Data Redundancy and Reduced-Scan Reconstruction Algorithms in 2D Reflectivity Tomography

 

Abstract

In reflectivity tomography, a weakly reflecting object that is immersed in an acoustically homogeneous background medium is interrogated with a wideband ultrasonic pulse and the corresponding reflected signal is measured at the source location as a function of time. The goal of reflectivity tomography is to reconstruct a function that describes the reflectivity  of the inhomogeneous object, from knowledge of the reflected signal measured at different source-receiver positions. In this work, we identify symmetries in the reflectivity tomography data function and demonstrate that they can be exploited to reduce the amount of data that needs to be measured in order to accurately reconstruct the reflectivity function.  Concepts from  microlocal analysis will be utilized to understand  the numerical stability of our proposed reconstruction procedure.  Numerical results will be presented that corroborate our theoretical assertions.