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In medical SPECT imaging, we seek to simultaneously obtain the internal radioactive sources and the attenuation map using not only ballistic measurements but also first order scattering measurements. The problem is modeled using the…

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…

Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints.…

We consider the inverse problem of denoising an image where each point (pixel) is an element of a target set, which we refer to as a target-valued image. The target sets considered are either (i) a closed convex set of Euclidean space or…

Numerous diffusion model (DM)-based methods have been proposed for solving inverse imaging problems. Among these, a recent line of work has demonstrated strong performance by formulating sampling as an optimization procedure that enforces…

This article proposes diffusion LMS strategies for distributed estimation over adaptive networks that are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing,…

We employ electrostatic conversion drift calculations to match CCD pixel signal covariances observed in flat field exposures acquired using candidate sensor devices for the LSST Camera. We thus constrain pixel geometry distortions present…

In intensity-modulated radiation therapy, optimal intensity distributions of incoming beams are decomposed into linear combinations of leaf openings of a multileaf collimator (segments). In order to avoid inefficient dose delivery, the…

We study nonconvex distributed optimization in multi-agent networks with time-varying (nonsymmetric) connectivity. We introduce the first algorithmic framework for the distributed minimization of the sum of a smooth (possibly nonconvex and…

In this paper the use of nonlinear cross-diffu\-sion systems to model image restoration is investigated, theoretically and numerically. In the first case, well-posedness, scale-space properties and long time behaviour are analyzed. From a…

We give a method for proactively identifying small, plausible shifts in distribution which lead to large differences in model performance. These shifts are defined via parametric changes in the causal mechanisms of observed variables, where…

Atmospheric lidar observations provide a unique capability to directly observe the vertical column of cloud and aerosol scattering properties. Detector and solar background noise, however, hinder the ability of lidar systems to provide…

We analyze a nonlocal diffusion operator having as special cases the fractional Laplacian and fractional differential operators that arise in several applications. In our analysis, a nonlocal vector calculus is exploited to define a weak…

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…

In this paper, we consider a broad class of nonsmooth and nonconvex fractional programs, where the numerator can be written as the sum of a continuously differentiable convex function whose gradient is Lipschitz continuous and a proper…

The subdiffusion model that involves a Caputo fractional derivative in time is widely used to describe anomalously slow diffusion processes. In this work we aim at recovering the locations of small conductivity inclusions in the model from…

We consider the numerical approximation of the ill-posed data assimilation problem for stationary convection-diffusion equations and extend our previous analysis in [Numer. Math. 144, 451--477, 2020] to the convection-dominated regime.…

This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary…

Optimization constrained by high-fidelity computational models has potential for transformative impact. However, such optimization is frequently unattainable in practice due to the complexity and computational intensity of the model. An…

The Diffusion Probabilistic Model (DPM) has recently gained popularity in the field of computer vision, thanks to its image generation applications, such as Imagen, Latent Diffusion Models, and Stable Diffusion, which have demonstrated…