Related papers: Diffuse Interface Methods for Inverse Problems: Ca…
We investigate the convergence rates of variational posterior distributions for statistical inverse problems involving nonlinear partial differential equations (PDEs). Departing from exact Bayesian inference, variational inference…
This paper presents CQT-Diff, a data-driven generative audio model that can, once trained, be used for solving various different audio inverse problems in a problem-agnostic setting. CQT-Diff is a neural diffusion model with an architecture…
Boundary integral methods are attractive for solving homogeneous linear constant coefficient elliptic partial differential equations on complex geometries, since they can offer accurate solutions with a computational cost that is linear or…
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
Diffusion models have become a popular approach for image generation and reconstruction due to their numerous advantages. However, most diffusion-based inverse problem-solving methods only deal with 2D images, and even recently published 3D…
A nonlinear optimization method is proposed for the solution of inverse medium problems with spatially varying properties. To avoid the prohibitively large number of unknown control variables resulting from standard grid-based…
A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants from scattering data. Potential…
We present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated as shape optimization prob- lems whose objective…
In this paper, we consider inverse shape problems coming from diffuse optical tomography and inverse scattering. In both problems, our goal is to reconstruct small volume interior regions from measured data on the exterior surface of an…
The forward problem here is the Cauchy problem for a 1D hyperbolic PDE with a variable coefficient in the principal part of the operator. That coefficient is the spatially distributed dielectric constant. The inverse problem consists of the…
We analyse a diffuse interface type approximation, known as the diffuse domain approach, of a linear coupled bulk-surface elliptic partial differential system. The well-posedness of the diffuse domain approximation is shown using weighted…
The Bayesian approach to inverse problems provides a practical way to solve ill-posed problems by augmenting the observation model with prior information. Due to the measure-theoretic underpinnings, the approach has raised theoretical…
We consider inverse problems estimating distributed parameters from indirect noisy observations through discretization of continuum models described by partial differential or integral equations. It is well understood that the errors…
Recently it has been shown that using diffusion models for inverse problems can lead to remarkable results. However, these approaches require a closed-form expression of the degradation model and can not support complex degradations. To…
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…
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…
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…
Diffuse domain methods (DDMs) have gained significant attention for solving partial differential equations (PDEs) on complex geometries. These methods approximate the domain by replacing sharp boundaries with a diffuse layer of thickness…
In recent years we have witnessed a growth in mathematics for deep learning, which has been used to solve inverse problems of partial differential equations (PDEs). However, most deep learning-based inversion methods either require paired…
A problem of a wave identification is formulated. An example is considered in conditions of one-dimensional Cauchy problem for conventional string equation in matrix form and its inhomogeneous two-component version. The acoustic and…