63 citations · 200 across the 10 of their papers we have counts for
13 papers
Variational Multiscale Nonparametric Regression: Algorithms and Implementation
Miguel del Alamo, Housen Li, Axel Munk +1
Many modern statistically efficient methods come with tremendous computational challenges, often leading to large-scale optimisation problems. In this work, we examine such computa…
What is resolution? A statistical minimax testing perspective on super-resolution microscopy
Gytis Kulaitis, Axel Munk, Frank Werner
As a general rule of thumb the resolution of a light microscope (i.e. the ability to discern objects) is predominantly described by the full width at half maximum (FWHM) of its poi…
A photomultiplier tube test stand and on-site measurements to characterise the performance of Photonis XP3062 photomultiplier tubes at increased background light conditions and lower gain
J. Zorn, K. Daumiller, R. Engel +4
Photomultiplier tubes (PMTs) are widely used in astroparticle physics experiments to detect light flashes (e.g. fluorescence or Cherenkov light) from extensive air showers (EASs) i…
Bump detection in the presence of dependency: Does it ease or does it load?
Farida Enikeeva, Axel Munk, Markus Pohlmann +1
We provide the asymptotic minimax detection boundary for a bump, i.e. an abrupt change, in the mean function of a stationary Gaussian process. This will be characterized in terms o…
Convergence Analysis of (Statistical) Inverse Problems under Conditional Stability Estimates
Frank Werner, Bernd Hofmann
Conditional stability estimates require additional regularization for obtaining stable approximate solutions if the validity area of such estimates is not completely known. In this…
Multidimensional multiscale scanning in Exponential Families: Limit theory and statistical consequences
Claudia König, Axel Munk, Frank Werner
We consider the problem of finding anomalies in a -dimensional field of independent random variables , each distributed according to a…
Empirical Risk Minimization as Parameter Choice Rule for General Linear Regularization Methods
Housen Li, Frank Werner
We consider the statistical inverse problem to recover from noisy measurements where is Gaussian white noise and a compact operator between Hilbert spaces…
Multiscale scanning in inverse problems
Katharina Proksch, Frank Werner, Axel Munk
In this paper we propose a multiscale scanning method to determine active components of a quantity w.r.t. a dictionary from observations in an inverse regress…
Convergence Rates for Exponentially Ill-Posed Inverse Problems with Impulsive Noise
Claudia König, Frank Werner, Thorsten Hohage
This paper is concerned with exponentially ill-posed operator equations with additive impulsive noise on the right hand side, i.e. the noise is large on a small part of the domain…
Bump detection in heterogeneous Gaussian regression
Farida Enikeeva, Axel Munk, Frank Werner
We analyze the effect of a heterogeneous variance on bump detection in a Gaussian regression model. To this end we allow for a simultaneous bump in the variance and specify its imp…
Convergence Rates for Inverse Problems with Impulsive Noise
Thorsten Hohage, Frank Werner
We study inverse problems F(f) = g with perturbed right hand side g^{obs} corrupted by so-called impulsive noise, i.e. noise which is concentrated on a small subset of the domain o…
Convergence rates in expectation for Tikhonov-type regularization of Inverse Problems with Poisson data
Frank Werner, Thorsten Hohage
In this paper we study a Tikhonov-type method for ill-posed nonlinear operator equations $\gdag = F(\udag)$ where $\gdag$ is an integrable, non-negative function. We assume that da…
Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data
Thorsten Hohage, Frank Werner
We study Newton type methods for inverse problems described by nonlinear operator equations in Banach spaces where the Newton equations ar…