Infusing known operators in convolutional neural networks for lateral strain imaging in ultrasound elastography

Convolutional Neural Networks (CNN) have been employed for displacement estimation in ultrasound elastography (USE). High-quality axial strains (derivative of the axial displacement in the axial direction) can be estimated by the proposed networks. In contrast to axial strain, lateral strain, which is highly required in Poisson's ratio imaging and elasticity reconstruction, has a poor quality. The main causes include low sampling frequency, limited motion, and lack of phase information in the lateral direction. Recently, physically inspired constraint in unsupervised regularized elastography (PICTURE) has been proposed. This method took into account the range of the feasible lateral strain defined by the rules of physics of motion and employed a regularization strategy to improve the lateral strains. Despite the substantial improvement, the regularization was only applied during the training; hence it did not guarantee during the test that the lateral strain is within the feasible range. Furthermore, only the feasible range was employed, other constraints such as incompressibility were not investigated. In this paper, we address these two issues and propose kPICTURE in which two iterative algorithms were infused into the network architecture in the form of known operators to ensure the lateral strain is within the feasible range and impose incompressibility during the test phase.