相关论文: Microlocal analysis of a spindle transform
The conserved densities of hydrodynamic type system in Riemann invariants satisfy a system of linear second order partial differential equations. For linear systems of this type Darboux introduced Laplace transformations, generalising the…
We study the effect of marginal and irrelevant deformations on the renormalization of operators near a CFT fixed point. New divergences in a given operator are determined by its OPE with the operator D that generates the deformation. This…
Fredholm-type backstepping transformation, introduced by Coron and L\"u, has become a powerful tool for rapid stabilization with fast development over the last decade. Its strength lies in its systematic approach, allowing to deduce rapid…
This thesis is concerned with problems related to Synthetic Aperture Radar (SAR). The thesis is structured as follows: The first chapter explains what SAR is, and the physical and mathematical background is illuminated. The following…
This work proposes a very simple random matrix model, the Flip Matrix Model, liable to approximate the behavior of a two dimensional electron in a weak random potential. Its construction is based on a phase space analysis, a suitable…
Non-stationary signals are ubiquitous in real life. Many techniques have been proposed in the last decades which allow decomposing multi-component signals into simple oscillatory mono-components, like the groundbreaking Empirical Mode…
We study the renormalization group flow of the Lagrangian for statistical and quantum systems by representing their path integral in terms of a tensor network. Using a tensor-entanglement-filtering renormalization (TEFR) approach that…
Motivated by applications in unmanned aerial based ground penetrating radar for detecting buried landmines, we consider the problem of imaging small point like scatterers situated in a lossy medium below a random rough surface. Both the…
The light field reconstruction from the focal stack can be mathematically formulated as an ill-posed integral equation inversion problem. Although the previous research about this problem has made progress both in practice and theory, its…
When modeling propagation and scattering phenomena using integral equations discretized by the boundary element method, it is common practice to approximate the boundary of the scatterer with a mesh comprising elements of size approximately…
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…
Set representations are the foundation of various set-based approaches in state estimation, reachability analysis and fault diagnosis. In this paper, we investigate spectrahedral shadows, a class of nonlinear geometric objects previously…
This note investigates the explicit convergence rates of nonlocal peridynamic operators to their classical (local) counterparts in $L^q$-norm. Previous results used Fourier series and hence were restricted to showing convergence in $L^2$.…
A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…
The theory of sampling and the reconstruction of data has a wide range of applications and a rich collection of techniques. For many methods a core problem is the estimation of the number of samples needed in order to secure a stable and…
In this work, we consider the problem of reconstructing the shape of a three dimensional impenetrable sound-soft axis-symmetric obstacle from measurements of the scattered field at multiple frequencies. This problem has important…
Generative models have demonstrated significant success in anomaly detection and segmentation over the past decade. Recently, diffusion models have emerged as a powerful alternative, outperforming previous approaches such as GANs and VAEs.…
We introduce a deep learning (DL) framework for inverse problems in imaging, and demonstrate the advantages and applicability of this approach in passive synthetic aperture radar (SAR) image reconstruction. We interpret image recon-…
The Landauer "residual resistivity dipole" is a well-known concept in electron transport through a disordered medium. It is formed when a defect/scatterer reflects an impinging electron causing negative charges to build up on one side of…
The purpose of this article is to investigate the structure of singular measures from a microlocal perspective. Motivated by the result of De Philippis-Rindler [10] and the notions of wave cone of Murat-Tartar [19,20,26,27] and of…