相关论文: Microlocal analysis of a spindle transform
In this paper, we study the inverse random source scattering problem for the biharmonic Schrodinger equation in two and three dimensions. The driven source is assumed to be a generalized microlocally isotropic Gaussian random function whose…
In this paper, we consider the Forward--Backward proximal splitting algorithm to minimize the sum of two proper convex functions, one of which having a Lipschitz continuous gradient and the other being partly smooth relative to an active…
The translation of an operator is defined by using conjugation with time-frequency shifts. Thus, one can define $\Lambda$-shift-invariant subspaces of Hilbert-Schmidt operators, finitely generated, with respect to a lattice $\Lambda$ in…
The data-driven reduced order models (ROMs) have recently emerged as an efficient tool for the solution of the inverse scattering problems with applications to seismic and sonar imaging. One specification of this approach is that it…
We present an alternative proof of the result by P. Gerard and S. Grellier, stating that given two real sequences $(\lambda_n)_{n=1}^\infty$, $(\mu_n)_{n=1}^\infty$ satisfying the intertwining relations \[ |\lambda_1| > |\mu_1| >…
In this work, we are devoted to the reconstruction of an unknown initial value from the terminal data. The asymptotic and root-distribution properties of Mittag-Leffler functions are used to establish stability of the backward problem.…
First we recall the definition of locally residual currents and their basic properties. We prove in this first section a trace theorem, that we use later. Then we define the Abel-Radon transform of a current ${\cal R}(\alpha)$, on a…
We use microlocal radial estimates to prove the full limiting absorption principle for $P$, a self-adjoint 0th order pseudodifferential operator satisfying hyperbolic dynamical assumptions as of Colin de Verdi\`ere and Saint-Raymond. We…
We analyse an operator arising in the description of singular solutions to the two-dimensional Keller-Segel problem. It corresponds to the linearised operator in parabolic self-similar variables, close to a concentrated stationary state.…
Given a compact surface of revolution with Laplace-beltrami operator $\Delta$, we consider the spectral projector $P_{\lambda,\delta}$ on a polynomially narrow frequency interval $[\lambda-\delta,\lambda + \delta]$, which is associated to…
We employ techniques from optimal transport in order to prove decay of transfer operators associated to iterated functions systems and expanding maps, giving rise to a new proof without requiring a Doeblin-Fortet (or Lasota-Yorke)…
In this article, we consider two bistatic cases arising in synthetic aperture radar imaging: when the transmitter and receiver are both moving with different speeds along a single line parallel to the ground in the same direction or in the…
Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the…
This paper studies a prototype of inverse obstacle scattering problems whose governing equation is the Helmholtz equation in two dimensions. An explicit method to extract information about the location and shape of unknown obstacles from…
The two-dimensional Radon transform of the Wigner quasiprobability is introduced in canonical form and the functions playing a role in its inversion are discussed. The transformation properties of this Radon transform with respect to…
Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two…
We consider the application of a subspace migration (SM) algorithm to quickly identify small objects in microwave imaging. In various problems, it is easy to measure the diagonal elements of the scattering matrix if the location of the…
Mapping land surface disturbances supports disaster response, resource and ecosystem management, and climate adaptation efforts. Synthetic aperture radar (SAR) is an invaluable tool for disturbance mapping, providing consistent time-series…
In this paper we develop a general, systematic, microlocal framework for the Fredholm analysis of non-elliptic problems, including high energy (or semiclassical) estimates, which is stable under perturbations. This framework is relatively…
A recent Faraday wave experiment with two-frequency forcing reports two types of `superlattice' patterns that display periodic spatial structures having two separate scales [1]. These patterns both arise as secondary states once the primary…