# Physically Inspired Constraint for Unsupervised Regularized Ultrasound Elastography

arXiv: https://arxiv.org/abs/2206.02225 · HTML: https://mlsanity.com/paper/2206.02225/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 16 references that are in the map.
- First posted on arXiv 5 Jun 2022.

## Builds on (most cited first, 5 of 5)

- [Iterative Residual Refinement for Joint Optical Flow and Occlusion Estimation](https://mlsanity.com/paper/1904.05290/) (2019)
- [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)
- [Bi-Directional Semi-Supervised Training of Convolutional Neural Networks for Ultrasound Elastography Displacement Estimation](https://mlsanity.com/paper/2201.13340/) (2022)
- [An Unsupervised Approach to Ultrasound Elastography with End-to-end Strain Regularisation](https://mlsanity.com/paper/2008.09572/) (2020)

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

- [Lateral Strain Imaging using Self-supervised and Physically Inspired Constraints in Unsupervised Regularized Elastography](https://mlsanity.com/paper/2212.08740/) (2022)
- [Infusing known operators in convolutional neural networks for lateral strain imaging in ultrasound elastography](https://mlsanity.com/paper/2211.00172/) (2022)

## Abstract (arXiv)

Displacement estimation is a critical step of virtually all Ultrasound Elastography (USE) techniques. Two main features make this task unique compared to the general optical flow problem: the high-frequency nature of ultrasound radio-frequency (RF) data and the governing laws of physics on the displacement field. Recently, the architecture of the optical flow networks has been modified to be able to use RF data. Also, semi-supervised and unsupervised techniques have been employed for USE by considering prior knowledge of displacement continuity in the form of the first- and second-derivative regularizers. Despite these attempts, no work has considered the tissue compression pattern, and displacements in axial and lateral directions have been assumed to be independent. However, tissue motion pattern is governed by laws of physics in USE, rendering the axial and the lateral displacements highly correlated. In this paper, we propose Physically Inspired ConsTraint for Unsupervised Regularized Elastography (PICTURE), where we impose constraints on the Poisson's ratio to improve lateral displacement estimates. Experiments on phantom and in vivo data show that PICTURE substantially improves the quality of the lateral displacement estimation.