Related papers: An iterative method in a probabilistic approach to…
Diffusion models have recently been shown to excel in many image reconstruction tasks that involve inverse problems based on a forward measurement operator. A common framework uses task-agnostic unconditional models that are later…
It is proposed to use apertures with large acceptance angles to reduce the integration time when studying the emissivity of laser induced plasmas by means of the Abel inversion method. The spatial resolution lost due to contributions of…
We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…
A common task in experimental sciences is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modeling). When complex dynamical systems are considered, such as…
Plasma diagnostics often employ computerized tomography to estimate emissivity profiles from a finite, and often limited, number of line-integrated measurements. Decades of algorithmic refinement have brought considerable improvements, and…
In this paper, we consider the inverse problem of determining some coefficients within a coupled nonlinear parabolic system, through boundary observation of its non-negative solutions. In the physical setup, the non-negative solutions…
When using the finite element method (FEM) in inverse problems, its discretization error can produce parameter estimates that are inaccurate and overconfident. The Bayesian finite element method (BFEM) provides a probabilistic model for the…
High-contrast imaging for the detection and characterization of exoplanets relies on the instrument's capability to block out the light of the host star. Some current post-processing methods for calibrating out the residual speckles use…
An imaging refractrometer can be used to describe the properties of a high-energy density plasma by analyzing the transverse intensity distribution of a laser beam that has passed through the plasma. The output of the refractrometer can be…
We analyze coordinated Hinode XRT and EIS observations of a non-flaring active region to investigate the thermal properties of coronal plasma taking advantage of the complementary diagnostics provided by the two instruments. In particular…
We introduce Linearly Constrained Diffusion Implicit Models (CDIM), a fast and accurate approach to solving noisy linear inverse problems using diffusion models. Traditional diffusion-based inverse methods rely on numerous projection steps…
We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…
Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…
The traditional Thomson scattering diagnostic is based on measurement of the wavelength spectrum of scattered light, where electron temperature measurements are inferred from thermal broadening of the scattered laser light. At sufficiently…
In collisional ionization equilibrium (CIE), the X-ray spectrum from a plasma depends on the distribution of emission measure over temperature (DEM). Due to the well-known ill conditioning problem, no precisely resolved DEM can be inverted…
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…
The inverse scattering problem, whose goal is to reconstruct an unknown scattering object from its scattered wave, is essential in fundamental wave physics and its wide applications in imaging sciences. However, it remains challenging to…
In a previous paper we have described a technique to derive constraints on the differential emission measure (DEM) distribution, a measure of the temperature distribution, of collisionally ionized hot plasmas from their X-ray emission line…
Diffusion models have emerged as powerful learned priors for Bayesian inverse problems (BIPs). Diffusion-based solvers rely on a presumed likelihood for the observations in BIPs to guide the generation process. Likelihood misspecification…
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we…