# Lateral Strain Imaging using Self-supervised and Physically Inspired Constraints in Unsupervised Regularized Elastography

arXiv: https://arxiv.org/abs/2212.08740 · HTML: https://mlsanity.com/paper/2212.08740/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 59 references that are in the map.
- First posted on arXiv 16 Dec 2022.

## Builds on (most cited first, 17 of 17)

- [PWC-Net: CNNs for Optical Flow Using Pyramid, Warping, and Cost Volume](https://mlsanity.com/paper/1709.02371/) (2017)
- [UnFlow: Unsupervised Learning of Optical Flow with a Bidirectional Census Loss](https://mlsanity.com/paper/1711.07837/) (2017)
- [Iterative Residual Refinement for Joint Optical Flow and Occlusion Estimation](https://mlsanity.com/paper/1904.05290/) (2019)
- [SelFlow: Self-Supervised Learning of Optical Flow](https://mlsanity.com/paper/1904.09117/) (2019)
- [Learning by Analogy: Reliable Supervision from Transformations for Unsupervised Optical Flow Estimation](https://mlsanity.com/paper/2003.13045/) (2020)
- [MaskFlownet: Asymmetric Feature Matching with Learnable Occlusion Mask](https://mlsanity.com/paper/2003.10955/) (2020)
- [Learning with Known Operators reduces Maximum Training Error Bounds](https://mlsanity.com/paper/1907.01992/) (2019)
- [Semi-Supervised Training of Optical Flow Convolutional Neural Networks in Ultrasound Elastography](https://mlsanity.com/paper/2007.01421/) (2020)
- [Ultrasound Elasticity Imaging Using Physics-based Models And Learning-based Plug-And-Play Priors](https://mlsanity.com/paper/2103.14096/) (2021)
- [Bi-Directional Semi-Supervised Training of Convolutional Neural Networks for Ultrasound Elastography Displacement Estimation](https://mlsanity.com/paper/2201.13340/) (2022)
- [Global Ultrasound Elastography Using Convolutional Neural Network](https://mlsanity.com/paper/1805.07493/) (2018)
- [An Unsupervised Approach to Ultrasound Elastography with End-to-end Strain Regularisation](https://mlsanity.com/paper/2008.09572/) (2020)
- [Physically Inspired Constraint for Unsupervised Regularized Ultrasound Elastography](https://mlsanity.com/paper/2206.02225/) (2022)
- [Virtual Source Synthetic Aperture for Accurate Lateral Displacement Estimation in Ultrasound Elastography](https://mlsanity.com/paper/2012.10562/) (2020)
- [Combining physics-based modeling and deep learning for ultrasound elastography](https://mlsanity.com/paper/2107.13120/) (2021)
- [Fast Strain Estimation and Frame Selection in Ultrasound Elastography using Machine Learning](https://mlsanity.com/paper/2110.08668/) (2021)
- [Second-Order Ultrasound Elastography with L1-norm Spatial Regularization](https://mlsanity.com/paper/2201.02226/) (2022)

## Built on by (most cited first, 2 of 2)

- [DefCor-Net: Physics-Aware Ultrasound Deformation Correction](https://mlsanity.com/paper/2308.03865/) (2023)
- [Denoising Plane Wave Ultrasound Images Using Diffusion Probabilistic Models](https://mlsanity.com/paper/2408.10987/) (2024)

## Abstract (arXiv)

Convolutional Neural Networks (CNN) have shown promising results for displacement estimation in UltraSound Elastography (USE). Many modifications have been proposed to improve the displacement estimation of CNNs for USE in the axial direction. However, the lateral strain, which is essential in several downstream tasks such as the inverse problem of elasticity imaging, remains a challenge. The lateral strain estimation is complicated since the motion and the sampling frequency in this direction are substantially lower than the axial one, and a lack of carrier signal in this direction. In computer vision applications, the axial and the lateral motions are independent. In contrast, the tissue motion pattern in USE is governed by laws of physics which link the axial and lateral displacements. In this paper, inspired by Hooke's law, we first propose Physically Inspired ConsTraint for Unsupervised Regularized Elastography (PICTURE), where we impose a constraint on the Effective Poisson's ratio (EPR) to improve the lateral strain estimation. In the next step, we propose self-supervised PICTURE (sPICTURE) to further enhance the strain image estimation. Extensive experiments on simulation, experimental phantom and in vivo data demonstrate that the proposed methods estimate accurate axial and lateral strain maps.