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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 gained traction as a powerful class of deep generative priors, excelling in a wide range of image restoration tasks due to their exceptional ability to model data distributions. To solve image restoration…
Here we introduce a new reconstruction technique for two-dimensional Bragg Scattering Tomography (BST), based on the Radon transform models of [arXiv preprint, arXiv:2004.10961 (2020)]. Our method uses a combination of ideas from multibang…
This paper aims to solve numerically the two-dimensional inverse medium scattering problem with far-field data. This is a challenging task due to the severe ill-posedness and strong nonlinearity of the inverse problem. As already known, it…
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…
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…
A deep learning-assisted inversion method is proposed to solve the inhomogeneous background imaging problem. Three non-iterative methods, namely the distorted-Born (DB) major current coefficients method, the DB modified Born approximation…
The problem of reconstructing an object from the measurements of the light it scatters is common in numerous imaging applications. While the most popular formulations of the problem are based on linearizing the object-light relationship,…
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…
Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance.…
A two-step shape reconstruction method for diffuse optical tomography (DOT) is presented which uses adjoint fields and level sets. The propagation of near-infrared photons in tissue is modeled by the time-dependent linear transport…
The dose of X-ray radiation and the scanning time are crucial factors in computed tomography (CT) for clinical applications. In this work, we introduce a multi-source static CT imaging system designed to rapidly acquire sparse view and…
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…
Magnetic Resonance (MR) image reconstruction from under-sampled acquisition promises faster scanning time. To this end, current State-of-The-Art (SoTA) approaches leverage deep neural networks and supervised training to learn a recovery…
We introduce Diffusion Active Learning, a novel approach that combines generative diffusion modeling with data-driven sequential experimental design to adaptively acquire data for inverse problems. Although broadly applicable, we focus on…
Diffusion models have established new state of the art in a multitude of computer vision tasks, including image restoration. Diffusion-based inverse problem solvers generate reconstructions of exceptional visual quality from heavily…
This paper proposes a novel approach to spectral computed tomography (CT) material decomposition that uses the recent advances in generative diffusion models (DMs) for inverse problems. Spectral CT and more particularly photon-counting CT…
We develop an imaging algorithm that exploits strong scattering to achieve super-resolution in changing random media. The method processes large and diverse array datasets using sparse dictionary learning, clustering, and multidimensional…
This paper is concerned with the inverse scattering problem by an unbounded rough surface. A direct imaging method is proposed to reconstruct the rough surface from the scattered near-field Cauchy data generating by point sources and…
Inverse problems, such as accelerated MRI reconstruction, are ill-posed and an infinite amount of possible and plausible solutions exist. This may not only lead to uncertainty in the reconstructed image but also in downstream tasks such as…