Related papers: Quasi-Optimal Filtering in Inverse Problems
Consider a problem where a set of feasible observations are provided by an expert and a cost function is defined that characterizes which of the observations dominate the others and are hence, preferred. Our goal is to find a set of linear…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
Using the simple case of Blasius similarity solution, we illustrate a recently developed general method that reduces a strongly nonlinear problem into a weakly nonlinear analysis. The basic idea is to find a quasi-solution $F_0$ that…
Existing approaches to diffusion-based inverse problem solvers frame the signal recovery task as a probabilistic sampling episode, where the solution is drawn from the desired posterior distribution. This framework suffers from several…
Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement. Using a quantum noise model to describe the stochastic evolution of the open quantum system and working in parallel with classical indeterministic…
The classical approach to inverse problems is based on the optimization of a misfit function. Despite its computational appeal, such an approach suffers from many shortcomings, e.g., non-uniqueness of solutions, modeling prior knowledge,…
We consider the inverse problem of reconstructing an effective model for a prototypical diffusion process in strongly heterogeneous media based on coarse measurements. The approach is motivated by quasi-local numerical effective forward…
This paper addresses the problem of approximating an unknown function from point evaluations. When obtaining these point evaluations is costly, minimising the required sample size becomes crucial, and it is unreasonable to reserve a…
The use of quantum stochastic models is widespread in dynamical reduction, simulation of open systems, feedback control and adaptive estimation. In many applications only part of the information contained in the filter's state is actually…
Likelihood-free (a.k.a. simulation-based) inference problems are inverse problems with expensive, or intractable, forward models. ODE inverse problems are commonly treated as likelihood-free, as their forward map has to be numerically…
The formalism of Wiener filtering is developed here for the purpose of reconstructing the large scale structure of the universe from noisy, sparse and incomplete data. The method is based on a linear minimum variance solution, given data…
The aim of this paper is to provide a variational interpretation of the nonlinear filter in continuous time. A time-stepping procedure is introduced, consisting of successive minimization problems in the space of probability densities. The…
We develop a new statistical model for photographic images, in which the local responses of a bank of linear filters are described as jointly Gaussian, with zero mean and a covariance that varies slowly over spatial position. We optimize…
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…
In this paper, we develop {finite-time horizon} causal filters using the nonanticipative rate distortion theory. We apply the {developed} theory to {design optimal filters for} time-varying multidimensional Gauss-Markov processes, subject…
The likelihood function is a fundamental component in Bayesian statistics. However, evaluating the likelihood of an observation is computationally intractable in many applications. In this paper, we propose a non-parametric approximation of…
In this work, we broadly connect kernel-based filtering (e.g. approaches such as the bilateral filters and nonlocal means, but also many more) with general variational formulations of Bayesian regularized least squares, and the related…
We propose optimal dimensionality reduction techniques for the solution of goal-oriented linear-Gaussian inverse problems, where the quantity of interest (QoI) is a function of the inversion parameters. These approximations are suitable for…
We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…
We study quasi-convex optimization problems, where only a subset of the constraints can be sampled, and yet one would like a probabilistic guarantee on the obtained solution with respect to the initial (unknown) optimization problem. Even…