Related papers: Applying Bayesian Inference and deterministic anis…
Phase retrieval (PR), also sometimes referred to as quadratic sensing, is a problem that occurs in numerous signal and image acquisition domains ranging from optics, X-ray crystallography, Fourier ptychography, sub-diffraction imaging, and…
Experimentally obtained X-ray diffraction (XRD) patterns can be difficult to solve, precluding the full characterization of materials, pharmaceuticals, and geological compounds. Herein, we propose a method based upon a multi-objective…
Within the framework of linear elasticity we assume the availability of internal full-field measurements of the continuum deformations of a non-homogeneous isotropic solid. The aim is the quantitative reconstruction of the associated…
We have previously reported a Bayesian algorithm for determining the coordinates of points in three-dimensional space from uncertain constraints. This method is useful in the determination of biological molecular structure. It is limited,…
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…
Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in…
Inverse problems in physical or biological sciences often involve recovering an unknown parameter that is random. The sought-after quantity is a probability distribution of the unknown parameter, that produces data that aligns with…
We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…
Recent experiments at free-electron laser x-ray sources have been able to resolve the intensity distributions about Bragg peaks in nanocrystals of large biomolecules. Information derived from small shifts in the peak positions augment the…
One emerging approach for the fabrication of complex architectures on the nanoscale is to utilize particles customized to intrinsically self-assemble into a desired structure. Inverse methods of statistical mechanics have proven…
Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…
Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…
Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…
In ill-posed inverse problems, it is commonly desirable to obtain insight into the full spectrum of plausible solutions, rather than extracting only a single reconstruction. Information about the plausible solutions and their likelihoods is…
We consider a popular nonsmooth formulation of the real phase retrieval problem. We show that under standard statistical assumptions, a simple subgradient method converges linearly when initialized within a constant relative distance of an…
The instantaneous two-dimensional wall shear rate is assessed through an inverse problem using mass transfer data from a three-segment electrodiffusion probe. The method is validated numerically in complex flow conditions involving (i) high…
We address the inverse problem of cosmic large-scale structure reconstruction from a Bayesian perspective. For a linear data model, a number of known and novel reconstruction schemes, which differ in terms of the underlying signal prior,…
We consider the inverse problem of estimating parameters of a driven diffusion (e.g., the underlying fluid flow, diffusion coefficient, or source terms) from point measurements of a passive scalar (e.g., the concentration of a pollutant).…
Ptychography is an imaging technique which involves a sample being illuminated by a coherent, localized probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the…
Procedural material models have been gaining traction in many applications thanks to their flexibility, compactness, and easy editability. We explore the inverse rendering problem of procedural material parameter estimation from…