Tensor Regression with Applications in Neuroimaging Data Analysis

Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays (tensors). Traditional statistical and computational methods are proving insufficient for analysis of these high-throughput data due to their ultrahigh dimensionality as well as complex structure. In this article, we propose a new family of tensor regression models that efficiently exploit the special structure of tensor covariates. Under this framework, ultrahigh dimensionality is reduced to a manageable level, resulting in efficient estimation and prediction. A fast and highly scalable estimation algorithm is proposed for maximum likelihood estimation and its associated asymptotic properties are studied. Effectiveness of the new methods is demonstrated on both synthetic and real MRI imaging data.Comment: 27 pages, 4 figure

Infant Brain Atlases from Neonates to 1- and 2-Year-Olds

Background: Studies for infants are usually hindered by the insufficient image contrast, especially for neonates. Prior knowledge, in the form of atlas, can provide additional guidance for the data processing such as spatial normalization, label propagation, and tissue segmentation. Although it is highly desired, there is currently no such infant atlas which caters for all these applications. The reason may be largely due to the dramatic early brain development, image processing difficulties, and the need of a large sample size. Methodology: To this end, after several years of subject recruitment and data acquisition, we have collected a unique longitudinal dataset, involving 95 normal infants (56 males and 39 females) with MRI scanned at 3 ages, i.e., neonate, 1-yearold, and 2-year-old. State-of-the-art MR image segmentation and registration techniques were employed, to construct which include the templates (grayscale average images), tissue probability maps (TPMs), and brain parcellation maps (i.e., meaningful anatomical regions of interest) for each age group. In addition, the longitudinal correspondences between agespecific atlases were also obtained. Experiments of typical infant applications validated that the proposed atlas outperformed other atlases and is hence very useful for infant-related studies. Conclusions: We expect that the proposed infant 0–1–2 brain atlases would be significantly conducive to structural and functional studies of the infant brains. These atlases are publicly available in our website

CORRECTED CONFIDENCE BANDS FOR FUNCTIONAL DATA USING PRINCIPAL COMPONENTS

Functional principal components (FPC) analysis is widely used to decompose and express functional observations. Curve estimates implicitly condition on basis functions and other quantities derived from FPC decompositions; however these objects are unknown in practice. In this paper, we propose a method for obtaining correct curve estimates by accounting for uncertainty in FPC decompositions. Additionally, pointwise and simultaneous confidence intervals that account for both model- based and decomposition-based variability are constructed. Standard mixed-model representations of functional expansions are used to construct curve estimates and variances conditional on a specific decomposition. A bootstrap procedure is implemented to understand the uncertainty in principal component decomposition quantities. Iterated expectation and variance formulas combine both sources of uncertainty by combining model-based conditional estimates across the distribution of decompositions. Our method compares favorably to competing approaches in simulation studies that include both densely- and sparsely-observed functions. We apply our method to sparse observations of CD4 cell counts and to dense white-matter tract profiles. Code for the analyses and simulations is publicly available, and our method is implemented as the IVfpca() function in the R package refund on CRAN