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We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…
Solving image inverse problems (e.g., super-resolution and inpainting) requires generating a high fidelity image that matches the given input (the low-resolution image or the masked image). By using the input image as guidance, we can…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…
This work introduces a sampling method capable of solving Bayesian inverse problems in function space. It does not assume the log-concavity of the likelihood, meaning that it is compatible with nonlinear inverse problems. The method…
The choice of prior is central to solving ill-posed imaging inverse problems, making it essential to select one consistent with the measurements $y$ to avoid severe bias. In Bayesian inverse problems, this could be achieved by evaluating…
Diffusion of point-like non interacting particles in a two-dimensional (2D) channel of varying cross section is considered. The particles are biased by a constant force in the transverse direction. We apply our recurrence mapping procedure,…
Existing diffusion-based methods for inverse problems sample from the posterior using score functions and accept the generated random samples as solutions. In applications that posterior mean is preferred, we have to generate multiple…
We consider the inverse problem of denoising an image where each point (pixel) is an element of a target set, which we refer to as a target-valued image. The target sets considered are either (i) a closed convex set of Euclidean space or…
Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…
Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is…
We provide a new perspective on the study of parameterized optimization problems. Our approach combines methods for post-optimal sensitivity analysis and ordinary differential equations to quantify the uncertainty in the minimizer due to…
This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…
We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…
Used as priors for Bayesian inverse problems, diffusion models have recently attracted considerable attention in the literature. Their flexibility and high variance enable them to generate multiple solutions for a given task, such as…
Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…
We present a method to estimate dense depth by optimizing a sparse set of points such that their diffusion into a depth map minimizes a multi-view reprojection error from RGB supervision. We optimize point positions, depths, and weights…
In this paper we propose optimisation methods for variational regularisation problems based on discretising the inverse scale space flow with discrete gradient methods. Inverse scale space flow generalises gradient flows by incorporating a…
We review the problem of finding paths in Cayley graphs of groups and group actions, using the Rubik's cube as an example, and we list several more examples of significant mathematical interest. We then show how to formulate these problems…
Consider a set of discounted optimal stopping problems for a one-parameter family of objective functions and a fixed diffusion process, started at a fixed point. A standard problem in stochastic control/optimal stopping is to solve for the…
In this article, we discuss the numerical solution of diffusion equations on random surfaces within the isogeometric framework. We describe in detail, how diffusion problems on random surfaces can be modelled and how quantities of interest…