Related papers: Microlocal aspects of bistatic synthetic aperture …
In this article, we analyze the microlocal properties of the linearized forward scattering operator $F$ and the normal operator $F^{*}F$ (where $F^{*}$ is the $L^{2}$ adjoint of $F$) which arises in Synthetic Aperture Radar imaging for the…
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…
Here we present a novel microlocal analysis of generalized Radon transforms which describe the integrals of $L^2$ functions of compact support over surfaces of revolution of $C^{\infty}$ curves $q$. We show that the Radon transforms are…
We present novel microlocal and injectivity analyses of ellipsoid and hyperboloid Radon transforms. We introduce a new Radon transform, $R$, which defines the integrals of a compactly supported $L^2$ function, $f$, over ellipsoids and…
We study the existence and suppression of artifacts for a Doppler-based Synthetic Aperture Radar (DSAR) system. The idealized air- or space-borne system transmits a continuous wave at a fixed frequency and a co-located receiver measures the…
Synthetic aperture radar (SAR) can measure the phase with antenna and microwave, which cannot be directly extended to visible light imaging due to phase lost. In this letter, we reported an active remote sensing with visible light via…
We consider a linearized inverse problem, arising in offshore seismic exploration, for an isotropic wave equation with sound speed assumed to be a small, singular perturbation of a smooth background. Under an assumption of at most fold…
We present a novel microlocal analysis of a non-linear ray transform, $\mathcal{R}$, arising in Compton Scattering Tomography (CST). Due to attenuation effects in CST, the integral weights depend on the reconstruction target, $f$, which has…
In the analysis of many synthetic aperture radar (SAR) experiments the possibility of passive background signals being recorded simultaneously and corrupting the image is often overlooked. Our work addresses this by considering the…
We give a detailed microlocal study of X-ray transforms over geodesics-like families of curves with conjugate points of fold type. We show that the normal operator is the sum of a pseudodifferential operator and a Fourier integral operator.…
An analysis of the stability of the spindle transform, introduced in ("Three dimensional Compton scattering tomography" arXiv:1704.03378 [math.FA]), is presented. We do this via a microlocal approach and show that the normal operator for…
Given a smooth embedding of manifolds $i: X \hookrightarrow M$ and a Fourier integral operator $\Phi$ acting on $M$, obtained by quantization of a canonical transformation, consider its trace $i^!(\Phi)$ on $X$ (in the sense of relative…
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…
Based on a plane-wave expansion of the observation data in quasi-planar multi-static scattering scenarios, an improved formalism for image creation utilizing back-projection in the spatial domain is derived. The underlying integral…
We establish sharp $L^2$-Sobolev estimates for classes of pseudodifferential operators with singular symbols whose non-pseudodifferential (Fourier integral operator) parts exhibit two-sided fold singularities. The operators considered…
This letter proposes a synthetic aperture radar (SAR) image registration method named Feature-Area Optimization (FAO). First, the traditional area-based optimization model is reconstructed and decomposed into three key but uncertain…
Let $\omega ,\omega_0$ be appropriate weight functions and $q\in [1,\infty ]$. We introduce the wave-front set, $\WF_{\mathscr FL^q_{(\omega)}}(f)$ of $f\in \mathscr S'$ with respect to weighted Fourier Lebesgue space $\mathscr…
Fourier ptychography (FP) is a powerful light-based synthetic aperture imaging technique that allows one to reconstruct a high-resolution, wide field-of-view image by computationally integrating a diverse collection of low-resolution,…
We establish a general result about the recovery of the analytic wavefront set of a distribution from the analytic wavefront set of its transform coming from a classical elliptic analytic Fourier integral operator (FIO) satisfying some…
Synthetic aperture radar (SAR) is a tomographic sensor that measures 2D slices of the 3D spatial Fourier transform of the scene. In many operational scenarios, the measured set of 2D slices does not fill the 3D space in the Fourier domain,…