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Uncertainty quantification plays an important role in achieving trustworthy and reliable learning-based computational imaging. Recent advances in generative modeling and Bayesian neural networks have enabled the development of…
In this paper, we characterize the rectifiability (both uniform and not) of an Ahlfors regular set, E, of arbitrary co-dimension by the behavior of a regularized distance function in the complement of that set. In particular, we establish a…
The analysis of spatial data from biological imaging technology, such as imaging mass spectrometry (IMS) or imaging mass cytometry (IMC), is challenging because of a competitive sampling process which convolves signals from molecules in a…
Let $E \subset \mathbb R^d$, $d \ge 2$, be compact, and let $\phi(x,y)$ be a smooth function satisfying the Phong--Stein rotational curvature condition on $\{\phi(x,y)=1\}$. We prove that if $\dim_{\mathcal H}(E)>1$, then $$…
We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…
Recovering physical properties of objects in motion is a core task across scientific and industrial applications. When the relative motion between the object and the sensing apparatus provides sufficient angular coverage, Computerized…
We propose a Bayesian uncertainty quantification method for large-scale imaging inverse problems. Our method applies to all Bayesian models that are log-concave, where maximum-a-posteriori (MAP) estimation is a convex optimization problem.…
Across many scientific disciplines, multiple observations are collected from the same experimental units, and in modern datasets these observations often arise as non-Euclidean random objects. In such settings, the incorporation of random…
Infinite-dimensional, holomorphic functions have been studied in detail over the last several decades, due to their relevance to parametric differential equations and computational uncertainty quantification. The approximation of such…
A survey is given of recent developments on the resummed small-$x$ evolution, in a framework based on the renormalization group equation, of non--singlet and singlet structure functions in both unpolarized and polarized deep--inelastic…
Finite mixture models are statistical models which appear in many problems in statistics and machine learning. In such models it is assumed that data are drawn from random probability measures, called mixture components, which are…
Statistical systems, in which spontaneous symmetry breaking can be accompanied by spontaneous local symmetry restoration, are considered. A general approach to describing such systems is formulated, based on the notion of weighted Hilbert…
Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…
A classical result of Norbert Wiener characterises doubly shift-invariant subspaces for square integrable functions on the unit circle with respect to a finite positive Borel measure $\mu$, as being the ranges of the multiplication maps…
We consider a conjecture attributed to Muckenhoupt and Wheeden which suggests a positive relationship between the continuity of the Hardy-Littlewood maximal operator and the Hilbert transform in the weighted setting. Although continuity of…
We tensorize the Faber spline system from [14] to prove sequence space isomorphisms for multivariate function spaces with higher mixed regularity. The respective basis coefficients are local linear combinations of discrete function values…
The structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group is related to a notion of Hilbert modules endowed with inner products taking values in spaces of unbounded operators. A…
We propose an estimation approach to analyse correlated functional data which are observed on unequal grids or even sparsely. The model we use is a functional linear mixed model, a functional analogue of the linear mixed model. Estimation…
Identifying when different images are of the same object despite changes caused by imaging technologies, or processes such as growth, has many applications in fields such as computer vision and biological image analysis. One approach to…