We consider the problem of
imaging in a region where ultrasonic waves are multiply scattered.
A transducer emits ultrasonic pulses in tissue where they scatter
from a heterogeneity (e.g. a tumor) in the region of interest
(ROI). The reflected signals are recorded and used to produce an
image of tissue. Many of the conventional imaging methods assume
the wave has scattered just once (Born-approximation) from the
heterogeneity before returning to the sensor to be recorded. In
reality, waves can scatter several times before returning to the
detector. The purpose of this paper is to show how this
restriction (the Born approximation or weak, single-scattering
approximation) can be partially removed by incorporating a-priori
known environmental scatterers, such as a cavity wall or bones
into the background velocity model in the context of acoustic
medical imaging. We also show how the partial removal of the Born
approximation assumption leads to an enhanced angular resolution
of heterogeneities that are present. We will illustrate our method
using a locally planar scatterer, which is one of the simplest
possible environments for the scatterer.
This paper develops a method for forming a synthetic-aperture image of a flat surface seen through a homogeneous layer of a material that is dispersive, i.e., its wave speed varies with frequency.
We outline first a simplified scalar model for electromagnetic wave propagation in a dispersive medium; the resulting equation could also be used for acoustics. We show that the backscattered signal can be viewed as a Fourier integral operator applied to the ground reflectivity funciton. The reconstruction method, which is based on backprojection, can be used for arbitrary sensor paths and corrects for the radiated beam pattern, the source waveform, and geometrical spreading factors. The method correctly reconstructs the singularities (such as edges) that are visible from the sensor.
KEYWORDS: Data modeling, Reflectivity, Chemical mechanical planarization, Mathematical modeling, 3D modeling, Kinematics, Reflectors, Wavelets, Detection and tracking algorithms, Inverse problems
Differential semblance measures are unique amongst velocity inversion objectives in having well-defined and smooth high frequency asymptotics. A version appropriate for analysis of CMP gathers and layered models is particularly easy to analyze and economical for numerical experimentation. For model-consistent data, the DS objective measures the discrepancy in takeoff slowness of rays, weighted by the energy in the data -- without of course requiring that events be identified or rays traced. Numerical experiments with synthetic data illustrate the theoretical properties.
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