Related papers: Applying Bayesian Inference and deterministic anis…
Beamforming in ultrasound imaging has significant impact on the quality of the final image, controlling its resolution and contrast. Despite its low spatial resolution and contrast, delay-and-sum is still extensively used nowadays in…
Ultrashort laser pulses enable attosecond-scale measurements and drive breakthroughs across science and technology, but their routine use hinges on reliable pulse characterization. Frequency-Resolved Optical Gating (FROG) is a leading…
In many signal processing problems arising in practical applications, we wish to reconstruct an unknown signal from its phaseless measurements with respect to a frame. This inverse problem is known as the phase retrieval problem. For each…
Laser-induced electron diffraction is an evolving tabletop method, which aims to image ultrafast structural changes in gas-phase polyatomic molecules with sub-{\AA}ngstr\"om spatial and femtosecond temporal resolution. Here, we provide the…
Inferring unknown initial states in shock-dominated compressible flows from sparse and noisy measurements is a challenging ill-posed inverse problem due to nonlinear wave interactions and limited sensing. In this work, we develop a…
In this paper, we propose a novel Bayesian approach for nonparametric estimation in Wicksell's problem. This has important applications in astronomy for estimating the distribution of the positions of the stars in a galaxy given projected…
The inverse approach is computationally efficient in aerodynamic design as the desired target performance distribution is prespecified. However, it has some significant limitations that prevent it from achieving full efficiency. First, the…
This study presents a noise-robust framework for 1-bit diffraction tomography, a novel imaging approach that relies on intensity-only binary measurements obtained through coded apertures. The proposed reconstruction scheme leverages random…
Diffusion magnetic resonance imaging datasets suffer from low Signal-to-Noise Ratio, especially at high b-values. Acquiring data at high b-values contains relevant information and is now of great interest for microstructural and…
Parameter estimation of gravitational wave data is often computationally expensive, requiring simplifying assumptions such as circularisation of binary orbits. Although, if included, the sub-dominant effects like orbital eccentricity may…
We address the feasibility of imaging geometric and orbital structure of a polyatomic molecule on an attosecond time-scale using the laser induced electron diffraction (LIED) technique. We present numerical results for the highest molecular…
Infrared Reflection Absorption Spectroscopy (IRAS) on dielectric single crystals is challenging because the optimal incidence angles for light-adsorbate interaction coincide with regions of low IR reflectivity. Here, we introduce an…
We formulate and investigate a statistical inverse problem of a random tomographic nature, where a probability density function on $\mathbb{R}^3$ is to be recovered from observation of finitely many of its two-dimensional projections in…
Deconvolution of astronomical images is a key aspect of recovering the intrinsic properties of celestial objects, especially when considering ground-based observations. This paper explores the use of diffusion models (DMs) and the Diffusion…
We formulate and solve a Bayesian inverse Navier-Stokes (N-S) problem that assimilates velocimetry data in order to jointly reconstruct a 3D flow field and learn the unknown N-S parameters, including the boundary position. By hardwiring a…
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…
The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in…
Nonlinear stochastic motion presents significant challenges for Bayesian particle tracking. To address this challenge, this paper proposes a framework to construct an invertible transformation that maps the nonlinear state-space model (SSM)…
The resonant nonlinear refraction of 4-5 $\mu$m light in CO and CO$_2$ gas at a peak intensity of 15 MW/cm$^2$ was demonstrated using time- and frequency-resolved measurements of self-focusing and self-defocusing. The nonlinearity of these…
We consider the high energy physics unfolding problem where the goal is to estimate the spectrum of elementary particles given observations distorted by the limited resolution of a particle detector. This important statistical inverse…