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This paper develops a class of Bayesian non- and semiparametric methods for estimating regression curves and surfaces. The main idea is to model the regression as locally linear, and then place suitable local priors on the local parameters.…
Large-scale inhomogeneities and anisotropies are modeled using the Long Wavelength Iteration Scheme. In this scheme solutions are obtained as expansions in spatial gradients, which are taken to be small. It is shown that the choice of…
Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries…
The numerical analysis of elastic wave propagation in unbounded media may be difficult to handle due to spurious waves reflected at the model artificial boundaries. Several sophisticated techniques such as nonreflecting boundary conditions,…
In this paper, we consider a problem inspired by the real-world need to identify the topographical features of ocean basins. Specifically we consider the problem of estimating the bottom impermeable boundary to an inviscid, incompressible,…
The 2D phase unwrapping problem seeks to recover a phase image from its observation modulo 2$\pi$, and is a crucial step in a variety of imaging applications. In particular, it is one of the most time-consuming steps in the interferometric…
Mapping the seafloor with underwater imaging cameras is of significant importance for various applications including marine engineering, geology, geomorphology, archaeology and biology. For shallow waters, among the underwater imaging…
Elongated anisotropic Gaussian filters are used for the orientation estimation of fibers. In cases where computed tomography images are noisy, roughly resolved, and of low contrast, they are the method of choice even if being efficient only…
This paper is concerned with a space-time adaptive numerical method for instationary porous media flows with nonlinear interaction between porosity and pressure, with focus on problems with discontinuous initial porosities. A convergent…
Posterior distributions on parameters computed from experimental data using Bayesian techniques are only as accurate as the models used to construct them. In many applications these models are incomplete, which both reduces the prospects of…
Multi-azimuth walkaway vertical seismic profiling (VSP) is an established technique for the estimation of in situ slowness surfaces and inferring anisotropy parameters. Normally, this the technique requires the assumption of lateral…
An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…
This work develops a unified framework for inferring, representing, and statistically characterizing an anisotropic strength surface directly from molecular dynamics data. Large-scale tensile loading simulations are used to generate failure…
Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they…
Purpose: Undersampling is used to reduce the scan time for high-resolution 3D magnetic resonance imaging. In order to achieve better image quality and avoid manual parameter tuning, we propose a probabilistic Bayesian approach to recover…
This paper proposes a new Bayesian strategy for the smooth estimation of altimetric parameters. The altimetric signal is assumed to be corrupted by a thermal and speckle noise distributed according to an independent and non identically…
Mechanical stress within biological tissue can indicate an anomaly, or can be vital of its function, such as stresses in arteries. Measuring these stresses in tissue is challenging due to the complex, and often unknown, nature of the…
In the context of the ultrasonic determination of mechanical properties, it is common to use oblique incident waves to characterize fluid-immersed anisotropic samples. The lateral displacement of the ultrasonic field owing to leaky guided…
This study analyzes steady periodic hydroelastic waves propagating on the water surface of finite depth beneath nonlinear elastic membranes. Unlike previous work \cite{BaldiT,BaldiT1,Toland,Toland1}, our formulation accommodates rotational…
We give uniqueness theorem and reconstruction algorithm for the nonlinearized problem of finding the dielectric anisotropy f of the medium from non-overdetermined polarization tomography data. We assume that the medium has uniform…