A statistical framework for model-based inverse problems in ultrasound elastography

TL;DR

This paper introduces a statistical framework for ultrasound elastography that accounts for measurement errors in displacement data, improving the robustness and accuracy of elasticity imaging through a novel optimization approach.

Contribution

It presents a new statistical model and fixed-point algorithm for inverse elasticity problems that incorporate measurement noise, advancing model-based elastography techniques.

Findings

The method effectively handles noisy displacement data.

It improves the robustness of elasticity imaging.

Preliminary results show enhanced accuracy.

Abstract

Model-based computational elasticity imaging of tissues can be posed as solving an inverse problem over finite elements spanning the displacement image. As most existing quasi-static elastography methods count on deterministic formulations of the forward model resulting in a constrained optimization problem, the impact of displacement observation errors has not been well addressed. To this end, we propose a new statistical technique that leads to a unified optimization problem for elasticity imaging. Our statistical model takes the imperfect nature of the displacement measurements into account, and leads to an observation model for the Young's modulus that involves signal dependent colored noise. To solve the resulting regularized optimization problem, we propose a fixed-point algorithm that leverages proximal splitting methods. Preliminary qualitative and quantitative results demonstrate the effectiveness and robustness of the proposed methodology.