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Cryo-electron microscopy (Cryo-EM) enables high-resolution imaging of biomolecules, but structural heterogeneity remains a major challenge in 3D reconstruction. Traditional methods assume a discrete set of conformations, limiting their…
A crucial step in single particle analysis (SPA) of cryogenic electron microscopy (Cryo-EM), 2D classification and alignment takes a collection of noisy particle images to infer orientations and group similar images together. Averaging…
Covariance matrix estimates are an essential part of many signal processing algorithms, and are often used to determine a low-dimensional principal subspace via their spectral decomposition. However, exact eigenanalysis is computationally…
Estimating a covariance matrix is an important task in applications where the number of variables is larger than the number of observations. Shrinkage approaches for estimating a high-dimensional covariance matrix are often employed to…
This paper is the first in a set that analyses the covariance matrices of clustering statistics obtained from several approximate methods for gravitational structure formation. We focus here on the covariance matrices of anisotropic…
We revisit the topic of common lines between projection images in single particle cryo-electron microscopy (cryo-EM). We derive a novel low-rank constraint on a certain $2n \times n$ matrix storing properly-scaled basis vectors for the…
Motivated by the problem of determining the atomic structure of macromolecules using single-particle cryo-electron microscopy (cryo-EM), we study the sample and computational complexities of the sparse multi-reference alignment (MRA) model:…
In dealing with high-dimensional data, factor models are often used for reducing dimensions and extracting relevant information. The spectrum of covariance matrices from power data exhibits two aspects: 1) bulk, which arises from random…
The likelihood function for cosmological parameters, given by e.g. weak lensing shear measurements, depends on contributions to the covariance induced by the nonlinear evolution of the cosmic web. As nonlinear clustering to date has only…
We present a comparison between various algorithms of inference of covariance and precision matrices in small datasets of real vectors, of the typical length and dimension of human brain activity time series retrieved by functional Magnetic…
Preparing thermal states on a quantum computer can have a variety of applications, from simulating many-body quantum systems to training machine learning models. Variational circuits have been proposed for this task on near-term quantum…
We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…
We propose a flexible dual functional factor model for modelling high-dimensional functional time series. In this model, a high-dimensional fully functional factor parametrisation is imposed on the observed functional processes, whereas a…
Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…
In this article, a compliance minimisation scheme for designing spatially varying orthotropic porous structures is proposed. With the utilisation of conformal mapping, the porous structures here can be generated by two controlling field…
In this paper, we exploit the spiked covariance structure of the clutter plus noise covariance matrix for radar signal processing. Using state-of-the-art techniques high dimensional statistics, we propose a nonlinear shrinkage-based…
Constraining cosmology using weak gravitational lensing consists of comparing a measured feature vector of dimension $N_b$ with its simulated counterpart. An accurate estimate of the $N_b\times N_b$ feature covariance matrix $\mathbf{C}$ is…
Matrix valued data has become increasingly prevalent in many applications. Most of the existing clustering methods for this type of data are tailored to the mean model and do not account for the dependence structure of the features, which…
We introduce a technique for estimating a structured covariance matrix from observations of a random vector which have been sketched. Each observed random vector $\boldsymbol{x}_t$ is reduced to a single number by taking its inner product…
Cryo-electron microscopy provides 2-D projection images of the 3-D electron scattering intensity of many instances of the particle under study (e.g., a virus). Both symmetry (rotational point groups) and heterogeneity are important aspects…