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Feature-based visual structure and motion reconstruction pipelines, common in visual odometry and large-scale reconstruction from photos, use the location of corresponding features in different images to determine the 3D structure of the…
In mobile robotics, scan matching of point clouds using Iterative Closest Point (ICP) allows estimating sensor displacements. It may prove important to assess the associated uncertainty about the obtained rigid transformation, especially…
The structural characterization of hetero-aggregates in 3D is of great interest, e.g., for deriving process-structure or structure-property relationships. However, since 3D imaging techniques are often difficult to perform as well as time…
This paper studies the multi-task high-dimensional linear regression models where the noise among different tasks is correlated, in the moderately high dimensional regime where sample size $n$ and dimension $p$ are of the same order. Our…
We propose a flexible yet interpretable model for high-dimensional data with time-varying second order statistics, motivated and applied to functional neuroimaging data. Motivated by the neuroscience literature, we factorize the covariances…
One of the outstanding analytical problems in X-ray single particle imaging (SPI) is the classification of structural heterogeneity, which is especially difficult given the low signal-to-noise ratios of individual patterns and that even…
Principal component analysis (PCA) plays an important role in the analysis of cryo-EM images for various tasks such as classification, denoising, compression, and ab-initio modeling. We introduce a fast method for estimating a compressed…
In this self-contained chapter, we revisit a fundamental problem of multivariate statistics: estimating covariance matrices from finitely many independent samples. Based on massive Multiple-Input Multiple-Output (MIMO) systems we illustrate…
Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…
Device-to-device variability in experimental noise critically impacts reproducibility, especially in automated, high-throughput systems like additive manufacturing farms. While manageable in small labs, such variability can escalate into…
Cryo-Electron Microscopy (Cryo-EM) is a Nobel prize-winning technology for determining the 3D structure of particles at near-atomic resolution. A fundamental step in the recovering of the 3D single-particle structure is to align its 2D…
This paper is the first work to propose a network to predict a structured uncertainty distribution for a synthesized image. Previous approaches have been mostly limited to predicting diagonal covariance matrices. Our novel model learns to…
In this paper, we propose a novel high-dimensional time-varying coefficient estimator for noisy high-frequency observations with a factor structure. In high-frequency finance, we often observe that noises dominate the signal of underlying…
Clustering analysis is one of the most widely used statistical tools in many emerging areas such as microarray data analysis. For microarray and other high-dimensional data, the presence of many noise variables may mask underlying…
We present a supervised machine learning-based method using convolutional neural networks to estimate the covariance matrix of Gaussian quantum states in the presence of thermal noise. Unlike computationally intensive density matrix…
The covariance matrix of the matter power spectrum is a key element of the statistical analysis of galaxy clustering data. Independent realisations of observational measurements can be used to sample the covariance, nevertheless statistical…
Purpose: To develop a fast, general-purpose framework for voxelwise noise characterization in linear and nonlinear iterative MRI reconstructions, recovering the image-domain noise variance from which SNR, $g$-factor, and related…
Cosmological parameter estimation requires that the likelihood function of the data is accurately known. Assuming that cosmological large-scale structure power spectra data are multivariate Gaussian-distributed, we show the accuracy of…
Estimation of a precision matrix (i.e., inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence of abnormal observations is exacerbated in a high dimensional setting as the…
Many applications in mechanical, acoustic, and electronic engineering require estimating complex dynamical models, often represented as additive multi-input multi-output (MIMO) transfer functions with structural constraints. This paper…