21 citations · 57 across the 10 of their papers we have counts for
11 papers
Random tree Besov priors: Data-driven regularisation parameter selection
Hanne Kekkonen, Andreas Tataris
We develop a data-driven algorithm for automatically selecting the regularisation parameter in Bayesian inversion under random tree Besov priors. One of the key challenges in Bayes…
Crocheting Mathematics
Hanne Kekkonen
Crochet provides a superior method for the production of two-dimensional surfaces from one-dimensional material. Compared to any of the other known processes to generate constant f…
Crocheting Bour's minimal surfaces
Hanne Kekkonen
Minimal surfaces can be though as a mathematical generalisation of surfaces formed by soap films. We consider Bour's minimal surfaces that are intrinsically surface…
Exploring Mathematics with Curvagon Tiles
Hanne Kekkonen
Building blocks and tiles are an excellent way of learning about geometry and mathematics in general. There are several versions of tiles that are either snapped together or connec…
Do the Angles of a Triangle Add up to 180°? -- Introducing Non-Euclidean Geometry
Hanne Kekkonen
How can we convince students, who have mainly learned to follow given mathematical rules, that mathematics can also be fascinating, creative, and beautiful? In this paper I discuss…
Consistency of Bayesian inference with Gaussian process priors for a parabolic inverse problem
Hanne Kekkonen
We consider the statistical nonlinear inverse problem of recovering the absorption term in the heat equation $$ \partial_tu-\frac{1}{2}Δu+fu=0 \quad \text{on $\mathcal{O}\tim…
Random tree Besov priors -- Towards fractal imaging
Hanne Kekkonen, Matti Lassas, Eero Saksman +1
We propose alternatives to Bayesian a priori distributions that are frequently used in the study of inverse problems. Our aim is to construct priors that have similar good edge-pre…
Bernstein-von Mises theorems and uncertainty quantification for linear inverse problems
Matteo Giordano, Hanne Kekkonen
We consider the statistical inverse problem of recovering an unknown function from a linear measurement corrupted by additive Gaussian white noise. We employ a nonparametric Ba…
Large Noise in Variational Regularization
Martin Burger, Tapio Helin, Hanne Kekkonen
In this paper we consider variational regularization methods for inverse problems with large noise that is in general unbounded in the image space of the forward operator. We intro…
Posterior consistency and convergence rates for Bayesian inversion with hypoelliptic operators
Hanne Kekkonen, Matti Lassas, Samuli Siltanen
Bayesian approach to inverse problems is studied in the case where the forward map is a linear hypoelliptic pseudodifferential operator and measurement error is additive white Gaus…
Analysis of regularized inversion of data corrupted by white Gaussian noise
Hanne Kekkonen, Matti Lassas, Samuli Siltanen
Tikhonov regularization is studied in the case of linear pseudodifferential operator as the forward map and additive white Gaussian noise as the measurement error. The measurement…