Recovery of wave speeds and density of mass across a heterogeneous smooth interface from acoustic and elastic wave reflection operators

Photoacoustic Tomography in a Rectangular Reflecting Cavity

Almost all known image reconstruction algorithms for photoacoustic and thermoacoustic tomography assume that the acoustic waves leave the region of interest after a finite time. This assumption is reasonable if the reflections from the detectors and surrounding surfaces can be neglected or filtered out (for example, by time-gating). However, when the object is surrounded by acoustically hard detector arrays, and/or by additional acoustic mirrors, the acoustic waves will undergo multiple reflections. (In the absence of absorption they would bounce around in such a reverberant cavity forever). T…

从外部柯西数据恢复声-引力方程组中的分段光滑参数

Recovery of piecewise smooth parameters in an acoustic-gravitational system of equations from exterior Cauchy data

针对主象征与声波算子一致的声-引力系统反问题，利用高频波证明在特定几何条件下，有界域外的解算子可唯一确定域内分段光滑的波速和质量密度。

Uniqueness to Inverse Acoustic and Electromagnetic Scattering From Locally Perturbed Rough Surfaces

In this paper, we consider inverse time-harmonic acoustic and electromagnetic scattering from locally perturbed rough surfaces in three dimensions. The scattering interface is supposed to be the graph of a Lipschitz continuous function with compact support. It is proved that an acoustically sound-soft or sound-hard surface can be uniquely determined by the far-field pattern of infinite number of incident plane waves with distinct directions. Moreover, a single point source or plane wave can be used to uniquely determine a scattering surface of polyhedral type. These uniqueness results apply to…

Recovery of discontinuous Lamé parameters from local dynamic boundary data

Consider an isotropic elastic medium $Ω\subset \mathbb{R}^3$ whose Lamé parameters are piecewise smooth. In the elastic wave initial value inverse problem, we are given the solution operator for the elastic wave equation, but only outside $Ω$ and only for initial data supported outside $Ω$. Using the recently introduced scattering control series in the acoustic case, we prove that piecewise smooth Lamé parameters are uniquely determined by this map under certain geometric conditions. We also show the extent that multiple scattering in the interior may be suppressed and eliminated with access t…

The purely singular 1-D acoustic reflection problem

This paper analyzes the nonlinear correspondence between the reflectivity profile (model) and the plane wave impulse response at the boundary (data) for a three-dimensional half space consisting of a sequence of homogeneous horizontal layers. This correspondence is of importance in geophysical imaging, where it has been studied for more than half a century from a variety of perspectives. The main contribution of the present paper is to derive something new in the context of a time-limited deterministic approach: (i) an exact finite (non-asymptotic) formula for the data in terms of the model, (…

Recovery of Pressure and Wave Speed for Photoacoustic Imaging under a Condition of Relative Uncertainty

In this paper, we study the photoacoustic tomography problem for which we seek to recover both the initial state of the pressure field and the wave speed of the medium from the knowledge of a single boundary measurement. The goal is to propose practical assumptions to define a set of initial conditions and wave speeds over which uniqueness for this inverse problem is guaranteed. The main result of the paper is that given two sets of wave speeds and pressure profiles, they cannot produce the same acoustic measurements if the relative difference between the wave speeds is much smaller than the r…

声波方程中密度重建的线性化边界控制方法

Linearized Boundary Control Method for Density Reconstruction in Acoustic Wave Equations

本文提出一种线性化边界控制方法，用于从线性化Neumann-to-Dirichlet映射重建声波方程中的密度扰动，并给出稳定性估计及数值验证。

Uniqueness to inverse acoustic scattering from coated polygonal obstacles with a single incoming wave

It is proved that a connected polygonal obstacle coated by thin layers together with its surface impedance function can be determined uniquely from the far field pattern of a single incident plane wave. Our proof is based on the Schwarz reflection principle for the Helmholtz equation satisfying the impedance boundary condition on a flat boundary.