Asymptotic properties of eigenmatrices of a large sample covariance matrix

Let $S_n=\frac{1}{n}X_nX_n^*$ where $X_n=\{X_{ij}\}$ is a $p\times n$ matrix with i.i.d. complex standardized entries having finite fourth moments. Let $Y_n(\mathbf {t}_1,\mathbf {t}_2,\sigma)=\sqrt{p}({\mathbf {x}}_n(\mathbf {t}_1)^*(S_n+\sigma I)^{-1}{\mathbf {x}}_n(\mathbf {t}_2)-{\mathbf {x}}_n(\mathbf {t}_1)^*{\mathbf {x}}_n(\mathbf {t}_2)m_n(\sigma))$ in which $\sigma>0$ and $m_n(\sigma)=\int\frac{dF_{y_n}(x)}{x+\sigma}$ where $F_{y_n}(x)$ is the Mar\v{c}enko--Pastur law with parameter $y_n=p/n$; which converges to a positive constant as $n\to\infty$, and ${\mathbf {x}}_n(\mathbf {t}_1)$ and ${\mathbf {x}}_n(\mathbf {t}_2)$ are unit vectors in ${\Bbb{C}}^p$, having indices $\mathbf {t}_1$ and $\mathbf {t}_2$, ranging in a compact subset of a finite-dimensional Euclidean space. In this paper, we prove that the sequence $Y_n(\mathbf {t}_1,\mathbf {t}_2,\sigma)$ converges weakly to a $(2m+1)$-dimensional Gaussian process. This result provides further evidence in support of the conjecture that the distribution of the eigenmatrix of $S_n$ is asymptotically close to that of a Haar-distributed unitary matrix.Comment: Published in at http://dx.doi.org/10.1214/10-AAP748 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Learning associations between clinical information and motion-based descriptors using a large scale MR-derived cardiac motion atlas

The availability of large scale databases containing imaging and non-imaging data, such as the UK Biobank, represents an opportunity to improve our understanding of healthy and diseased bodily function. Cardiac motion atlases provide a space of reference in which the motion fields of a cohort of subjects can be directly compared. In this work, a cardiac motion atlas is built from cine MR data from the UK Biobank (~ 6000 subjects). Two automated quality control strategies are proposed to reject subjects with insufficient image quality. Based on the atlas, three dimensionality reduction algorithms are evaluated to learn data-driven cardiac motion descriptors, and statistical methods used to study the association between these descriptors and non-imaging data. Results show a positive correlation between the atlas motion descriptors and body fat percentage, basal metabolic rate, hypertension, smoking status and alcohol intake frequency. The proposed method outperforms the ability to identify changes in cardiac function due to these known cardiovascular risk factors compared to ejection fraction, the most commonly used descriptor of cardiac function. In conclusion, this work represents a framework for further investigation of the factors influencing cardiac health.Comment: 2018 International Workshop on Statistical Atlases and Computational Modeling of the Hear

Scanning tunneling microscopy investigation of 2H-MoS_2: A layered semiconducting transition‐metal dichalcogenide

Scanning tunneling microscopy (STM) has been enormously successful in solving several important problems in the geometric and electronic structure of homogeneous metallic and semiconducting surfaces. A central question which remains to be answered with respect to the study of compound surfaces, however, is the extent to which the chemical identity of constituent atoms may be established. Recently, progress in this area was made by Feenstra et al. who succeeded in selectively imaging either Ga or As atoms on the GaAs (110) surface. So far this is the only case where such selectivity has been achieved. In an effort to add to our understanding of compound surface imaging we have undertaken a vacuum STM study of 2H-MoS_2, a material which has two structurally and electronically different atomic species at its surface

