On the Intensity-based Inversion Method for Quantitative Quasi-Static Elastography

TL;DR

This paper analyzes the intensity-based inversion method (IIM) for estimating material parameters in quasi-static elastography, highlighting its stability, convergence, and application to optical coherence elastography through theoretical and numerical studies.

Contribution

It provides a comprehensive convergence analysis of IIM, compares it to two-step methods, and demonstrates its effectiveness in optical coherence elastography simulations.

Findings

IIM is more stable to measurement noise than two-step approaches.

The paper offers a full convergence analysis of IIM in linear elastography.

Numerical examples validate the effectiveness of IIM in optical coherence elastography.

Abstract

In this paper, we consider the intensity-based inversion method (IIM) for quantitative material parameter estimation in quasi-static elastography. In particular, we consider the problem of estimating the material parameters of a given sample from two internal measurements, one obtained before and one after applying some form of deformation. These internal measurements can be obtained via any imaging modality of choice, for example ultrasound, optical coherence or photo-acoustic tomography. Compared to two-step approaches to elastography, which first estimate internal displacement fields or strains and then reconstruct the material parameters from them, the IIM is a one-step approach which computes the material parameters directly from the internal measurements. To do so, the IIM combines image registration together with a model-based, regularized parameter reconstruction approach. This combination has the advantage of avoiding some approximations and derivative computations typically found in two-step approaches, and results in the IIM being generally more stable to measurement noise. In the paper, we provide a full convergence analysis of the IIM within the framework of inverse problems, and detail its application to linear elastography. Furthermore, we discuss the numerical implementation of the IIM and provide numerical examples simulating an optical coherence elastography (OCE) experiment.