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Register a new userA functional approach to deconvolve dynamic neuroimaging data
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Added by
John Aston
Publication date
2014
fields
Mathematical Statistics
and research's language is
English
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Positron Emission Tomography (PET) is an imaging technique which can be used to investigate chemical changes in human biological processes such as cancer development or neurochemical reactions. Most dynamic PET scans are currently analyzed based on the assumption that linear first order kinetics can be used to adequately describe the system under observation. However, there has recently been strong evidence that this is not the case. In order to provide an analysis of PET data which is free from this compartmental assumption, we propose a nonparametric deconvolution and analysis model for dynamic PET data based on functional principal component analysis. This yields flexibility in the possible deconvolved functions while still performing well when a linear compartmental model setup is the true data generating mechanism. As the deconvolution needs to be performed on only a relative small number of basis functions rather than voxel by voxel in the entire 3-D volume, the methodology is both robust to typical brain imaging noise levels while also being computationally efficient. The new methodology is investigated through simulations in both 1-D functions and 2-D images and also applied to a neuroimaging study whose goal is the quantification of opioid receptor concentration in the brain.
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The Argo data is a modern oceanography dataset that provides unprecedented global coverage of temperature and salinity measurements in the upper 2,000 meters of depth of the ocean. We study the Argo data from the perspective of functional data analysis (FDA). We develop spatio-temporal functional kriging methodology for mean and covariance estimation to predict temperature and salinity at a fixed location as a smooth function of depth. By combining tools from FDA and spatial statistics, including smoothing splines, local regression, and multivariate spatial modeling and prediction, our approach provides advantages over current methodology that consider pointwise estimation at fixed depths. Our approach naturally leverages the irregularly-sampled data in space, time, and depth to fit a space-time functional model for temperature and salinity. The developed framework provides new tools to address fundamental scientific problems involving the entire upper water column of the oceans such as the estimation of ocean heat content, stratification, and thermohaline oscillation. For example, we show that our functional approach yields more accurate ocean heat content estimates than ones based on discrete integral approximations in pressure. Further, using the derivative function estimates, we obtain a new product of a global map of the mixed layer depth, a key component in the study of heat absorption and nutrient circulation in the oceans. The derivative estimates also reveal evidence for density
Evolutionary models of languages are usually considered to take the form of trees. With the development of so-called tree constraints the plausibility of the tree model assumptions can be addressed by checking whether the moments of observed variables lie within regions consistent with trees. In our linguistic application, the data set comprises acoustic samples (audio recordings) from speakers of five Romance languages or dialects. We wish to assess these functional data for compatibility with a hereditary tree model at the language level. A novel combination of canonical function analysis (CFA) with a separable covariance structure provides a method for generating a representative basis for the data. This resulting basis is formed of components which emphasize language differences whilst maintaining the integrity of the observational language-groupings. A previously unexploited Gaussian tree constraint is then applied to component-by-component projections of the data to investigate adherence to an evolutionary tree. The results indicate that while a tree model is unlikely to be suitable for modeling all aspects of the acoustic linguistic data, certain features of the spoken Romance languages highlighted by the separable-CFA basis may indeed be suitably modeled as a tree.
Motivated by the analysis of high-dimensional neuroimaging signals located over the cortical surface, we introduce a novel Principal Component Analysis technique that can handle functional data located over a two-dimensional manifold. For this purpose a regularization approach is adopted, introducing a smoothing penalty coherent with the geodesic distance over the manifold. The model introduced can be applied to any manifold topology, can naturally handle missing data and functional samples evaluated in different grids of points. We approach the discretization task by means of finite element analysis and propose an efficient iterative algorithm for its resolution. We compare the performances of the proposed algorithm with other approaches classically adopted in literature. We finally apply the proposed method to resting state functional magnetic resonance imaging data from the Human Connectome Project, where the method shows substantial differential variations between brain regions that were not apparent with other approaches.
One of the classic concerns in statistics is determining if two samples come from thesame population, i.e. homogeneity testing. In this paper, we propose a homogeneitytest in the context of Functional Data Analysis, adopting an idea from multivariatedata analysis: the data depth plot (DD-plot). This DD-plot is a generalization of theunivariate Q-Q plot (quantile-quantile plot). We propose some statistics based onthese DD-plots, and we use bootstrapping techniques to estimate their distributions.We estimate the finite-sample size and power of our test via simulation, obtainingbetter results than other homogeneity test proposed in the literature. Finally, weillustrate the procedure in samples of real heterogeneous data and get consistent results.
Early detection of changes in the frequency of events is an important task, in, for example, disease surveillance, monitoring of high-quality processes, reliability monitoring and public health. In this article, we focus on detecting changes in multivariate event data, by monitoring the time-between-events (TBE). Existing multivariate TBE charts are limited in the sense that, they only signal after an event occurred for each of the individual processes. This results in delays (i.e., long time to signal), especially if it is of interest to detect a change in one or a few of the processes. We propose a bivariate TBE (BTBE) chart which is able to signal in real time. We derive analytical expressions for the control limits and average time-to-signal performance, conduct a performance evaluation and compare our chart to an existing method. The findings showed that our method is a realistic approach to monitor bivariate time-between-event data, and has better detection ability than existing methods. A large benefit of our method is that it signals in real-time and that due to the analytical expressions no simulation is needed. The proposed method is implemented on a real-life dataset related to AIDS.
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