Testing linear hypotheses in high-dimensional regressions

For a multivariate linear model, Wilk's likelihood ratio test (LRT) constitutes one of the cornerstone tools. However, the computation of its quantiles under the null or the alternative requires complex analytic approximations and more importantly, these distributional approximations are feasible only for moderate dimension of the dependent variable, say $p\le 20$. On the other hand, assuming that the data dimension $p$ as well as the number $q$ of regression variables are fixed while the sample size $n$ grows, several asymptotic approximations are proposed in the literature for Wilk's \bLa including the widely used chi-square approximation. In this paper, we consider necessary modifications to Wilk's test in a high-dimensional context, specifically assuming a high data dimension $p$ and a large sample size $n$. Based on recent random matrix theory, the correction we propose to Wilk's test is asymptotically Gaussian under the null and simulations demonstrate that the corrected LRT has very satisfactory size and power, surely in the large $p$ and large $n$ context, but also for moderately large data dimensions like $p=30$ or $p=50$. As a byproduct, we give a reason explaining why the standard chi-square approximation fails for high-dimensional data. We also introduce a new procedure for the classical multiple sample significance test in MANOVA which is valid for high-dimensional data.Comment: Accepted 02/2012 for publication in "Statistics". 20 pages, 2 pages and 2 table

Deep learning for cardiac image segmentation: A review

Deep learning has become the most widely used approach for cardiac image segmentation in recent years. In this paper, we provide a review of over 100 cardiac image segmentation papers using deep learning, which covers common imaging modalities including magnetic resonance imaging (MRI), computed tomography (CT), and ultrasound (US) and major anatomical structures of interest (ventricles, atria and vessels). In addition, a summary of publicly available cardiac image datasets and code repositories are included to provide a base for encouraging reproducible research. Finally, we discuss the challenges and limitations with current deep learning-based approaches (scarcity of labels, model generalizability across different domains, interpretability) and suggest potential directions for future research

Large-scale Quality Control of Cardiac Imaging in Population Studies: Application to UK Biobank

In large population studies such as the UK Biobank (UKBB), quality control of the acquired images by visual assessment is unfeasible. In this paper, we apply a recently developed fully-automated quality control pipeline for cardiac MR (CMR) images to the first 19,265 short-axis (SA) cine stacks from the UKBB. We present the results for the three estimated quality metrics (heart coverage, inter-slice motion and image contrast in the cardiac region) as well as their potential associations with factors including acquisition details and subject-related phenotypes. Up to 14.2% of the analysed SA stacks had sub-optimal coverage (i.e. missing basal and/or apical slices), however most of them were limited to the first year of acquisition. Up to 16% of the stacks were affected by noticeable inter-slice motion (i.e. average inter-slice misalignment greater than 3.4 mm). Inter-slice motion was positively correlated with weight and body surface area. Only 2.1% of the stacks had an average end-diastolic cardiac image contrast below 30% of the dynamic range. These findings will be highly valuable for both the scientists involved in UKBB CMR acquisition and for the ones who use the dataset for research purposes

Stratified decision forests for accurate anatomical landmark localization in cardiac images

Accurate localization of anatomical landmarks is an important step in medical imaging, as it provides useful prior information for subsequent image analysis and acquisition methods. It is particularly useful for initialization of automatic image analysis tools (e.g. segmentation and registration) and detection of scan planes for automated image acquisition. Landmark localization has been commonly performed using learning based approaches, such as classifier and/or regressor models. However, trained models may not generalize well in heterogeneous datasets when the images contain large differences due to size, pose and shape variations of organs. To learn more data-adaptive and patient specific models, we propose a novel stratification based training model, and demonstrate its use in a decision forest. The proposed approach does not require any additional training information compared to the standard model training procedure and can be easily integrated into any decision tree framework. The proposed method is evaluated on 1080 3D highresolution and 90 multi-stack 2D cardiac cine MR images. The experiments show that the proposed method achieves state-of-theart landmark localization accuracy and outperforms standard regression and classification based approaches. Additionally, the proposed method is used in a multi-atlas segmentation to create a fully automatic segmentation pipeline, and the results show that it achieves state-of-the-art segmentation accuracy