Related papers: Internal and external potential-field estimation f…
Vertical land motion (VLM) observations obtained from Interferometric Synthetic Aperture Radar (InSAR) have transformed our understanding of crustal deformation processes over the past 3 decades. However, these observations are often…
Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models…
The non-linearities of the dynamics of Earth artificial satellites are encapsulated by two formal integrals that are customarily computed by perturbation methods. Standard procedures begin with a Hamiltonian simplification that removes…
Hyperspectral imaging has become a significant source of valuable data for astronomers over the past decades. Current instrumental and observing time constraints allow direct acquisition of multispectral images, with high spatial but low…
Seismic waves are the most sensitive probe of the Earth's interior we have. With the dense data sets available in exploration, images of subsurface structures can be obtained through processes such as migration. Unfortunately, relating…
Consider a problem where a set of feasible observations are provided by an expert and a cost function is defined that characterizes which of the observations dominate the others and are hence, preferred. Our goal is to find a set of linear…
Seismic acoustic impedance plays a crucial role in lithological identification and subsurface structure interpretation. However, due to the inherently ill-posed nature of the inversion problem, directly estimating impedance from post-stack…
We present a study of unbiased reconstruction of cosmic microwave background (CMB) polarization maps from data collected by modern ground-based observatories. Atmospheric emission is a major source of correlated noise in such experiments,…
Intra-pixel sensitivity variations (IPSVs) in charge-coupled devices (CCDs) and complementary metal-oxide-semiconductor (CMOS) detectors constitute a significant source of astrometric error for undersampled stellar observations. Since…
A statistical method for reconstructing large scale structure behind the Zone of Avoidance is presented. It also corrects for shot-noise and for redshift distortion in galaxy surveys. The galaxy distribution is expanded in an orthogonal set…
In this paper, we consider the inverse problem of determining the location and the shape of a sound-soft obstacle from the modulus of the far-field data for a single incident plane wave. By adding a reference ball artificially to the…
Purpose: Field monitoring using field probes allows for accurate measurement of magnetic field perturbations, such as from eddy currents, during MRI scanning. However, errors may result when the spatial variation of the fields is not…
We investigate the use of spatial interpolation methods for reconstructing the horizontal near-surface wind field given a sparse set of measurements. In particular, random Fourier features is compared to a set of benchmark methods including…
This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…
High-contrast imaging from space must overcome two major noise sources to successfully detect a terrestrial planet angularly close to its parent star: photon noise from diffracted star light, and speckle noise from star light scattered by…
This paper examines issues of data completion and location uncertainty, popular in many practical PDE-based inverse problems, in the context of option calibration via recovery of local volatility surfaces. While real data is usually more…
This paper considers the recovery of a rank $r$ positive semidefinite matrix $X X^T\in\mathbb{R}^{n\times n}$ from $m$ scalar measurements of the form $y_i := a_i^T X X^T a_i$ (i.e., quadratic measurements of $X$). Such problems arise in a…
In this work, we investigate the inverse problem of recovering a potential coefficient in an elliptic partial differential equation from the observations at deterministic sampling points in the domain subject to random noise. We employ a…
The goal of inversion is to estimate the model which generates the data of observations with a specific modeling equation. One general approach to inversion is to use optimization methods which are algebraic in nature to define an objective…
A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants from scattering data. Potential…