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Distributed scatterers in InSAR (DS-InSAR) processing are essential for retrieving surface deformation in areas lacking strong point targets. Conventional workflows typically involve selecting statistically homogeneous pixels based on…
We consider the inverse scattering problem of retrieving the structural parameters of a stratified medium consisting of dispersive materials, given knowledge of the complex reflection coefficient in a finite frequency range. It is shown…
This paper is concerned with the inverse random source problem for a stochastic time fractional diffusion equation, where the source is assumed to be driven by a Gaussian random field. The direct problem is shown to be well-posed by…
The inverse scattering problem is of critical importance in a number of fields, including medical imaging, sonar, sensing, non-destructive evaluation, and several others. The problem of interest can vary from detecting the shape to the…
In this article, we study Bayesian inverse problems with multi-layered Gaussian priors. We first describe the conditionally Gaussian layers in terms of a system of stochastic partial differential equations. We build the computational…
This paper is concerned with time domain forward scattering and inverse scattering problems with a single moving point source as the emitter. Approximate solutions are provided for the forward scattering problem with a moving emitter.…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…
We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and…
In this paper we propose and analyse a hybrid numerical-asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of sound-soft nonconvex polygons. The approximation space is enriched…
This paper concerns the random source problems for the time-harmonic acoustic and elastic wave equations in two and three dimensions. The goal is to determine the compactly supported external force from the radiated wave field measured in a…
The problem of obtaining spectral densities from lattice data has been receiving great attention due to its importance in our understanding of scattering processes in Quantum Field Theory, with applications both in the Standard Model and…
Bayesian imaging inverse problems in astrophysics and cosmology remain challenging, particularly in low-data regimes, due to complex forward operators and the frequent lack of well-motivated priors for non-Gaussian signals. In this paper,…
In this paper, we consider two time-harmonic inverse scattering problems of reconstructing penetrable inhomogeneous obstacles from near field measurements. First we appeal to the Born approximation for reconstructing small isotropic…
We present a Newton-like method to solve inverse problems and to quantify parameter uncertainties. We apply the method to parameter reconstruction in optical scatterometry, where we take into account a priori information and measurement…
We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…
Gaussian process regression techniques have been used in fluid mechanics for the reconstruction of flow fields from a reduction-of-dimension perspective. A main ingredient in this setting is the construction of adapted covariance functions,…
In this article, we consider the general task of performing Gaussian process regression (GPR) on pointwise observations of solutions of the 3 dimensional homogeneous free space wave equation.In a recent article, we obtained promising…
Established image recovery methods in fast ultrasound imaging, e.g. delay-and-sum, trade the image quality for the high frame rate. Cutting-edge inverse scattering methods based on compressed sensing (CS) disrupt this tradeoff via a priori…
The characterization of intermittency in turbulence has its roots in the K62 theory, and if no proper definition is to be found in the literature, statistical properties of intermittency were studied and models were developed in attempt to…
Diffusion models have made remarkable progress in solving various inverse problems, attributing to the generative modeling capability of the data manifold. Posterior sampling from the conditional score function enable the precious data…