Related papers: Stabilities of Shape Identification Inverse Proble…
Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…
We consider the inverse problem of determining an electromagnetic potential appearing in an infinite cylindrical domain from boundary measurements. More precisely, we prove the stable recovery of some general class of magnetic field and…
Many inverse problems arising in engineering and applied sciences involve unknown quantities with pronounced spatial inhomogeneity, such as localized defects or spatially varying material properties, making reliable uncertainty…
Recent advances in reconstruction methods for inverse problems leverage powerful data-driven models, e.g., deep neural networks. These techniques have demonstrated state-of-the-art performances for several imaging tasks, but they often do…
This paper extends the work of Clarke [1] on the Bayesian foundations of the biomagnetic inverse problem. It derives expressions for the expectation and variance of the a posteriori source current probability distribution given a prior…
We introduce a level set based approach to Bayesian geometric inverse problems. In these problems the interface between different domains is the key unknown, and is realized as the level set of a function. This function itself becomes the…
Inverse design of morphing slender structures with programmable curvature has significant applications in various engineering fields. Most existing studies formulate it as an optimization problem, which requires repeatedly solving the…
In electrocardiography, the "classic" inverse problem is the reconstruction of electric potentials at a surface enclosing the heart from remote recordings at the body surface and an accurate description of the anatomy. The latter being…
We consider optimal sensor placement for hyper-parameterized linear Bayesian inverse problems, where the hyper-parameter characterizes nonlinear flexibilities in the forward model, and is considered for a range of possible values. This…
We consider the problem of determining the unknown boundary values of a solution of an elliptic equation outside a bounded open set $B$ from the knowledge of the values of this solution on a boundary of an arbitrary Lipschitz bounded domain…
We consider an inverse problem of identifying the unknown cavities in a heat conductor. Using the Neumann-to-Dirichlet map as an input data, we develop a linear sampling type method for the heat equation. A new feature is that there is a…
This paper suggests a framework for the learning of discretizations of expensive forward models in Bayesian inverse problems. The main idea is to incorporate the parameters governing the discretization as part of the unknown to be estimated…
In inverse problems, we often have access to data consisting of paired samples $(x,y)\sim p_{X,Y}(x,y)$ where $y$ are partial observations of a physical system, and $x$ represents the unknowns of the problem. Under these circumstances, we…
The classical Calder\'on problem with partial data is known to be log-log stable in some special cases, but even the uniqueness problem is open in general. We study the partial data stability of an analogous inverse fractional conductivity…
This paper is concerned with a Bayesian approach to testing hypotheses in statistical inverse problems. Based on the posterior distribution $\Pi \left(\cdot |Y = y\right)$, we want to infer whether a feature $\langle\varphi,…
Generally, the normal displacement-based formation control has a sensing mode that requires the agent not only to have certain knowledge of its direction, but also to gather its local information characterized by nonnegative coupling…
Posterior distributions arising in ill-posed Bayesian inverse problems are often both analytically intractable and highly sensitive to parameters of the chosen prior family. We aim to understand the sensitivity of intractable posterior…
A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which…
Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in…
We develop and implement a Bayesian approach for the estimation of the shape of a two dimensional annular domain enclosing a Stokes flow from sparse and noisy observations of the enclosed fluid. Our setup includes the case of direct…