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Inferring 3D structures from sparse, unposed observations is challenging due to its unconstrained nature. Recent methods propose to predict implicit representations directly from unposed inputs in a data-driven manner, achieving promising…
Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. In this paper, we reveal that recent methods can be uniformly interpreted as employing a…
We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To…
Inverse scattering problems, such as those in electromagnetic imaging using phaseless data (PD-ISPs), involve imaging objects using phaseless measurements of wave scattering. Such inverse problems can be highly non-linear and ill-posed…
Inverse problems are prevalent across various disciplines in science and engineering. In the field of computer vision, tasks such as inpainting, deblurring, and super-resolution are commonly formulated as inverse problems. Recently,…
We propose a general framework for conditional sampling in PDE-based inverse problems, targeting the recovery of whole solutions from extremely sparse or noisy measurements. This is accomplished by a function-space diffusion model and…
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…
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…
This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches -- which typically assume full knowledge of the forward model or access to paired degraded and…
In this paper, a general model of wireless channels is established based on the physics of wave propagation. Then the problems of inverse scattering and channel prediction are formulated as nonlinear filtering problems. The solutions to the…
Diffusion models have recently shown considerable potential in solving Bayesian inverse problems when used as priors. However, sampling from the resulting denoising posterior distributions remains a challenge as it involves intractable…
We propose a novel iterative numerical method to solve the three-dimensional inverse obstacle scattering problem of recovering the shape of the obstacle from far-field measurements. To address the inherent ill-posed nature of the inverse…
An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…
Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of…
Geophysical inverse problems are often ill-posed and admit multiple solutions. Conventional discriminative methods typically yield a single deterministic solution, which fails to model the posterior distribution, cannot generate diverse…
We consider a class of inverse problems characterized by forward operators that are partially specified, non-smooth, and non-differentiable. Although generative inverse solvers have made significant progress, we find that these forward…
Seismic data are commonly modeled by a high-frequency single scattering approximation. This amounts to a linearization in the medium coefficient about a smooth background. The discontinuities are contained in the medium perturbation. The…
We consider the inverse scattering problem for inhomogeneous media of compact support governed by the fractional s-Helmholtz equation, with $0<s<1$, in dimensions $d=1,2,3$. In particular, we study the determination of the support of the…
Denoising diffusion models have emerged as the go-to generative framework for solving inverse problems in imaging. A critical concern regarding these models is their performance on out-of-distribution tasks, which remains an under-explored…
This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…