Ultrasound Elasticity Imaging Using Physics-Based Models and Learning-Based Plug-and-Play Priors

Abstract

Existing physical model-based imaging methods for ultrasound elasticity reconstruction utilize fixed variational regularizers that may not be appropriate for the application of interest or may not capture complex spatial prior information about the underlying tissues. On the other hand, end-to-end learning-based methods count solely on the training data, not taking advantage of the governing physical laws of the imaging system. Integrating learning-based priors with physical forward models for ultrasound elasticity imaging, we present a joint reconstruction framework which guarantees that learning driven reconstructions are consistent with the underlying physics. For solving the elasticity inverse problem as a regularized optimization problem, we propose a plug-and-play (PnP) reconstruction approach in which each iteration of the elasticity image estimation process involves separate updates incorporating data fidelity and learningbased regularization. In this methodology, the data fidelity term is developed using a statistical linear algebraic model of quasi-static equilibrium equation revealing the relationship of the observed displacement fields to the unobserved elastic modulus. The regularizer comprises a convolutional neural network (CNN) based denoiser that captures the learned prior structure of the underlying tissues. Preliminary simulation results demonstrate the robustness and effectiveness of the proposed approach with limited training datasets and noisy displacement measurements.

Combining physics-based modeling and deep learning for ultrasound elastography

“…To have a simplified representation of the governing PDEs, finite element methods (FEM) [15] is employed to discretize the medium cross-section. The resulting global stiffness equation of ultrasound elastography problem can be represented by [9]:…”

“…This infusing scheme results in both guaranteed elasticity reconstructions with the physical imaging model and exploiting complex data-driven information even with a limited training dataset [7]. One group of methods for integrating physics-based modeling and deep learning priors including Plug-and-Play (PnP) [8,9,10,11] and regularization by denoising (RED) [12] seeks to learn a data-adaptive denoiser and then exploits it into a regularized optimization problem as the proximal operator of regularizer or the gradient of the regularizer. The other group of methods is based on unfolding the iterations of the minimization task in terms of a layer in a neural network including PI-GAN [13].…”

Regularization by Adversarial Learning for Ultrasound Elasticity Imaging

“…Estimating the elastic modulus x as an inverse problem can be fulfilled by solving a constrained optimization problem. In this regard, the forward model (1) needs to be formulated as a linear representation with respect to the unknown elasticity modulus [2]. To this end, we establish the matrix D(u) ∈ R 2N ×N which has the following relation with K(x) using a 3D tensor Ψ ∈ R N ×2N ×2N constructed from the equilibrium equations:…”

“…based on which we can interpret (4) as a linear observation model involving signal dependent colored noise. This statistical forward model which incorporates the noise statistics paves the way for formulating the elastic inverse problem using a regularized optimization problem [2] as follows:…”

“…Considering medical imaging challenges including time-efficient image reconstruction as well as reliable and robust reconstructed elastic images, numerous advances have been proposed. One major concern in existing model-based approaches [1], [2] is how to capture the appropriate prior information about the complex structure of the underlying tissues and how to incorporate this prior knowledge into the image reconstruction scheme. By the advent of deep neural networks (DNNs) [3], various end-to-end learning-based methods [4][5][6][7][8] have been proposed which try to learn both the physical model and the prior information about the underlying tissues.…”