Principal component analysis (PCA) along with its extensions to manifolds and outlier
contaminated data have been indispensable in computer vision and machine learning. In …

When generalizing schemes for real-valued data approximation or decomposition to data
living in Riemannian manifolds, tangent space-based schemes are very attractive for the …

The J-orthogonal matrix, also referred to as the hyperbolic orthogonal matrix, is a class of
special orthogonal matrix in hyperbolic space, notable for its advantageous properties …

The emergence of COVID-19 in late 2019 in Wuhan, China, has led to a global health crisis
that has claimed many lives worldwide. A thorough understanding of the available COVID …

We consider the optimization problem with a generally quadratic matrix constraint of the form
$ X^ TAX= J $, where $ A $ is a given nonsingular, symmetric $ n\times n $ matrix and $ J …

Abstract Principal Component Analysis technique was applied to correlated multispectral
data to convert it into uncorrelated data for the purpose of benefiting from its use in the …

This thesis develops theory and algorithms for a Riemannian geometric approach to inverse
problems in cryogenic electron microscopy (Cryo-EM). It is divided into two parts, motivated …