonstrate that our approach is effective in identifying the truly localized patterns of the voxels while maintaining robustness to discover truly distributed pattern. In addition, we show that localized or clustered patterns can be artificially identified as distributed if without proper usage of the spatial correlation information in fMRI data. Copyright © 2016 John Wiley & Sons, Ltd.

Estimating multivariate similarity between neuroimaging datasets with sparse canonical correlation analysis: an application to perfusion imaging

An increasing number of neuroimaging studies are based on either combining more than one data modality (inter-modal) or combining more than one measurement from the same modality (intra-modal). To date, most intra-modal studies using multivariate statistics have focused on differences between datasets, for instance relying on classifiers to differentiate between effects in the data. However, to fully characterize these effects, multivariate methods able to measure similarities between datasets are needed. One classical technique for estimating the relationship between two datasets is canonical correlation analysis (CCA). However, in the context of high-dimensional data the application of CCA is extremely challenging. A recent extension of CCA, sparse CCA (SCCA), overcomes this limitation, by regularizing the model parameters while yielding a sparse solution. In this work, we modify SCCA with the aim of facilitating its application to high-dimensional neuroimaging data and finding meaningful multivariate image-to-image correspondences in intra-modal studies. In particular, we show how the optimal subset of variables can be estimated independently and we look at the information encoded in more than one set of SCCA transformations. We illustrate our framework using Arterial Spin Labeling data to investigate multivariate similarities between the effects of two antipsychotic drugs on cerebral blood flow.

Randomized structural sparsity via constrained block subsampling for improved sensitivity of discriminative voxel identification

In this paper, we consider voxel selection for functional Magnetic Resonance Imaging (fMRI) brain data with the aim of finding a more complete set of probably correlated discriminative voxels, thus improving interpretation of the discovered potential biomarkers. The main difficulty in doing this is an extremely high dimensional voxel space and few training samples, resulting in unreliable feature selection. In order to deal with the difficulty, stability selection has received a great deal of attention lately, especially due to its finite sample control of false discoveries and transparent principle for choosing a proper amount of regularization. However, it fails to make explicit use of the correlation property or structural information of these discriminative features and leads to large false negative rates. In other words, many relevant but probably correlated discriminative voxels are missed. Thus, we propose a new variant on stability selection "randomized structural sparsity", which incorporates the idea of structural sparsity. Numerical experiments demonstrate that our method can be superior in controlling for false negatives while also keeping the control of false positives inherited from stability selection.

Multiscale properties of weighted total variation flow with applications to denoising and registration

Images consist of structures of varying scales: large scale structures such as flat regions, and small scale structures such as noise, textures, and rapidly oscillatory patterns. In the hierarchical (BV, L(2)) image decomposition, Tadmor, et al. (2004) start with extracting coarse scale structures from a given image, and successively extract finer structures from the residuals in each step of the iterative decomposition. We propose to begin instead by extracting the finest structures from the given image and then proceed to extract increasingly coarser structures. In most images, noise could be considered as a fine scale structure. Thus, starting the image decomposition with finer scales, rather than large scales, leads to fast denoising. We note that our approach turns out to be equivalent to the nonstationary regularization in Scherzer and Weickert (2000). The continuous limit of this procedure leads to a time-scaled version of total variation flow. Motivated by specific clinical applications, we introduce an image depending weight in the regularization functional, and study the corresponding weighted TV flow. We show that the edge-preserving property of the multiscale representation of an input image obtained with the weighted TV flow can be enhanced and localized by appropriate choice of the weight. We use this in developing an efficient and edge-preserving denoising algorithm with control on speed and localization properties. We examine analytical properties of the weighted TV flow that give precise information about the denoising speed and the rate of change of energy of the images. An additional contribution of the paper is to use the images obtained at different scales for robust multiscale registration. We show that the inherently multiscale nature of the weighted TV flow improved performance for registration of noisy cardiac MRI images, compared to other methods such as bilateral or Gaussian filtering. A clinical application of the multiscale registration algorithm is also demonstrated for aligning viability assessment magnetic resonance (MR) images from 8 patients with previous myocardial infarctions.