A paraxial approach for the inverse problem of vibro-acoustic imaging in frequency domain

TL;DR

This paper introduces a paraxial modeling approach for vibro-acoustic imaging in the frequency domain, enabling the reconstruction of acoustic interaction parameters using a Landweber-Kaczmarz method.

Contribution

It develops a novel paraxial model for vibro-acoustography and proposes an inverse reconstruction method to determine interaction parameters from acoustic data.

Findings

Successful formulation of PDE systems for directed beam propagation

Development of a Landweber-Kaczmarz reconstruction algorithm

Potential for high-resolution imaging without speckles

Abstract

This paper presents a paraxial modeling approach for vibro-acoustography, a high-frequency ultrasound imaging technique that makes use of the excited low-frequency field to achieve a higher resolution while avoiding speckles. We start from a general second order wave equation, introduce a second order perturbation and make use of a paraxial change of variables to pass over to directed beams. Depending on the relation between the second order perturbation and the directivity of the beams this leads to different systems of PDEs that involve a spatially variable parameter governing the interaction of the incoming beams to generate the propagating acoustic field. We then consider the inverse problem of determining this parameter for one of these models where we present a Landweber-Kaczmarz reconstruction method to obtain a spatial image of the region of interest.