arXiv subjects

Emilia L. K. Blåsten

Publications and source records attributed to Emilia L. K. Blåsten.

5 recordsLinked to original sources

arXiv2026

Mathematical framework for perception-driven parameter choice in image denoising

We approach image denoising from a perception-driven perspective: how can we select the parameters that are best suited for human visual perception? We combine research methods in mathematics and psychology to develop a mathematical framework for measuring perceived similarity. We construct a sample set of differently denoised photographs by using the same base image as input data and by tuning the parameter value in a total variation denoising algorithm. A comparison test is conducted with human participants to survey perceived differences between the images. Analyzing the results with psychometric scaling provides us with a HaarPSI value to use as a threshold in discretizing parameter grids. As a result, we obtain psychometrically scaled, openly available image sets that are ready to use in further experiments in perception-driven imaging, as well as a framework for ensuing experiments involving comparison tests.

eess.IV↗

arXiv2026

Recovering a (1+1)-dimensional wave equation from a single white noise boundary measurement

We consider the following inverse problem: Suppose a $(1+1)$-dimensional wave equation on $\mathbb{R}_+$ with zero initial conditions is excited with a Neumann boundary data modelled as a white noise process. Given also the Dirichlet data at the same point, determine the unknown first order coefficient function of the system. We first establish that direct problem is well-posed. The inverse problem is then solved by showing that correlations of the boundary data determine the Neumann-to-Dirichlet operator in the sense of distributions, which is known to uniquely identify the coefficient. This approach has applications in acoustic measurements of internal cross-sections of fluid pipes such as pressurised water supply pipes and vocal tract shape determination.

math.AP↗

arXiv2025

On the growth properties of interior transmission eigenfunctions near corners

We investigate the localization and vanishing of $L^2$ interior transmission eigenfunctions at corners. Past numerical computations suggest that these eigenfunctions localize at non-convex corners. This phenomenon has, however, not been proven theoretically. We show that localization does indeed occur for some eigenfunctions at a non-convex corner. We also investigate the vanishing of interior transmission eigenfunctions at a convex corner. We prove that these eigenfunctions vanish at convex corners with reduced smoothness assumptions compared to earlier results.

math.AP↗

arXiv2023

The Fourier, Hilbert and Mellin transforms on a half-line

We are interested in the singular behaviour at the origin of solutions to the equation $\mathscr{H} ρ= e$ on a half-axis, where $\mathscr H$ is the one-sided Hilbert transform, $ρ$ an unknown solution and $e$ a known function. This is a simpler model problem on the path to understanding wave field singularities caused by curve-shaped scatterers in a planar domain. We prove that $ρ$ has a singularity of the form $\mathscr M[e](1/2) / \sqrt{t}$ where $\mathscr M$ is the Mellin transform. To do this we use specially built function spaces $\mathscr M'(a,b)$ by Zemanian, and these allow us to precisely investigate the relationship between the Mellin and Hilbert transforms. Fourier comes into play in the sense that the Mellin transform is simpy the Fourier transform on the locally compact Abelian multiplicative group of the half-line, and as a more familiar operator it guides our investigation.

math.AP↗

arXiv2022

On corners scattering stably and stable shape determination by a single far-field pattern

In this paper, we establish two sharp quantitative results for the direct and inverse time-harmonic acoustic wave scattering. The first one is concerned with the recovery of the support of an inhomogeneous medium, independent of its contents, by a single far-field measurement. For this challenging inverse scattering problem, we establish a sharp stability estimate of logarithmic type when the medium support is a polyhedral domain in $\mathbb{R}^n$, $n=2,3$. The second one is concerned with the stability for corner scattering. More precisely if an inhomogeneous scatterer, whose support has a corner, is probed by an incident plane-wave, we show that the energy of the scattered far-field possesses a positive lower bound depending only on the geometry of the corner and bounds on the refractive index of the medium there. This implies the impossibility of approximate invisibility cloaking by a device containing a corner and made of isotropic material. Our results sharply quantify the qualitative corner scattering results in the literature, and the corresponding proofs involve much more subtle analysis and technical arguments. As a significant byproduct of this study, we establish a quantitative Rellich's theorem that continues smallness of the wave field from the far-field up to the interior of the inhomogeneity. The result is of significant mathematical interest for its own sake and is surprisingly not yet known in the literature.

math.AP↗