相关论文: Reconstruction of quasi-local numerical effective …
Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…
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 consider the inverse problem of quantitative reconstruction of properties (e.g., bulk modulus, density) of visco-acoustic materials based on measurements of responding waves after stimulation of the medium. Numerical reconstruction is…
We approximate a diffusion equation with highly oscillatory coefficients with a diffusion equation with constant coefficients. The approach is put in action in contexts where only partial information (namely the global energy stored in the…
Computational modelling of diffusion in heterogeneous media is prohibitively expensive for problems with fine-scale heterogeneities. A common strategy for resolving this issue is to decompose the domain into a number of non-overlapping…
Inverse problems arise in a multitude of applications, where the goal is to recover a clean signal from noisy and possibly (non)linear observations. The difficulty of a reconstruction problem depends on multiple factors, such as the ground…
Image reconstruction under multiple light scattering is crucial in a number of applications such as diffraction tomography. The reconstruction problem is often formulated as a nonconvex optimization, where a nonlinear measurement model is…
We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…
In the reconstruction process of unknown multiple scattering objects in inverse medium scattering problems, the first important step is to effectively locate some approximate domains that contain all inhomogeneous media. Without such an…
Optical diffraction tomography relies on solving an inverse scattering problem governed by the wave equation. Classical reconstruction algorithms are based on linear approximations of the forward model (Born or Rytov), which limits their…
The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn…
Most existing MRI reconstruction methods perform tar-geted reconstruction of the entire MR image without tak-ing specific tissue regions into consideration. This may fail to emphasize the reconstruction accuracy on im-portant tissues for…
Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random,…
We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization…
Diffusion models have made remarkable progress in solving various inverse problems, attributing to the generative modeling capability of the data manifold. Posterior sampling from the conditional score function enable the precious data…
We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…
The inverse scattering problem from the multi-frequency backscattering data is a long-standing open problem. We advance the theory by proving a local uniqueness result. Moreover, we introduce a direct sampling method for quantitatively…
We propose to homogenize a periodic (along one direction) structure, first in order to verify the quasi-static prediction of its response to an acoustic wave arising from mixing theory, then to address the question of what becomes of this…
We consider the inverse scattering problem to reconstruct a local perturbation of a given inhomogeneous periodic layer in $\mathbb{R}^d$, $d=2,3$, using near field measurements of the scattered wave on an open set of the boundary above the…
Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also…